How to Display Nodal Forces in Ansys Mechanical

 Ansys Mechanical offers two methods to visualize nodal forces:

 * ENFO Vectors (Workbench):

   * In the Results tree, navigate to the solution containing the nodal forces you want to display.

Mat Foundation with SOG Loading: Impact Evaluation

 Here's how to determine the effects of SOG loading on your mat foundation:

 * Evaluate Load Transfer: Since the SOG rests on the soil, analyze if there's significant load transfer to the underlying mat. If the SOG is sufficiently thick and stiff, it might distribute the equipment loads over a larger area, potentially reducing the stress on the mat.

The error message "Not enough constraints applied to prevent rigid body motion" in Ansys

 The error message "Not enough constraints applied to prevent rigid body motion" in Ansys Mechanical indicates that your PMSM rotor model is missing essential constraints to prevent it from undergoing unrealistic movements during the simulation. Here are some troubleshooting steps to address this:

Why I cannot apply a constant speed in the Harmonic Response? (Like the "rotational velocity" in the static structural analysis)

 In harmonic response analysis, applying a constant speed like in static structural analysis isn't possible because harmonic analysis focuses on the response of a system to varying excitation forces over a range of frequencies.

How to model crack propagation in Ansys ?

 Ansys offers functionalities to model crack propagation through the Ansys Mechanical software and the SMART Crack Growth feature. Here's a general breakdown of the process:

1. Pre-Processing:

• Geometry and Mesh: Define the geometry of your model in Ansys Workbench. Ansys Mechanical's Unstructured Mesh Method (UMM) can automatically generate a mesh suitable for crack simulations, reducing preprocessing time [Ansys white paper on SMART Crack Growth & Fracture Modeling].
• Material Properties: Assign material properties to your model, including the fracture toughness which plays a critical role in crack growth behavior.

💥💥💥 What is more difficult, CFD Analysis or Structural Analysis to learn ?

 That is a difficult question to answer, as both CFD analysis and structural analysis have their own challenges and complexities. However, some possible factors that could affect the difficulty of learning either one are:

- The mathematical background and familiarity with the governing equations and numerical methods. CFD analysis typically involves solving nonlinear partial differential equations, such as the Navier-Stokes equations, which can be challenging to understand and implement. Structural analysis usually involves solving linear or nonlinear systems of equations, which may be easier to grasp and solve¹²³.

- The type and scope of the problem and the desired accuracy of the solution. CFD analysis can deal with a variety of fluid phenomena, such as turbulence, multiphase flow, heat transfer, chemical reactions, etc. Structural analysis can also handle different types of loading, deformation, failure, material behavior, etc. Depending on the problem, the solution may require different levels of mesh refinement, boundary conditions, convergence criteria, etc¹²⁴.

- The availability and usability of the software and tools. CFD analysis and structural analysis both rely on specialized software and tools that can perform the numerical simulations and provide the results. The software and tools may vary in their features, capabilities, interfaces, documentation, support, etc. The user may need to learn how to use the software and tools effectively and efficiently¹²⁴⁵.

Therefore, the difficulty of learning CFD analysis or structural analysis may depend on the individual's background, interest, motivation, and resources. There is no definitive answer to which one is more difficult, as both have their own merits and challenges. However, both are valuable skills that can help in designing and optimizing various systems and applications.

Source: 

(1) How accurate is FEA and CFD simulation? - The SOLIDWORKS Blog. https://blogs.solidworks.com/solidworksblog/2014/05/how-accurate-is-fea-and-cfd-simulation.html.

(2) FEA vs. CFD: The Differences and Applications of Simulation Tools. https://resources.system-analysis.cadence.com/blog/msa2021-fea-vs-cfd-the-differences-and-applications-of-simulation-tools.

(3) What's the Difference Between FEA and CFD? - Enterfea. https://enterfea.com/whats-the-difference-between-fea-and-cfd/.

(4) FEA/CFD Analysis for Fluid-Structure Interaction Studies. https://resources.system-analysis.cadence.com/blog/msa2021-fea-cfd-analysis-for-fluid-structure-interaction-studies.

(5) FEA vs. CFD Thermal Analysis - When to Use Which?. https://www.pages.mechartes.com/resources/2021/10/23/fea-vs-cfd-analysis-when-to-use-which-in-thermal-analysis.

Which software is commonly used for CFD and Structural Analysis?

There are many software packages that can be used for CFD and structural analysis, depending on the type and complexity of the problem, the desired accuracy and efficiency, and the user's preference and budget. However, some of the most commonly used software are:

- For CFD analysis, some popular software are **Ansys Fluent**, **Autodesk CFD**, **SimScale**, and **COMSOL Multiphysics**. These software offer a range of features and capabilities for simulating various fluid phenomena, such as turbulence, multiphase flow, heat transfer, chemical reactions, etc. They also have user-friendly interfaces, advanced solvers, and cloud-based platforms¹²³⁴.

- For structural analysis, some widely used software are **STAAD**, **RAM**, **Tekla Structures**, and **SkyCiv**. These software allow engineers to design and analyze different types of structures and materials, such as concrete, steel, and joist. They also support BIM and 3D modeling, interoperability, and collaboration⁵⁶⁷ .

Of course, there are many other software that can be used for CFD and structural analysis, and the choice may depend on the specific needs and preferences of the user. 

Source: 

(1) CFD Software: Fluid Dynamics Simulation Software - Ansys. https://www.ansys.com/products/fluids.

(2) Autodesk CFD Software | Get Prices & Buy Official CFD 2024. https://www.autodesk.com/products/cfd/overview.

(3) Computational Fluid Dynamics (CFD) Simulation Software | SimScale. https://www.simscale.com/product/cfd/.

(4) List of structural engineering software - Wikipedia. https://en.wikipedia.org/wiki/List_of_structural_engineering_software.

(5) Structural Analysis and Detailing | Bentley Systems | Infrastructure .... https://www.bentley.com/software/structural-analysis-and-detailing/.

(6) Structural Engineering Software to Learn in 2023: Top 10 Best. https://tribby3d.com/blog/structural-engineering-software/.

(7) Structural Analysis and Design | SkyCiv Engineering. https://skyciv.com/.

What is less difficult to learn, Ansys Mechanical or Ansys CFD (Fluent, CFX) ?

There is no definitive answer to which one is less difficult to learn, as both Ansys Mechanical and Ansys CFD (Fluent, CFX) have their own merits and challenges. However, based on the information I found from the web search results, some possible factors that could affect the difficulty of learning either one are:

- The type and scope of the problem and the desired accuracy of the solution. Ansys Mechanical can handle different types of loading, deformation, failure, material behavior, etc. Ansys CFD can deal with a variety of fluid phenomena, such as turbulence, multiphase flow, heat transfer, chemical reactions, etc. Depending on the problem, the solution may require different levels of mesh refinement, boundary conditions, convergence criteria, etc¹²⁴.

- The mathematical background and familiarity with the governing equations and numerical methods. Ansys Mechanical usually involves solving linear or nonlinear systems of equations, which may be easier to grasp and solve. Ansys CFD typically involves solving nonlinear partial differential equations, such as the Navier-Stokes equations, which can be challenging to understand and implement¹²³.

- The availability and usability of the software and tools. Ansys Mechanical and Ansys CFD both rely on specialized software and tools that can perform the numerical simulations and provide the results. The software and tools may vary in their features, capabilities, interfaces, documentation, support, etc. The user may need to learn how to use the software and tools effectively and efficiently¹²⁴.

Therefore, the difficulty of learning Ansys Mechanical or Ansys CFD may depend on the individual's background, interest, motivation, and resources. 

