**About the Book**

**"Practical Finite Element Analysis for Mechanical Engineers"** is a book about the practical aspect of finite element analysis for structural engineers.

## The objective is to offer the best practical methods and guidelines for the development and validation of finite element models.

## It gives to the structural engineers the keys to developing accurate and reliable finite element models by avoiding the most frequent errors. It contains around 100 examples which illustrate the different modeling techniques.

This book is intended for all structural engineers who wish to solve problems using FEA: for experienced engineers and for students who wish to learn what FEA is, how it works and what are the good modeling practices to develop accurate and reliable finite element models. As a prerequisite it is assumed the reader has a basic understanding of physics and in particular statics and strength of materials before reading this book.

While there is much information in the published literature regarding the theory of the finite element method, there is little on practical modeling techniques by FEA for mechanical engineers. Often engineers learn the basic FEA rules from textbooks; however, the vast majority of them learn FEA through years of experience in developing finite element models.

In this book, I do not explain the reader how to use a FE software, I present the best practical methods and guidelines for the development and validation of finite element models. My objective is to give mechanical structural engineers the keys to developing accurate and reliable finite element models by avoiding the most frequent errors.

I organized the book in such a way that the reader will not be obliged to read it from first to last page. He will be able to pick up information here and there according to his needs. Some information is repeated in different chapters to make them stand-alone while some information contained in one chapter is referenced by others. However, for the beginners in FEA, I would suggest reading the book in the order of the chapters to understand all the subtleties and the ins and outs.

In this first edition, I cover the static, buckling and modal analysis for linear and non-linear structural behaviors. In the second edition I will cover the analysis of composite structures and the dynamic analysis (frequency response and transient).

### What you will learn in this Book?

Introduction chapter to explain the reader what Finite Element Analysis is.

- The methods to solve an engineering problem
- The different numerical methods
- What is a partial differential equation?
- What is FEA?

### BROWSE THE TABLE OF CONTENTS IN DETAIL

#### Visit each chapter to see the content in detail

**Table of Contents**

**Chapter 1 - Defining Finite Element Analysis**

1.1 - Overview

1.2 - Methods to Solve an Engineering Problem

1.3 - The Different Numerical Methods

1.4 - Introduction to Partial Differential Equations

1.5 - What is Finite Element Analysis?

**Table of Contents**

**Chapter 2 - Working with FEA**

2.1 - From Mathematics to Computer Science

2.2 - The Magic of Discretization

2.3 - Pre-Processing

2.4 - Solving

Direct Solver

Iterative Solver

2.5 - Post-Processing

2.6 - Summary of the FEA Process

2.7 - The Capabilities of Finite Element Solvers

2.8 - How accurate is FEA?

CAD Simplification

The Discretization

Modeling of the Joints

Material

Loading

Boundary Conditions

Behaviors Captured by the FEM

Conclusion

2.9 - Why Do Finite Element Analysis?

2.10 - How FEA Can Help You?

2.11 - What Do You Need to Perform a FE Simulation?

**Table of Contents**

**Chapter 3 - Becoming a FEA Expert**

3.1 - Overview

3.2 - What Do You Have to Learn in the FEA Field?

3.3 - Guide to FEA Learning

3.4 - What You Will Learn in This Book?

3.5 - The Wheel of Structural FEA Competencies

3.6 - Conclusion

**Table of Contents**

**Chapter 4 - The History of FEA**

4.1 - The Pioneers

4.2 - The FEA Timeline

**Table of Contents**

**Chapter 5 - The Basis of the FEM Theory**

5.1 - Overview

5.2 - The Equilibrium Equation

5.3 - The Displacement Method

The Three Conditions

The Stiffness Matrix

Element Stiffness Matrix

Global Stiffness Matrix

The Linear Spring Model

Application to the Two-Spring System

Application to the Four-Spring System

Application to a Parallel-Spring System

5.4 - The Principle of Minimum Potential Energy

5.5 - Element Stiffness Matrix for Various Topologies

Overview

Degrees-of-Freedom

Shape Functions

1D Truss Element

Summary of the Displacement Method

Truss Element in Axial Loading

Truss Element in Torsion

Complete Stiffness Matrix of the Truss Element

Application to the Two-Rod Assembly

Generic Form of the Truss Element Stiffness Matrix

1D Beam Element

Euler-Bernoulli Beam Theory

Timoshenko Beam Theory

Bending and Torsion

Full Capabilities Beam

2D Elements

Overview

Membrane: The Constant Strain Triangle (CST)