Source:

(1) Physics Preference – Mechanical or CFD - Ansys Learning Forum. https://forum.ansys.com/forums/topic/physics-preference-mechanical-or-cfd/.

(2) Compare Ansys Mechanical vs. Autodesk CFD | G2. https://www.g2.com/compare/ansys-mechanical-vs-autodesk-cfd.

(3) Compare Ansys Fluent vs. Ansys Mechanical vs. Autodesk CFD - Slashdot. https://slashdot.org/software/comparison/Ansys-Fluent-vs-Ansys-Mechanical-vs-Autodesk-CFD/.

(4) Solver: Workbench Mechanical vs. Fluent - Ansys Learning Forum. https://forum.ansys.com/forums/topic/solver-workbench-mechanical-vs-fluent/.

Which one do you recommend for a beginner, Ansys Mechanical or CFD?

I cannot recommend one over the other, as both Ansys Mechanical and CFD have their own merits and challenges. However, based on the information from the web search results, some possible factors that could affect your choice are:

- Your interest and motivation. You should choose the software that aligns with your goals and interests, as this will help you stay motivated and engaged in learning. For example, if you are interested in fluid dynamics and want to simulate various fluid phenomena, you may prefer Ansys CFD. If you are interested in structural mechanics and want to analyze different types of loading and deformation, you may prefer Ansys Mechanical .

- Your background and resources. You should choose the software that matches your level of mathematical and numerical knowledge, as well as the availability and usability of the software and tools. For example, if you have a strong background in partial differential equations and nonlinear solvers, you may find Ansys CFD easier to learn. If you have a solid foundation in linear and nonlinear systems of equations, you may find Ansys Mechanical easier to learn . You should also consider the cost, features, documentation, and support of the software and tools .

- Your problem and accuracy. You should choose the software that can handle the type and complexity of the problem you want to solve, as well as the desired accuracy and efficiency of the solution. For example, if you want to solve a problem involving turbulence, multiphase flow, heat transfer, chemical reactions, etc., you may need Ansys CFD. If you want to solve a problem involving loading, deformation, failure, material behavior, etc., you may need Ansys Mechanical .

What are some good resources to learn Ansys Mechanical and CFD?

There are many resources to learn Ansys Mechanical and CFD, depending on your level of experience, interest, and goals. Some of the resources that I found from the web search results are:

- Ansys Academic Support | Tutorials & Training Materials¹: This is a website that provides free Innovation Courses, the Learning Forum support community, videos with technology tips and introductory tutorials with step-by-step directions for performing basic simulations, and more. You can find tutorials for both Ansys Mechanical and Ansys CFD, as well as other Ansys products and physics areas.

- Ansys Mechanical Getting Started² and Ansys Fluent Getting Started⁵: These are courses that teach the essential skills you need to start performing basic linear static structural analyses and computational fluid dynamics (CFD) simulations on your own using Ansys Mechanical and Ansys Fluent software. You can learn the complete end-to-end procedure, the best practices, and the common techniques for solving your own analysis problems.

- Ansys Computational Fluid Dynamics (CFD) Tutorials⁴: This is a YouTube playlist that contains 34 videos that explore more advanced topics in the fluid-focused arena. You can learn how to simulate various fluid phenomena, such as turbulence, multiphase flow, heat transfer, chemical reactions, etc. You can also learn how to use different features and capabilities of Ansys CFD software, such as dynamic mesh, moving and deforming mesh, etc.

- Absolute Beginners Guide to CFD simulation in ANSYS⁶: This is a Udemy course that teaches CFD simulation from scratch in Ansys workbench environment. You can learn how to clean geometry and create domain in Ansys Spaceclaim, create high quality mesh in Workbench meshing, run CFD simulation in Fluent for full aircraft, and set up compressible flow problem and accelerate solution convergence for density based solver in Fluent.

Source: 

(1) Ansys Academic Support | Tutorials & Training Materials. https://www.ansys.com/academic/learning-resources.

(2) Ansys Mechanical Getting Started | Ansys Training. https://www.ansys.com/training-center/course-catalog/structures/ansys-mechanical-getting-started.

(3) Ansys Fluent Getting Started | Ansys Training. https://www.ansys.com/training-center/course-catalog/fluids/ansys-fluent-getting-started.

(4) Ansys Computational Fluid Dynamics (CFD) Tutorials - YouTube. https://www.youtube.com/playlist?list=PLQMtm0_chcLyEB1EJLUoouugMYZNQUslG.

(5) Absolute Beginners Guide to CFD simulation in ANSYS | Udemy. https://www.udemy.com/course/absolute-beginners-guide-to-cfd-simulation-in-ansys/.

(6) Getting Started with Ansys Mechanical | Ansys Courses. https://courses.ansys.com/index.php/courses/getting-started-with-ansys-mechanical/.

💥💥💥 PrePOMAX vs Ansys Mechanical

 PrePoMax and Ansys Mechanical are both software packages for finite element analysis (FEA), but they have some differences in terms of features, capabilities, and costs. Here are some points of comparison:

- PrePoMax is an open-source pre- and postprocessor for CalculiX, which is also an open-source FEA solver¹. Ansys Mechanical is a commercial software that offers a comprehensive range of FEA capabilities, including structural, thermal, fluid, and electromagnetic analysis².

- PrePoMax is designed to be simple and easy to use, with a user-friendly graphical interface and a Windows application¹. Ansys Mechanical has a more complex and powerful interface, with a variety of tools and options for advanced users².

- PrePoMax is free to download and use, but it has limited support and documentation¹. Ansys Mechanical requires a license and a subscription fee, but it has extensive support and documentation, as well as online training and certification courses².

- PrePoMax supports basic FEA features, such as linear and nonlinear static and dynamic analysis, thermal and thermo-mechanical analysis, and modal analysis³. Ansys Mechanical supports more advanced FEA features, such as multiphysics coupling, optimization, fatigue, fracture, and contact analysis².

In summary, PrePoMax and Ansys Mechanical are both useful FEA software packages, but they cater to different needs and preferences of users. PrePoMax is suitable for beginners and hobbyists who want to perform simple and quick FEA simulations, while Ansys Mechanical is suitable for professionals and researchers who want to perform complex and accurate FEA simulations.

Source: 

(1) PrePoMax & CalculiX - Coupled thermo-mechanical analysis. https://www.youtube.com/watch?v=7zRpIbucvn0.

(2) Affordable FEA Packages for Home/Non-Commercial Use : r/fea - Reddit. https://www.reddit.com/r/fea/comments/iso315/affordable_fea_packages_for_homenoncommercial_use/.

(3) PrePoMax (CalculiX FEA) - Tutorial 26 - Thermo-mechanical ... - YouTube. https://www.youtube.com/watch?v=wRcTD1zSbLU.

(4)https://prepomax.fs.um.si/.

How PrePOMAX handle with complex geometries in comparision with Ansys Mechanical?

PrePoMax and Ansys Mechanical have different ways of handling complex geometries. PrePoMax uses the open-source Open Cascade platform to import the geometry from a variety of exchangeable CAD formats and stereolithography .stl files used for 3D printing¹. PrePoMax also allows you to mesh a solid or a shell based geometry using linear and parabolic finite elements, or to import the finite element mesh from a file¹². PrePoMax can handle complex geometries such as bolted joints with preload, as shown in this tutorial³.

Ansys Mechanical uses its own proprietary geometry engine to create, import, or modify the geometry of the model. Ansys Mechanical also offers a range of meshing options, such as automatic, manual, or mapped meshing, as well as adaptive mesh refinement and mesh quality checks. Ansys Mechanical can handle complex geometries such as composite structures, fluid-structure interactions, and nonlinear materials.

In summary, PrePoMax and Ansys Mechanical have different strengths and limitations when it comes to handling complex geometries. PrePoMax is more compatible with various CAD formats and 3D printing, while Ansys Mechanical is more versatile and robust in meshing and analysis.

Source: 

(1) PrePoMax. https://prepomax.fs.um.si/.

(2) PrePoMax 1.3.0 Manual - UM. https://prepomax.fs.um.si/wp-content/uploads/2022/04/PrePoMax-v1.3.0-manual.pdf.

(3) PrePoMax (CalculiX FEA) - Tutorial 34 - Bolted joint with preload. https://www.youtube.com/watch?v=ZSDf1bNXo8g.

Can PrePOMAX handle fluid-structure interactions?

According to the web search results, PrePoMax does not support fluid-structure interaction (FSI) analysis natively, but it can be coupled with other open-source software to perform FSI simulations. For example, one of the results³ shows how PrePoMax can be used with the Particle Finite Element Method (PFEM) to model the interaction between a fluid and a flexible structure. The authors of the paper used PrePoMax to create the finite element mesh and to post-process the results, while the PFEM solver was used to solve the coupled fluid-structure problem. The paper also provides some examples of FSI applications, such as a dam-break problem and a blood flow problem. Therefore, PrePoMax can handle FSI problems indirectly, but it requires some additional steps and tools.

Source: 

(1) FULLY EXPLICIT FLUID-STRUCTURE INTERACTION APPROACH BASED ON PFEM AND FEM. https://upcommons.upc.edu/bitstream/handle/2117/187110/Particles_2017-16_A%20fully%20explicit%20fluid-structure.pdf.

(2) PrePoMax 1.3.0 Manual - UM. https://prepomax.fs.um.si/wp-content/uploads/2022/04/PrePoMax-v1.3.0-manual.pdf.

(3) PrePoMax. https://prepomax.fs.um.si/.

(4) Documentation – PrePoMax. https://prepomax.fs.um.si/documentation/.

(5)https://prepomax.discourse.group/.

How can I install PrePOMAX on my computer?

To install PrePOMAX on your computer, you can follow these steps:

- Download the latest version of PrePOMAX from the official website¹. You can choose between the development version or the stable version, depending on your preference.

- Extract the downloaded .zip file to a non-system directory of your choice. You do not need to install anything else, as PrePOMAX is a portable software that runs on the Microsoft .NET Framework 4.8¹.

- Run the executable .exe file named PrePoMax v#.#.#.exe, where #.#.# is the version number. You should see the PrePOMAX graphical interface, where you can start creating or importing your FEM models.

That's it! You have successfully installed PrePOMAX on your computer. You can also check the documentation² and the forum³ for more information and support. I hope you enjoy using PrePOMAX for your FEM simulations. 😊

Source: 

(1) Downloads – PrePoMax - UM. https://prepomax.fs.um.si/downloads/.

(2) . https://bing.com/search?q=PrePOMAX+installation.

(3) PrePoMax. https://prepomax.fs.um.si/.

(4) Install Proxmox VE {Step-by-Step Guide} - phoenixNAP. https://phoenixnap.com/kb/install-proxmox.

(5)https://prepomax.fs.um.si/wp-content/uploads/2021/06/2021.06.29-PrePoMax-v1.1.0-manual.pdf.

(6) http://www.dhondt.de/calculix_2.20_4win.zip.

(7) https://gitlab.com/MatejB/PrePoMax

💥💥💥 How to model in PrePoMAX ?

PrePoMax is a freeware pre- and postprocessor for open-source Finite Element Analysis solver CalculiX¹. It offers a user-friendly GUI and supports many features provided by the CalculiX solver. To model in PrePoMax, you need to follow these general steps:

• Create or import a geometry using the Geometry menu².
• Generate a mesh using the Mesh menu².
• Define the FE model using the Model, Property, Interaction, Initial Condition, and Step menus².
• Export the input file for CalculiX using the File menu².
• Run the analysis using the Tools menu².
• Import the results file and visualize the output using the View menu².

You can find more detailed instructions and examples in the PrePoMax documentation¹ and video tutorials¹. I hope this helps you get started with PrePoMax. 😊

• The official PrePoMax website¹ has a section on documentation, where you can download the PrePoMax manual in PDF format. The manual covers the basic features and workflow of PrePoMax, as well as some examples and tips. You can also watch some video tutorials on YouTube that demonstrate the PrePoMax user experience.
• The PrePoMax 1.3.0 manual² is a detailed guide that explains how to use PrePoMax for various types of analysis, such as static, natural frequency, heat transfer, slip wear, etc. It also provides screenshots and step-by-step instructions for each analysis step, such as geometry, meshing, model, property, interaction, initial condition, step, results, etc.
• The PrePoMax user forum³ is a place where you can ask questions, share your experience, and get help from other PrePoMax users and developers. You can also find some useful posts and links to other resources on the forum.

• PrePoMax & CalculiX - Basic Tutorial: This video is a basic tutorial for how to use PrePoMax and CalculiX. It shows how to import a solid mesh from Salome, prepare the finite-element model, run the simulation, and post-process the results. It also has subtitles with brief instructions.
• PrePoMax (CalculiX FEA) - Tutorial 34 - Bolted joint with preload: This video shows how to create a simplified FEA model of a bolted joint with pre-tension. It covers the geometry, meshing, model, property, interaction, step, and results steps. It also provides a link to download the geometry file.
• PrePoMax (Calculix) Tutorial - Shell Example: This video shows how to perform a shell FEA analysis in PrePoMax using CalculiX. It demonstrates the geometry, meshing, model, property, interaction, step, and results steps. It also provides a link to a case description and the results of the test.

Based on  web search, some of the best users with PrePoMax tutorials on YouTube are:

• FEAnalyst¹: This user has a series of tutorials on how to use PrePoMax and CalculiX for various types of FEA analysis, such as static, natural frequency, heat transfer, slip wear, etc. The user provides step-by-step instructions, screenshots, and links to download the geometry files. The user also has a website² where you can find more information and resources.
• Matej Borovinšek³: This user is the developer of PrePoMax and has a basic tutorial on how to use PrePoMax and CalculiX. The user shows how to import a solid mesh from Salome, prepare the finite-element model, run the simulation, and post-process the results. The user also has subtitles with brief instructions and a link to download PrePoMax.
• Jakub Michalski⁴: This user has a playlist of videos on how to use PrePoMax and CalculiX for different types of FEA analysis, such as shell, beam, contact, etc. The user demonstrates the geometry, meshing, model, property, interaction, step, and results steps. The user also provides links to a case description and the results of the test.

Can I use PrePoMax for other solvers?

According to the PrePoMax website¹, PrePoMax is designed specifically for the CalculiX solver and does not support other solvers. However, you may be able to use PrePoMax to create and export a geometry and mesh that can be imported by other solvers that accept the .inp file format. You can also use PrePoMax to visualize the results of other solvers that produce the .frd file format. However, you will not be able to use PrePoMax to define the FE model, run the analysis, or access the advanced features of other solvers. For that, you will need to use a different pre- and postprocessor that is compatible with your solver of choice.

Can I use PrePoMax on a Mac?

Unfortunately, PrePoMax is not available for Mac OS. PrePoMax is based on the Microsoft .NET Framework 4.8, which is only compatible with Windows operating systems¹. You will need a Windows PC or a virtual machine to run PrePoMax. Alternatively, you can look for other pre- and postprocessors that support Mac OS and CalculiX, such as Salome-Meca² or Gmsh³. 

Can I run PrePoMax on Linux?