Membrane: The Linear Strain Triangle (LST)

Thin-Plate

Isoparametric Formulation

Thick-Plate

Shell

3D Solid Element

Linear Hexahedral Element

Quadratic Hexahedral Element

5.6 - How the Stiffness Matrix is Assembled?

Matrix Assembly

Taking Advantage of Sparsity and Symmetry

Banded Matrix

Skyline Matrix Storage

5.7 - How the FEM Equations Are Solved?

Direct Solution

Iterative Solution

**Table of Contents**

**Chapter 6 - Defining Your FEA Strategy**

6.1 - Overview

6.2 - The Time

6.3 - The 10 Steps to Follow

6.4 - Expose the Problem

6.5 - Define the Goals

6.6 - Analyze History

6.7 - Evaluate the Feasibility

6.8 - Evaluate the Boundaries and the Surrounding Environment

6.9 - Understand the Loading and Predict the Load Path

6.10 - Select the Element Types and the Model Size

6.11 - Predict the Final Results

6.12 - Review the Plan

6.13 - The 14 Questions You Should Be Able to Answer Before to Start Modeling

6.14 - Large Scale Modeling Techniques

6.15 - Conclusion

**Table of Contents**

**Chapter 7 - The Library of Elements**

7.1 - Overview

7.2 - Type of Elements

Overview

1D Elements

Truss Element

Beam Element

Spring Element

2D Elements

Type of 2D elements

Properties

Plane Stress & Plane Strain

Membranes

Plates

Shells

Orientation

Quadrilateral Vs Triangular

Linear Vs Quadratic Shell Elements

3D Elements

Type of 3D elements

Brick Vs Tetrahedral

Linear Vs Quadratic Solid Elements

Special Elements

1D Contact Elements

Mass Elements

R-Type Elements

7.3 - Criteria for the Element Selection

Type of Element

Degrees of Freedom

Capabilities

Cost

Accuracy

7.4 - How to Choose the Right Element?

Predict Your Structure Behavior

Experiment Your Library of Elements

The Geometry Size and Shape

Element Order: Linear or Quadratic?

Integration Scheme

Chose the Elements in Relation to the Solution

Time Allocated to the Analysis

Rules to Select the Right Elements

7.5 - Shear Locking

What is Shear Locking?

How to Prevent Shear Locking?

7.6 - Hourglassing

What is hourglassing?

How to Prevent Hourglassing?

7.7 - Examples

Quadrilateral Element Vs Triangular Elements

High-Order Tetrahedral Elements Vs Low-Order (TET10 VS TET4)

Effect of Integration Scheme on Shear Locking and Hourglassing

Example of Library of Elements

**Table of Contents**

**Chapter 8 - Meshing**

8.1 - Overview

8.2 - Understand the Elements Behavior

8.3 - How to Plan the Meshing?

Study the Geometry in Detail

Clean-up the Geometry

Select the Type of Elements

8.4 - How to Decide the Elements Size?

Factors Influencing the Meshing Size

Deflection/Stiffness or Stress?

Predict the Deformed Shape and Match It

Meshing of Critical Areas

Keep It Simple When the Design Is Not Mature

8.5 - How to Do a Mesh Refinement?

Why to Do Mesh Refinement?