It is possible to run PrePoMax on Linux, but it requires some additional steps and software. PrePoMax is based on the Microsoft .NET Framework 4.8, which is only compatible with Windows operating systems¹. However, you can use a software called Wine² to run Windows applications on Linux. Wine is a free and open-source compatibility layer that translates Windows API calls into Linux API calls. To use Wine, you need to install it on your Linux system and then run the PrePoMax executable file with Wine. You can find more information and instructions on how to install and use Wine on the official website² or on the WineHQ wiki.

Alternatively, you can use a virtual machine to run Windows on Linux and then install PrePoMax on the virtual machine. A virtual machine is a software that emulates a computer system and allows you to run different operating systems on the same hardware. Some popular virtual machine software for Linux are VirtualBox and VMware Workstation Player. You can find more information and instructions on how to install and use these software on their respective websites or on the Linux documentation.

💥💥💥 How to increase precision in Ansys Workbench calculations?

 One way to increase the precision of your calculations in Ansys Workbench is to use the double-precision solver option in Fluent. This option allows you to use more digits after the decimal point and reduce the numerical errors. You can find this option in the Fluent Launcher, under Options, as shown in this tutorial and this one. Alternatively, you can also increase the precision of values or number of decimal places in SpaceClaim by changing the Primary Precision option in File > SpaceClaim Options > Units. You can learn more about this option from this forum post. 

How do I know if my calculations are precise enough?

There are several factors that can affect the precision of your calculations in Ansys Workbench, such as the mesh quality, the solver settings, the convergence criteria, and the material model. You can check the precision of your calculations by comparing the results with analytical solutions, experimental data, or other reliable sources. You can also monitor the residuals and other quantities of interest during the solution process to ensure that they reach a steady or periodic state. Additionally, you can perform a sensitivity analysis or a mesh refinement study to evaluate how the results change with different input parameters or mesh sizes. You can find more information and examples on how to check the precision of your calculations from the following sources:

• How to know the calculation has converged
• Fundamental Calculations of equivalent stress and strain in ANSYS Workbench
• Steady Flow Past Cylinder Physics Setup
• Physics Setup — Lesson 5

Can you explain more about mesh quality and refinement study?

Sure, I can explain more about mesh quality and refinement study in Ansys Workbench. Mesh quality is a measure of how well the mesh elements represent the geometry and the physics of the problem. Mesh refinement is a process of increasing the number of mesh elements or improving their shape to achieve more accurate results.

Mesh quality depends on several factors, such as the element type, the element shape, the element size, and the element alignment. Different types of elements have different advantages and disadvantages for different problems. For example, tetrahedral elements are easy to generate and can fit complex geometries, but they may have lower accuracy and stability than hexahedral elements. The element shape affects how well the element can approximate the curvature of the geometry and the gradients of the solution. The element size determines how fine or coarse the mesh is, and how well it can capture the details of the problem. The element alignment refers to how well the mesh follows the direction of the flow or the stress.

Mesh refinement is a way to improve the mesh quality by increasing the number of elements or changing their shape. Mesh refinement can be done globally or locally. Global mesh refinement applies to the whole domain or a large region, and it increases the resolution of the mesh uniformly. Local mesh refinement applies to a specific area of interest, such as a boundary layer, a corner, or a crack, and it increases the resolution of the mesh selectively. Mesh refinement can also be done adaptively or manually. Adaptive mesh refinement is an automated process that adjusts the mesh based on some criteria, such as the error estimate, the solution gradient, or the user-defined function. Manual mesh refinement is a user-controlled process that modifies the mesh based on some parameters, such as the element size, the inflation factor, or the smoothing factor.

Mesh quality and refinement study is important for obtaining reliable and accurate results in Ansys Workbench. A good quality mesh can reduce the numerical errors and improve the convergence of the solution. A refined mesh can capture the features and phenomena of interest more accurately and resolve the variations of the solution more precisely. However, mesh quality and refinement also have some trade-offs, such as increased computational cost, memory requirement, and solution time. Therefore, it is necessary to balance between mesh quality and refinement and computational efficiency.

You can learn more about mesh quality and refinement study in Ansys Workbench from these sources:

• Generating Mesh in ANSYS Workbench | Part-1
• How to check the MESH Quality in Ansys Workbench | Mesh Metrics | Skewness | Orthogonal Quality
• Tutorial on Meshing in ANSYS Workbench I ANSYS Basic Tutorials Apply various Mesh on geometry
• Ansys sturcutal analysis tutorials 23: mesh convergence and refinement ; Stress history plot
• mesh refinment study - Ansys Learning Forum
• Using Adaptive Convergence with Ansys Mechanical — Lesson 5
• MESH QUALITY AND ADVENCED TOPICS ANSYS WORKBENCH 16.0 - Academia.edu

How do I choose the right element size for my mesh?

Choosing the right element size for your mesh depends on several factors, such as the geometry, the physics, the accuracy, and the computational cost of your problem. There is no universal rule for selecting the optimal element size, but there are some general guidelines and methods that can help you. Here are some of them:

• You can start with a coarse mesh and refine it gradually until you reach a desired level of accuracy or convergence. You can use global or local refinement, adaptive or manual refinement, or a combination of them. You can also use different types of elements, such as tetrahedral, hexahedral, or hybrid elements, depending on the complexity and curvature of your geometry.
• You can use mesh sizing controls to specify the element size for a selected body, face, edge, or vertex. You can also use the sphere of influence option to apply a local element size around a point of interest. You can access these options by right-clicking on the Mesh in the project tree and selecting Insert > Sizing.
• You can use mesh metrics to evaluate the quality of your mesh, such as the skewness, the aspect ratio, the orthogonal quality, or the smoothness. You can check these metrics by right-clicking on the Mesh in the project tree and selecting Mesh Metrics. You can also use mesh statistics to see the number and type of elements in your mesh. You can access these statistics by right-clicking on the Mesh in the project tree and selecting Statistics.
• You can compare your results with analytical solutions, experimental data, or other reliable sources to validate your mesh. You can also monitor the residuals and other quantities of interest during the solution process to ensure that they are within acceptable limits. You can also perform a sensitivity analysis or a mesh convergence study to evaluate how your results change with different input parameters or mesh sizes.

You can learn more about how to choose the right element size for your mesh in Ansys Workbench from these sources:

• Correct mesh size - a quick guide! - Enterfea
• Learn Everything about the Ansys Workbench | Mesh Sizing - Skill-Lync
• Sizing a Mesh | Ansys Innovation Courses
• Defining Element Size Of A Body In ANSYS® Mechanical(Illustrated Expression) - ML
• Changing The Element Size In ANSYS® Meshing(Iluustrated Expression) - ML

How do I know if my element size is too small or too large?

The element size is a key parameter that affects the accuracy and efficiency of your mesh and solution in Ansys Workbench. If your element size is too small, you may have a very fine mesh that can capture the details of your problem, but it will also increase the computational cost, memory requirement, and solution time. If your element size is too large, you may have a very coarse mesh that can reduce the computational cost, memory requirement, and solution time, but it will also introduce numerical errors and affect the convergence of your solution.

To know if your element size is too small or too large, you can use some methods and criteria to evaluate your mesh and solution quality. Here are some of them:

• You can compare your results with analytical solutions, experimental data, or other reliable sources to validate your mesh and solution. You can also monitor the residuals and other quantities of interest during the solution process to ensure that they are within acceptable limits.
• You can use mesh metrics to evaluate the quality of your mesh, such as the skewness, the aspect ratio, the orthogonal quality, or the smoothness. You can check these metrics by right-clicking on the Mesh in the project tree and selecting Mesh Metrics. You can also use mesh statistics to see the number and type of elements in your mesh. You can access these statistics by right-clicking on the Mesh in the project tree and selecting Statistics.
• You can perform a sensitivity analysis or a mesh convergence study to evaluate how your results change with different input parameters or mesh sizes. You can use global or local refinement, adaptive or manual refinement, or a combination of them. You can also use different types of elements, such as tetrahedral, hexahedral, or hybrid elements, depending on the complexity and curvature of your geometry.