The Mesh Refinement Process

Advantage and Disadvantage of Mesh Refinement

The Different Mesh Refinement Techniques

The Global Element Size Reduction

The Local Element Size Reduction

Increasing the Elements Order

The Manual Adjustment of the Mesh

Global Adaptive Mesh Refinement

Local Adaptive Mesh Refinement

The Convergence Study Methodology

On Which Extent Refine the Mesh?

Can I Use the Convergence Study for Other Models?

The Different Mesh Refinement Metrics

Guidelines for the Convergence Study

The Convergence Study Example

8.6 - What is a Physical Interface?

8.7 - What are the Preferred Shapes for 2D and 3D Models?

8.8 - How to Do a Mesh Transition?

Mesh Transition Using Various Forms of Elements

Mesh Transition Using Higher-Order Elements

Mesh Transition Between Dissimilar Element Types

Mesh Transition Using Extra Elements Between Incompatible Elements

Mesh Transition Using a R-type Interpolation Element

8.9 - 1D Meshing Rules

8.10 - 2D Meshing Rules

Why to Mesh 2D Instead of 3D?

The Mid-Surface Concept

The Two Rules Of Mid-Surface Creation

Variable Thickness

Comparison Between Linear and Parabolic Elements

Rules for Modeling Holes and Fillets

How to Check a 2D Mesh?

Mesh Quality

The Four Most Common 2D Meshing Errors

How to Improve My 2D Mesh Quality?

Other Recommendations About 2D Meshing

8.11 - 3D Meshing Rules

Do I Really Face a 3D Problem?

Tetra Meshing Techniques

Linear Vs Parabolic Tetra Elements

How to Check a Tetra Meshing?

Other Recommendations About 3D Tetra Meshing

Brick Meshing Techniques

How to Check a 3D Meshing?

**Table of Contents**

**Chapter 9 - Setting Your Units**

9.1 - The Consistent Systems of Units

9.2 - The Mass Problem

9.3 - Weight & Mass Density for Common Materials

9.4 - Engineering Units for Common Variables

**Table of Contents**

**Chapter 10 - Defining Loads & Boundary Conditions**

10.1 - Overview

10.2 - What is a Boundary Condition?

10.3 - Why Do We Need Boundary Conditions?

10.4 - What are the Roles of Boundary Conditions?

10.5 - The Different Types of Boundary Conditions

10.6 - Use the Boundary Conditions to Constrain a Model

What is a Rigid Body Mode?

What is a Mechanism?

How to Capture Mechanisms in My FEM?

The Types of Constraints

What Are Single-Point Constraints?

Examples of Constraints for 2D and 3D Problems

Supporting Two Dimensional Bodies

Supporting Three Dimensional Bodies

Compatibility of Boundary Conditions with Elements

Constraints and Enforced Displacement

How to Use Boundary Conditions to Model Symmetry and Anti-Symmetry?

10.7 - Use the Boundary Conditions to Simplify a Problem

10.8 - Strategy to Properly Define Your Boundary Conditions

Boundary Conditions Are Never Perfect

The 7 Questions You Should Answer to Successfully Define Your Boundary Conditions

Strategy

10.9 - How to Create Iso-Static Restraints?

10.10 - The Over-Stiffening and Under-Stiffening Problem

Over-Stiffening

Under-Stiffening

10.11 - How to Deal with the Singularities?

What Is a Singularity?

Are You Interested with the Results Around a Singularity?

Impact of a Singularity

Can I Ignore the Singularities?

How to Avoid a Singularity Due to a Punctual Loading?

10.12 - How to Load a Model?