You can learn more about how to know if your element size is too small or too large in Ansys Workbench from these sources:

• Sizing on Ansys Workbench 19.2
• Element size too small
• Meshing Element size

Can you explain more about the aspect ratio and orthogonal quality metrics?

Sure, I can explain more about the aspect ratio and orthogonal quality metrics in Ansys Workbench. These are two of the mesh metrics that you can use to evaluate the quality of your mesh elements.

The aspect ratio quantifies the shape of the elements, where 1 is a perfectly shaped element and the element shape is worse with a higher aspect ratio. The aspect ratio is defined as the ratio of the shortest length of the element to the longest length of the element¹. For example, a tetrahedral element has an aspect ratio of 1 if it is a regular tetrahedron, and a higher aspect ratio if it is elongated or flattened. A hexahedral element has an aspect ratio of 1 if it is a cube, and a higher aspect ratio if it is a rectangular prism or a parallelepiped. The aspect ratio affects the accuracy and stability of the solution, as well as the convergence rate. Generally, you should aim for an aspect ratio less than 20 for structural analysis and less than 1000 for fluid analysis².

The orthogonal quality quantifies the alignment of the elements with respect to the geometry and the physics of the problem. The orthogonal quality is defined as the minimum value of the dot product between the element face normal and the vector from the face centroid to the opposite node, for all faces of the element³. The orthogonal quality ranges from 0 to 1, where 1 is the best value and 0 is the worst value. For example, a tetrahedral element has an orthogonal quality of 1 if it is equilateral and orthogonal to the geometry, and a lower orthogonal quality if it is skewed or distorted. A hexahedral element has an orthogonal quality of 1 if it is aligned with the geometry and the flow or stress direction, and a lower orthogonal quality if it is misaligned or twisted. The orthogonal quality affects the accuracy and robustness of the solution, as well as the numerical diffusion and dispersion. Generally, you should aim for an orthogonal quality greater than 0.1 for most problems⁴.

You can check these metrics by right-clicking on the Mesh in the project tree and selecting Mesh Metrics. You can also use mesh statistics to see the number and type of elements in your mesh. You can access these statistics by right-clicking on the Mesh in the project tree and selecting Statistics.

You can learn more about how to improve these metrics by using different meshing methods, such as global or local refinement, adaptive or manual refinement, or different types of elements, such as tetrahedral, hexahedral, or hybrid elements. You can find some tutorials and examples from these sources:

• Explanations Of All Mesh Metric Options In ANSYS® Mechanical
• 网格划分（二）：网格质量评估（基于ANSYS2020）
• Is Your Mesh Good Enough?
• Ansys Workbench Mesh Quality || Skewness || Aspect Ratio || Orthogonal

💥💥💥 What is Design Xplorer in Ansys Workbench and what is used for ?

 Design Xplorer is a tool that helps you optimize your design by exploring different parameters and their effects on your objectives. You can use Design Xplorer to perform design of experiments, sensitivity analysis, response surface fitting, optimization, and robust design. Design Xplorer works with Ansys Workbench, which is a platform for simulation and engineering applications. You can use Design Xplorer to improve the performance, reliability, and efficiency of your design (1,2). 

Source: 

(1) ANSYS 2020 Workbench Tutorial | Introduction to Static Structural | 2020 R2. https://www.youtube.com/watch?v=qbsx1c-R_qU.

(2) Using Ansys DesignXplorer in Ansys Mechanical - YouTube. https://www.youtube.com/watch?v=EMUbHd-DGbc.

How does Design Xplorer work?

To use Design Xplorer, you need to follow these steps:

- Define your input parameters and output responses in Ansys Workbench

- Set up your design exploration method, such as what-if study, parameter correlation, design of experiments, optimization, or six sigma analysis

- Run the design exploration and view the results in charts, tables, or graphs

- Select the best design point based on your objectives and constraints

- Update your design model with the optimal parameters

You can learn more about Design Xplorer from the following resources:

- Introduction to Ansys DesignXplorer (CFD) | Ansys Training¹

- Using Ansys DesignXplorer in Ansys Mechanical | Ansys Virtual Academy - YouTube²

- DesignXplorer vs optiSLang for Workbench CFD Optimization³

I hope this helps you understand how Design Xplorer works. If you have any questions, feel free to ask me. 😊

Source:

(1)https://ketiv.com/ava.

(2)https://twitter.com/KetivTech.

(3) Introduction to Ansys DesignXplorer (CFD) | Ansys Training. https://www.ansys.com/training-center/course-catalog/fluids/introduction-to-ansys-designxplorer-cfd.

(4) Using Ansys DesignXplorer in Ansys Mechanical | Ansys Virtual ... - YouTube. https://www.youtube.com/watch?v=EMUbHd-DGbc.

(5) DesignXplorer vs optiSLang for Workbench CFD Optimization. https://forum.ansys.com/forums/topic/designxplorer-vs-optislang-for-workbench-cfd-optimization/.

(6)  https://facebook.com/KETIVTech/.

(7)  https://www.linkedin.com/company/keti.

(8) https://ketiv.com/blog/subscribe/.

(9) https://ketiv.com/avaIntroduction.

What is the difference between Design Xplorer and optiSLang?

Design Xplorer and optiSLang are both tools that can help you perform design exploration and optimization studies using Ansys Workbench. However, they have some differences in their features and capabilities. Here are some of the main differences:

- Design Xplorer is an integrated tool within Ansys Workbench, whereas optiSLang is a separate product that can be coupled with Ansys Workbench or other software tools¹².

- Design Xplorer includes a subset of the algorithms and methods that are available in optiSLang, such as design of experiments, response surface fitting, optimization, and six sigma analysis². OptiSLang offers more advanced and flexible algorithms and methods, such as meta-models of optimal prognosis, robustness evaluation, reliability analysis, and multidisciplinary optimization¹.

- Design Xplorer may be more suitable for simpler optimization problems or when you want to work within Ansys Workbench environment². OptiSLang may be more suitable for complex optimization problems or when you need to integrate different tools or workflows into your process¹.

You can learn more about the differences between Design Xplorer and optiSLang from the following resources:

Source:

(1) DesignXplorer vs optiSLang for Workbench CFD Optimization. https://forum.ansys.com/forums/topic/designxplorer-vs-optislang-for-workbench-cfd-optimization/.

(2) Optislang and designXplorer - Ansys Learning Forum. https://forum.ansys.com/forums/topic/optislang-and-designxplorer/.

(3)https://www.ansys.com/content/dam/amp/2023/january/quick-request/academic-product-bundle-reference-table-4-11-23.pdf.

Can I use Design Xplorer for structural simulations?

Yes, you can use Design Xplorer for structural simulations. Design Xplorer can work with Ansys Mechanical, which is a tool for finite element analysis (FEA) of structural and coupled-field problems¹. You can use Design Xplorer to study, quantify, and graph various structural responses on parts and assemblies, such as stress, strain, displacement, vibration, fatigue, etc². You can also use Design Xplorer to optimize your design by finding the best combination of input parameters that satisfy your objectives and constraints².

To use Design Xplorer for structural simulations, you need to have Ansys Workbench and Ansys Mechanical installed on your computer. You also need to define your input parameters and output responses in Ansys Workbench, and set up your design exploration method in Design Xplorer. 

Source:

(1) Introduction to Ansys DesignXplorer (FEA) | Ansys Training. https://www.ansys.com/training-center/course-catalog/structures/introduction-to-ansys-designxplorer-fea.

(2) Structural Analysis & Simulation Software | Ansys. https://www.ansys.com/products/structures.

(3) A Scalable Simulation Portfolio for Structural Designers. https://www.3ds.com/cloud/scalable-simulation-portfolio-structural-designers.

Can I use Design Xplorer for fluid dynamics simulations?

Yes, you can use Design Xplorer for fluid dynamics simulations. Design Xplorer can work with Ansys Fluent and Ansys CFX, which are tools for computational fluid dynamics (CFD) simulations². You can use Design Xplorer to study, quantify, and graph various fluid dynamics responses, such as pressure, velocity, temperature, turbulence, etc³. You can also use Design Xplorer to optimize your design by finding the best combination of input parameters that satisfy your objectives and constraints³.

To use Design Xplorer for fluid dynamics simulations, you need to have Ansys Workbench and Ansys Fluent or Ansys CFX installed on your computer. You also need to define your input parameters and output responses in Ansys Workbench, and set up your design exploration method in Design Xplorer. 

Source:

(1) CFD Software: Fluid Dynamics Simulation Software - Ansys. https://www.ansys.com/products/fluids.

(2) Insights from Sir James Dyson on accelerating product development .... https://www.computationalfluiddynamics.com.au/dyson-simulation-driven-product-development-with-design-exploration/.

(3) Fluids | Special Issue : Deep Learning for Fluid Simulation - MDPI. https://www.mdpi.com/journal/fluids/special_issues/deep_learning_fluid.

(4) Fluid Dynamics Simulation - Weber State University. https://physics.weber.edu/schroeder/fluids/.

(5) Marine Computational Fluid Dynamics (CFD): Simulation for ship design. https://resources.sw.siemens.com/en-US/e-book-marine-cfd-software.

What is the difference between Ansys Fluent and Design Xplorer?

Ansys Fluent and Design Xplorer are both tools that can help you perform fluid dynamics simulations using Ansys Workbench. However, they have different purposes and features. Here are some of the main differences:

- Ansys Fluent is a tool for computational fluid dynamics (CFD) simulations. It can solve complex fluid flow problems involving heat transfer, turbulence, multiphase flows, etc⁵. You can use Ansys Fluent to model and analyze the behavior of fluids in various engineering applications, such as aerodynamics, combustion, HVAC, etc⁵.

- Design Xplorer is a tool for design exploration and optimization. It can help you study the effects of different input parameters on your output responses, such as pressure, velocity, temperature, etc⁴. You can use Design Xplorer to find the optimal design that meets your objectives and constraints, such as minimizing drag, maximizing efficiency, etc⁴.

- Ansys Fluent is an integrated tool within Ansys Workbench, which means you can easily set up and run your CFD simulations using the Workbench interface. You can also use other Workbench tools, such as Ansys Meshing, Ansys CFD-Post, etc., to prepare and post-process your CFD models⁵.

- Design Xplorer is a separate tool that can be coupled with Ansys Workbench or other software tools. You need to define your input parameters and output responses in Ansys Workbench first, and then export them to Design Xplorer. You can also import your design points from Design Xplorer back to Ansys Workbench to update your CFD models².

Source: 

(1) Compare Ansys CFX vs. Ansys Fluent | G2. https://www.g2.com/compare/ansys-cfx-vs-ansys-fluent.

(2) Introduction to Ansys DesignXplorer (CFD) | Ansys Training. https://www.ansys.com/training-center/course-catalog/fluids/introduction-to-ansys-designxplorer-cfd.

(3) Connection between Design Explorer and stand alone Fluent sessions .... https://forum.ansys.com/forums/topic/connection-between-design-explorer-and-stand-alone-fluent-sessions/.

(4) Introduction to Ansys DesignXplorer (FEA) | Ansys Training. https://www.ansys.com/training-center/course-catalog/structures/introduction-to-ansys-designxplorer-fea.

(5) ANSYS DesignXplorer: Using Response Surfaces - Part 1 - Ansys Knowledge. https://ansyskm.ansys.com/forums/topic/ansys-designxplorer-using-response-surfaces-part-1/.

💥💥💥 How to prepare sensitivity analysis in Ansys Structural?

Sensitivity analysis is a method to study how the variation in the output of a model depends on the variation in the input parameters. It can help you to identify the most significant parameters that affect the model response, and to reduce the computational effort in structural optimization ¹.

There are different types of sensitivity analysis, such as local, global, and probabilistic. Local sensitivity analysis evaluates the effect of a small change in one input parameter at a time, while keeping the others fixed. Global sensitivity analysis evaluates the effect of varying all input parameters simultaneously over their entire range of values. Probabilistic sensitivity analysis incorporates uncertainty in the input parameters and outputs ².

To perform sensitivity analysis in Ansys Structural, you can use various tools and methods, depending on your problem and objectives. Some of the possible options are:

- Inserting a convergence object under the stress and entering the allowable change. You can also change the maximum number of refinement loop and depth needed under the Solution tab ³.

- Using DesignXplorer, which is an integrated tool for design exploration and optimization. It allows you to define design variables, objectives, and constraints, and to perform parametric studies, response surface analysis, optimization, and robust design analysis ⁴.

- Using global sensitivity analysis methods such as Sobol indices, correlation analysis, ANOVA, or FAST. These methods can help you to quantify the contribution of each input parameter to the output variance, and to rank them according to their importance 

Source:

(1) Global Sensitivity Analysis in Structural Optimization - LSDYNA. https://lsdyna.ansys.com/wp-content/uploads/attachments/f-i-03.pdf.

(2) How to perform mesh sensitivity study for stress - Ansys Knowledge. https://ansyskm.ansys.com/forums/topic/how-to-perform-mesh-sensitivity-study-for-stress/.

(3) What is Sensitivity Analysis? - Corporate Finance Institute. https://corporatefinanceinstitute.com/resources/financial-modeling/what-is-sensitivity-analysis/.

(4) Mesh Sensitivity Study for CFD Simulations - SimScale. https://www.simscale.com/knowledge-base/mesh-sensitivity-cfd/.

What is the difference between local and global sensitivity analysis?

The difference between local and global sensitivity analysis is that local sensitivity analysis evaluates the effect of a small change in one input parameter at a time, while keeping the others fixed. Global sensitivity analysis evaluates the effect of varying all input parameters simultaneously over their entire range of values ¹.

Local sensitivity analysis is easier to perform and requires less computational effort, but it has some limitations. It can only explore the model behavior around a specific point in the input space, and it cannot account for the interactions between the input parameters. It may also produce biased results if the model is nonlinear or has multiple optima ²³.

Global sensitivity analysis is more comprehensive and robust, but it requires more computational resources and sophisticated methods. It can reveal the global effects of each input parameter on the model output, including any interactive effects. It can also handle nonlinear models and uncertainty in the input parameters ¹².

Depending on your problem and objectives, you may choose different types of sensitivity analysis methods. For example, if you want to identify the most important parameters that affect the model output, you can use local sensitivity analysis or global sensitivity methods such as Sobol indices or ANOVA. If you want to study how the model output varies across the entire input space, you can use global sensitivity methods such as response surface analysis or Monte Carlo simulation ²⁴.

Source:

(1) Sensitivity Analysis: The Basics - Addressing Uncertainty in .... https://uc-ebook.org/docs/html/3_sensitivity_analysis_the_basics.html.

(2) Comparative Study of Global Sensitivity Analysis and Local Sensitivity .... https://www.mdpi.com/1996-1073/16/16/5915.

(3) COMPARISON OF SENSITIVITY ANALYSIS TECHNIQUES D. M. Hamby Savannah .... https://web.engr.oregonstate.edu/~hambydm/papers/senscomparison.pdf.

(4) What are global sensitivity and local sensitivity in differential .... https://stats.stackexchange.com/questions/370591/what-are-global-sensitivity-and-local-sensitivity-in-differential-privacy.