Type of Loadings

**Table of Contents**

**Chapter 11 - Material Modeling**

11.1 - Overview

11.2 - Isotropic Material

Define an Isotropic Material in a Finite Element Model

Stress and Strain

Stress-Strain Curve

Plastic and Elastic Strain

Strain Hardening

Ductile and Brittle Materials

Stress-Strain Curve Calculation: Ramberg-Osgood Equation

Stress-Strain Curve Calculation: Hollomon Equation

True Stress and Strain

Summary of the Typical Behaviors of Metallic Materials

11.3 - Two-Dimensional Orthotropic Material

11.4 - Two-Dimensional Anisotropic Material

11.5 - Three-Dimensional Anisotropic Material

11.6 - Three-Dimensional Orthotropic Material

**Table of Contents**

**Chapter 12 - Rigid Body Elements and Multi-Point Constraint**

12.1 - Overview

12.2 - Terminology

12.3 - R-type Elements

Introduction to R-type Elements

Small Displacement Theory

Two Nodes Rigid Element

Definition

Setup to weld two parts together

Setup to form a pin-jointed attachment

Setup to enforce equal translations only

Setup to enforce equal rotations only

Setup to model a compatibility of displacements

Key Points of the Two Nodes Rigid Element

N Nodes Rigid Element

Definition

Setup to rigidly weld multiple nodes to one other node

Key Points of the N Nodes Rigid Element

Interpolation Element

Definition

How the Interpolation Element Works?

Setup an Interpolation Element

Example 1: Load Through CG

Example 2: Load Not Through CG

Example 3: Transverse Load on a Beam

Example 4: Connect Incompatible Elements

Example 5: Connect 1D Model to 2D Model

Key Points of the Interpolation Element

R-Type Elements Summary

12.4 - Constraint Element: MPC

Definition

Setup an MPC

Example 1: Equal the Motions of Two Grids

Example 2: Compute Relative Displacement

Example 3: Enforce a Separation Between Nodes

Example 4: Average Motion

Example 5: Create a Linear Contact Between Nodes

12.5 - Methods for Rigid Element Solution

Linear Method

Lagrange Method

Available Methods for Various Solutions

**Table of Contents**

**Chapter 13 - Modeling Bolted Joints**

13.1 - Overview

13.2 - Do You Really Need to Model the Bolts in Your Model?

13.3 - The Various Finite Element Modeling Approaches for Fastened Joints

Fasteners Modeled with Rigid Elements

Fasteners Modeled with Discrete Spring Elements

Fasteners Modeled with Beam Elements

Fasteners Modeled with Connectors

Fasteners Modeled with the Rutman Method

Fastener Joint Behavior and Stiffness

Modeling of the Fastener Joint

Example of Rutman Fasteners Modeling

13.4 - How to Calculate Your Spring Fastener Stiffness?

Why to Calculate the Fastener Stiffness?

Parameters for the Fastener Stiffness Calculation

Axial Stiffness

Shear Stiffness

Tate & Rosenfeld Method

Swift Method

Huth Method

Bending Stiffness

Method 1

Method 2

Method 3

Torsional Stiffness

Method 1

Method 2

13.5 - How to Connect the Fastener Elements to the Surrounding Mesh?

Connect the Fastener When the Hole is Modeled

Beam Elements

Rigid Element

Connect the Fastener When the Hole is Not Modeled

13.6 - How to Capture the Prying Effect in a Bolted Joint Modeled with 1D Spring?

13.7 - Pin Joints

13.8 - Bolt Preload

13.9 - Conclusion

**Table of Contents**

**Chapter 14 - Modeling Contact**

14.1 - Overview

14.2 - What is a Contact?

Introduction

Definitions

Contact Strategy

Contact Force

Friction Force

Linear or Non-Linear?

14.3 - Contact Types

The Punctual Linear Contact

The Punctual Non-Linear Contact

The General Contact

14.4 - Contact Analysis Procedure

The Two Types of Contact Interaction

Glued contact

Touching contact

The Two Types of Contact Body

The Slave-Master Concept

Contact Detection

Node-to-Segment Contact

Segment-to-Segment contact

Contact Tolerance & Detection Algorithms

Specify the Contact Between Bodies

14.5 - Guidelines to Define Contact

Keep it Simple at the Beginning

Do Not Vary the Mesh Density Too Much

Pay Attention to the Rigid-Deformable Contact

Mesh Requirements

Penalty Based Contact Method

Preventing Rigid Body Motion in Contact Simulations

Isolate the Problems

Initial Contact

Avoid Cracks in the Contact Surfaces

Contact at Corners

MPC in Contact Surface

14.6 - Do You Really Need Contacts in Your Simulation?