(5) Do we need to do both local sensitivity analysis and global sensitivity .... https://stackoverflow.com/questions/67105593/do-we-need-to-do-both-local-sensitivity-analysis-and-global-sensitivity-analysis.

(6)  https://doi.org/10.3390/en16165915.

What is the difference between Sobol indices and ANOVA?

The difference between Sobol indices and ANOVA is that Sobol indices are a type of global sensitivity analysis, while ANOVA is a type of local sensitivity analysis ¹.

Sobol indices measure the contribution of each input parameter or a group of input parameters to the variance of the output of a model. They can also capture the interaction effects between the input parameters. Sobol indices are based on the ANOVA decomposition of the model output, but they require sampling the input parameters over their entire range of values ²³.

ANOVA, which stands for analysis of variance, is a statistical method to compare the means of different groups. It can also be used to decompose the output of a model into terms that depend on one or more input parameters. However, ANOVA assumes that the input parameters are fixed at certain levels, and it does not account for the variability or uncertainty in the input parameters. ANOVA can only measure the main effects of each input parameter, but not their interaction effects ¹⁴.

Therefore, Sobol indices and ANOVA have different objectives and assumptions. Sobol indices are more suitable for studying complex and nonlinear models with uncertain inputs, while ANOVA is more suitable for testing hypotheses and comparing groups with fixed inputs ¹².

Source: 

(1) Variance-based sensitivity analysis - Wikipedia. https://en.wikipedia.org/wiki/Variance-based_sensitivity_analysis.

(2) anova - Sobol Indices for Discrete Variables - Cross Validated. https://stats.stackexchange.com/questions/190843/sobol-indices-for-discrete-variables.

(3) HigherorderSobol’indices arXiv:1306.4068v1 [math.NA] 18 Jun 2013. https://arxiv.org/pdf/1306.4068.pdf.

(4) What do the specific values of the Sobol' indices mean?. https://stats.stackexchange.com/questions/471636/what-do-the-specific-values-of-the-sobol-indices-mean.

(5) Difference between Sobol indices and total Sobol indices?. https://stats.stackexchange.com/questions/70930/difference-between-sobol-indices-and-total-sobol-indices.

How to calculate Sobol indices in Ansys Structural?

To calculate Sobol indices in Ansys Structural, you can use the DesignXplorer tool, which is integrated with Ansys Workbench. DesignXplorer allows you to perform global sensitivity analysis using various methods, including Sobol indices ¹.

Here are the steps to calculate Sobol indices in Ansys Structural using DesignXplorer:

- Define your design variables, objectives, and constraints in the Workbench project.

- Launch DesignXplorer from the Workbench project page.

- In the Design Exploration tab, select Sensitivity Analysis from the drop-down menu.

- In the Sensitivity Analysis dialog box, select Sobol Indices as the method.

- Specify the number of samples and the seed for the random number generator.

- Select the output parameters that you want to analyze.

- Click Generate Samples to create the input samples for the Sobol indices calculation.

- Click Update Project to run the analysis and update the results in DesignXplorer.

- In the Results tab, select Sobol Indices from the drop-down menu.

- You can view the first-order and total-order Sobol indices for each output parameter in a table or a bar chart. You can also export the results to a CSV file.

Source:

(1) Global Sensitivity Analysis in Structural Optimization - LSDYNA. https://lsdyna.ansys.com/wp-content/uploads/attachments/f-i-03.pdf.

(2) Variance-based sensitivity analysis - Wikipedia. https://en.wikipedia.org/wiki/Variance-based_sensitivity_analysis.

(3) Computing Sobol Sensitivity Indexes - MATLAB Answers - MathWorks. https://www.mathworks.com/matlabcentral/answers/90230-computing-sobol-sensitivity-indexes.

(4) sobol_indices : Computation of Sobol' indices - R Package Documentation. https://rdrr.io/cran/sensobol/man/sobol_indices.html.

(5) A Tutorial on Sobol’ Global Sensitivity Analysis Applied to Biological .... https://link.springer.com/chapter/10.1007/978-3-030-51862-2_6.

How to interpret the results of Sobol indices analysis?

The results of Sobol indices analysis can help you to understand how the input parameters of your model affect the output variability. The Sobol indices are based on the ANOVA decomposition of the model output, but they account for the uncertainty and interactions of the input parameters ¹.

The first-order Sobol indices measure the contribution of each input parameter to the output variance, while keeping the other parameters fixed. They can tell you which parameters have the main effects on the output. The sum of the first-order indices is equal to or less than one ².

The total-order Sobol indices measure the contribution of each input parameter to the output variance, including all the interactions with other parameters. They can tell you which parameters have the most influence on the output, either individually or in combination with others. The sum of the total-order indices is equal to or greater than one ².

To interpret the results of Sobol indices analysis, you can compare the values of the first-order and total-order indices for each parameter. A high first-order index and a low total-order index indicate that the parameter has a strong main effect, but a weak interaction effect. A low first-order index and a high total-order index indicate that the parameter has a weak main effect, but a strong interaction effect. A high first-order index and a high total-order index indicate that the parameter has both a strong main effect and a strong interaction effect ³.

You can also plot the Sobol indices in a bar chart or a spider plot to visualize their relative importance and uncertainty. The confidence intervals of the Sobol indices depend on the number of samples and the bootstrap method used in the analysis. If the confidence intervals are too large or include zero, it means that the estimates are not reliable or significant ²⁴.

Source: 

(1) What do the specific values of the Sobol' indices mean?. https://stats.stackexchange.com/questions/471636/what-do-the-specific-values-of-the-sobol-indices-mean.

(2) Interpreting results from Sobol sensitivity analysis in R. https://stats.stackexchange.com/questions/43504/interpreting-results-from-sobol-sensitivity-analysis-in-r.

(3) Difference between Sobol indices and total Sobol indices?. https://stats.stackexchange.com/questions/70930/difference-between-sobol-indices-and-total-sobol-indices.

(4) sensitivity analysis - Intuition for Sobol Indices - Cross Validated. https://stats.stackexchange.com/questions/468869/intuition-for-sobol-indices.

(5) Negative sobol indices · Issue #102 · SALib/SALib · GitHub. https://github.com/SALib/SALib/issues/102.

How to compare the results of different sensitivity analysis methods?

Comparing the results of different sensitivity analysis methods can be challenging, because different methods may have different objectives, assumptions, and limitations. However, some general principles and tips for comparison are ¹²:

- Define the purpose and scope of the sensitivity analysis. What are the research questions and hypotheses that you want to test? What are the sources of uncertainty and variability in your model and data? What are the criteria for evaluating the model performance and robustness?

- Choose appropriate sensitivity analysis methods that match your purpose and scope. For example, if you want to identify the most influential parameters, you can use local or global sensitivity methods such as Sobol indices or ANOVA. If you want to explore the model behavior across the entire input space, you can use global sensitivity methods such as response surface analysis or Monte Carlo simulation.

- Compare the results of different sensitivity analysis methods using graphical and numerical summaries. For example, you can plot the sensitivity indices or measures in a bar chart or a spider plot to visualize their relative importance and uncertainty. You can also calculate the correlation or agreement between different sensitivity indices or measures to quantify their consistency or discrepancy.

- Interpret the results of different sensitivity analysis methods in the context of your research questions and hypotheses. For example, you can assess whether the results support or contradict your expectations, whether they reveal any new insights or surprises, whether they suggest any potential improvements or modifications for your model or data.

- Report the results of different sensitivity analysis methods transparently and comprehensively. For example, you should describe the methods and assumptions used, the input and output parameters considered, the sampling and estimation procedures applied, the uncertainty and variability involved, and the limitations and caveats acknowledged.