Are Bodies in Contact in Your Model?

Can a Body Touch a Rigid Support in Your Model?

Do You Have an Initial Contact?

Can You Predict Where the Contact Area Will Be?

14.7 - Examples

Punctual Linear Contact Between Two Nodes

Punctual Linear Contact on a Grounded Surface4

Punctual Non-Linear Contact

Glued Contact

Touching Contact

Contact between Deformable Bodies4

Contact Deformable-Rigid

**Table of Contents**

**Chapter 15 - Submodeling**

15.1 - What is Submodeling?

15.2 - Why to Do Submodeling?

15.3 - How to Do Submodeling?

Submodel a Global FEM

Extract a Part of the Global FEM

15.4 - Tips and Hints for Submodeling

15.5 - Displacement-Based Submodeling Vs Force-Based Submodeling

15.6 - Static Condensation

From FEM to Matrix

Terminology and Static Condensation Concept

The Static Condensation Process

The Two Phases of Static Condensation

Reduction Phase

Assembly Phase

Static Condensation Validation

What are the Limitations of the Static Condensation Process?

15.7 - Examples of Submodeling

Submodeling a Global FEM

Submodeling by Extracting a Component from the Global FEM

Submodeling by Static Condensation

**Table of Contents**

**Chapter 16 - Understanding FEM Outputs**

16.1 - Overview

16.2 - Standard Outputs

The Deformed Shapes

Element Force

  Forces in 1D Truss Element

Forces in 1D Beam Element

Example of Force and Moment Outputs in Truss and Beam Elements

Forces and Moments in 1D Spring Element

Forces and Moments in 2D Shell Elements

Forces in 3D Solid Elements

Stresses in Elements

How the FE Solver Computes the Stresses?

Various Type of Stresses

Example of Stress Calculation from Forces and Moments in a 2D Shell Element

Von Mises Stress or Principal Stress?

Forces at Boundary Conditions

Freebody Diagram

The Freebody Loads

The Freebody Interface

The Freebody Displacements

16.3 - The Basic Rules of Post-Processing

Displacement and Animation First

The Contour Plots

Select the Appropriate Stress Plot

Extrapolation

Shape Function

Average

Centroid

Min/Max

Example of Extrapolation

Select the Appropriate Type of Stress

Do Not Neglect the Convergence Test

Validate the Linear Assumption

Do Not Confuse Forces and Flows for 2D Shell Elements

Pay Attention to Coordinate Systems

Adjusting The Scale Of The Color Bar

Report the Maximum Stress Location

Top And Bottom Stresses For 2D Shell Elements

Graph the Results

Interpretation Of Results And Design Modifications

Export the Results in Reports

Use the Reading Elements

Vector Plot

**Table of Contents**

**Chapter 17 - Validating & Correlating Your FEA**

17.1 - Overview

17.2 - Accuracy Checks5

17.3 - Mathematical Validity Checks

Basic Concepts to Understand the Mathematical Checks

Singularities and Mechanisms

Key Points to Manage the Singularities

The Weight Check

The Applied Load Check

The Reacted Loads Check

The Post-Processor Checks

The Load Path

Mathematical Validity Check #1: Free-Free Modal Check

Purpose

Input Required5

Output Results5

Mathematical Validity Check #2: Unit Gravity Check

Purpose

Input Required

Output Results Checks

Mathematical Validity Check #3: Unit Enforced Displacements Check

Purpose

Input Required

Output Results Checks

Mathematical Validity Check #4: Thermal Equilibrium Check

Purpose

Input Required

Output Results Checks

17.4 - The Deformation Check

17.5 - Correlation

Objective

Strain Gauge Measurements

Validation Factor & Correlation Plot

The Validation Factors Computation

The Correlation Plot

17.6 - Document the Model Checkout

17.7 - Example of Mathematical Validity Checks

Example Introduction

Free-Free Modal Check

Unit Gravity Check

Unit Enforced Displacement Check

**Table of Contents**

**Chapter 18 - Improving Your Performance Computing**

18.1 - Overview

18.2 - CPU Power and Clock Speed

18.3 - Memory Size

18.4 - Cache Size

18.5 - Hard Drive Speed

18.6 - Parallel Computing

Overview

Parallel Computer Architectures: SMP Vs DMP

The Basics of High-Performance Computing (HPC)