Source: 

(1) Sensitivity Analysis and Model Validation | SpringerLink. https://link.springer.com/chapter/10.1007/978-3-319-43742-2_17.

(2) Principles and Methods of Sensitivity Analyses - The National Academies .... https://nap.nationalacademies.org/read/12955/chapter/7.

(3) How to compare qualitative tests – essential tips for ... - Finbiosoft. https://finbiosoft.com/method-comparison-diagnostic-accuracy-sensitivity-specificity/.

(4) 17.4 - Comparing Two Diagnostic Tests | STAT 509 - Statistics Online. https://online.stat.psu.edu/stat509/lesson/17/17.4.

(5) 9.7 Sensitivity analyses - Cochrane. http://handbook-5-1.cochrane.org/chapter_9/9_7_sensitivity_analyses.htm.

What are the advantages and disadvantages of different sensitivity analysis methods?

Sensitivity analysis is a method to study how the variation in the output of a model depends on the variation in the input parameters. It can help you to identify the most significant parameters that affect the model response, and to reduce the computational effort in structural optimization ¹.

There are different types of sensitivity analysis methods, such as local, global, and probabilistic. Each method has its own advantages and disadvantages, depending on the problem and objectives. Here are some of the main points to consider ²³:

- Local sensitivity analysis evaluates the effect of a small change in one input parameter at a time, while keeping the others fixed. It is easy to perform and requires less computational effort, but it can only explore the model behavior around a specific point in the input space, and it cannot account for the interactions between the input parameters. It may also produce biased results if the model is nonlinear or has multiple optima.

- Global sensitivity analysis evaluates the effect of varying all input parameters simultaneously over their entire range of values. It is more comprehensive and robust, but it requires more computational resources and sophisticated methods. It can reveal the global effects of each input parameter on the model output, including any interactive effects. It can also handle nonlinear models and uncertainty in the input parameters.

- Probabilistic sensitivity analysis incorporates uncertainty in the input parameters and outputs. It can provide information on the probability distribution of the model output, and the confidence intervals of the sensitivity measures. It can also perform risk analysis and robust design analysis. However, it requires a large number of samples and a reliable estimation of the input uncertainty.

Depending on your problem and objectives, you may choose different types of sensitivity analysis methods. For example, if you want to identify the most important parameters that affect the model output, you can use local sensitivity analysis or global sensitivity methods such as Sobol indices or ANOVA. If you want to study how the model output varies across the entire input space, you can use global sensitivity methods such as response surface analysis or Monte Carlo simulation.

Source:

(1) Advantages and Disadvantages of Sensitivity Analysis. https://efinancemanagement.com/investment-decisions/advantages-disadvantages-of-sensitive-analysis.

(2) A tutorial on sensitivity analyses in clinical trials: the what, why .... https://bmcmedresmethodol.biomedcentral.com/articles/10.1186/1471-2288-13-92.

(3) Sensitivity Analysis - Definition, Example, Interpretation, Methods | eFM. https://efinancemanagement.com/investment-decisions/sensitivity-analysis.

(4) Sensitivity Analysis - Advantages, Disadvantages, Application, Practices. https://sattvacfo.com/sensitivity-analysis-financial-modelling/.

(5) What Is a Sensitivity Analysis? Definition and Examples. https://www.indeed.com/career-advice/career-development/sensitivities-analysis.

How to choose a suitable sensitivity analysis method for my problem?

Choosing a suitable sensitivity analysis method for your problem depends on several factors, such as the purpose and scope of your analysis, the characteristics and complexity of your model, the availability and quality of your data, and the computational resources and time you have ¹².

Some general steps to help you choose a suitable sensitivity analysis method are:

- Define your research question and hypothesis. What do you want to learn from the sensitivity analysis? What are the expected outcomes and implications of your analysis?

- Identify the input and output parameters of your model. Which parameters are uncertain or variable, and which ones are fixed or constant? Which parameters are you interested in analyzing, and which ones are irrelevant or redundant?

- Assess the type and degree of uncertainty or variability in your input parameters. How can you describe or quantify the uncertainty or variability? What are the sources and distributions of the uncertainty or variability?

- Select a sensitivity analysis method that matches your purpose, model, data, and resources. Consider the advantages and disadvantages of different methods, such as local or global, deterministic or probabilistic, one-at-a-time or all-at-a-time, etc. You can use some criteria or guidelines to compare and evaluate different methods ³⁴.

- Perform the sensitivity analysis using the selected method. Follow the steps and procedures of the method, such as sampling, estimation, calculation, etc. Check the validity and reliability of the results.

- Interpret and report the results of the sensitivity analysis. Explain how the results answer your research question and hypothesis. Discuss the implications and limitations of the results. Provide graphical and numerical summaries of the results.

Source:

(1) Sensitivity Analysis - What Is It, Examples, Formula, How To Do?. https://www.wallstreetmojo.com/sensitivity-analysis/.

(2) 9.7 Sensitivity analyses - Cochrane. https://handbook-5-1.cochrane.org/chapter_9/9_7_sensitivity_analyses.htm.

(3) Sensitivity Analysis | Examples of Sensitivity Analysis - EDUCBA. https://www.educba.com/sensitivity-analysis/.

(4) How to Do Sensitivity Analysis in Excel (3 Easy Methods) - ExcelDemy. https://www.exceldemy.com/how-to-do-sensitivity-analysis-in-excel/.

(5) Which sensitivity analysis method should I use for my agent-based model .... https://research.wur.nl/en/publications/which-sensitivity-analysis-method-should-i-use-for-my-agent-based. 

Examples of using different methods for sensitivity analysis in Ansys Structural

There are different types of sensitivity analysis methods, such as local, global, and probabilistic. Each method has its own advantages and disadvantages, depending on the problem and objectives. You can use different methods to compare and evaluate the sensitivity of your model to different input parameters ².

One example of using different methods for sensitivity analysis in Ansys Structural is from a paper by Reuter et al. ¹. They compared the variance-based approach after Sobol, the correlation analysis, the linear and quadratic ANOVA approaches, and the FAST approach for a structural optimization problem of a composite laminate. They used DesignXplorer, which is an integrated tool for design exploration and optimization in Ansys Workbench, to perform the sensitivity analysis.

They found that the Sobol indices and the correlation coefficients gave consistent results for ranking the input parameters according to their importance. The ANOVA approaches and the FAST approach gave similar results for the main effects, but differed for the interaction effects. They also found that some input parameters had negligible effects on the output, and could be eliminated from the optimization problem.

Another example of using different methods for sensitivity analysis in Ansys Structural is from a paper by Camarda ². He used some innovative techniques for sensitivity analysis of discretized structural systems, such as a finite-difference step-size selection algorithm, a method for derivatives of iterative solutions, a Green's function technique for derivatives of transient response, a simultaneous calculation of temperatures and their derivatives, derivatives with respect to shape, and derivatives of optimum designs with respect to problem parameters.

He applied these techniques to various problems, such as thermal buckling of composite plates, transient thermal response of hypersonic vehicles, shape optimization of aircraft wings, and optimum design of space shuttle tiles. He showed that these techniques could improve the accuracy and efficiency of sensitivity analysis, and could provide valuable information for design and optimization.

Source:

(1) Global Sensitivity Analysis in Structural Optimization - LSDYNA. https://lsdyna.ansys.com/wp-content/uploads/attachments/f-i-03.pdf.

(2) Structural sensitivity analysis: Methods, applications, and needs. https://www.academia.edu/48673736/Structural_sensitivity_analysis_Methods_applications_and_needs.

(3) Study on Structure Sensitivity Analysis Using ANSYS PDS. https://www.scientific.net/AMR.243-249.1830.