18.7 - Recommendations to Speed-Up Your Simulations

System Optimization

Manage the Memory

Optimize the Output Requests

Make Use of the Multiple Cores (SMP)

About Hyper-Threading

**Table of Contents**

**Chapter 19 - Documenting Your FE Analysis**

19.1 - Overview

19.2 - Model Identification

19.3 - Source of Geometry

19.4 - Model Assumptions

19.5 - Simulation Parameters

19.6 - Verification & Validation

**Table of Contents**

**Chapter 20 - Linear Static Analysis**

20.1 - Overview

20.2 - What is Linear Static Analysis?

20.3 - How to Solve a Linear Static Problem?

20.4 - Characteristics of a Linear Analysis

Relation Load-Displacement

Stress-Strain Relation

Scalability

Superposition

Reversibility & Load History

Solution Setting

20.5. - How a FE Program Solves a Linear Problem?

20.6. - Examples of Linear Static Analysis

Characteristics of a Linear Static Analysis

How Material Affects Stress in a Linear Static Solution?

**Table of Contents**

**Chapter 21 - Non-Linear Static Analysis**

21.1. - Overview

21.2 - What is a Non-Linear System?

21.3 - Characteristics of a Non-Linear Analysis

Relation Load-Displacement

Stress-Strain Relation

Scalability

Superposition

Initial State of Stress

Load History

Reversibility

Solution Setting

21.4 - Geometric Non-Linearity

The Sources of Geometrical Non-Linearity

How Does Non-Linear Geometry Work?

Do You Really Need a Non-Linear Geometric Analysis?

The Follower Load Concept

Small or Large Strain?

Example of Geometric Non-Linearity

21.5 - Material Non-Linearity

Yield Criteria

Hardening Rules

Material Models

Engineering Stress-Strain or True Stress-Strain?

How Does Non-Linear Material Work?

Do You Really Need A Non-Linear Material Analysis?

21.6 - Boundary Non-Linearity

Variation of Loading

Variation of Constraints

Contacts

21.7 - Choosing the Right Elements for a Non-Linear Analysis

21.8 - How Do FE Solvers Compute the Non-Linear Problems?

Characterization and Formulation of a Non-Linear Problem

Newton-Raphson Method6

Modified Newton-Raphson Method

Examples of Newton-Raphson Method

Computational Methods in Non-Linear Analysis

The Equilibrium Path & The Critical Points

Adaptive Solution Strategies

Stiffness Matrix Update Strategies

Choosing the Incremental Load Step

Arc-Length Methods

Line Search Procedures

Convergence Criteria

How to Deal with the Convergence Issues?

Summary of the Iterative Solution Schemes

How to Select the Right Iterative Solution Scheme?

Summary of the Non-Linear Solution Strategy

21.9 - General Recommendations for Non-Linear Analysis

Understand the Non-Linear Features

Understand Your Problem and Structural Behavior

Understand the Difference Between a Linear Subcase and a Non-Linear Subcase

Simplify Your Model

Use an Adequate Mesh & Type of Elements

Apply Loading Gradually

Read Your Output

Full Newton-Raphson or Modified Newton-Raphson?

Convergence Problems

Keep an Eye on your Material Definition

21.10 - Common Mistakes in Non-Linear Analysis

21.11 - Examples of Non-Linear Static Analysis

Geometric Non-Linearity and History Path

Cumulative Effect of a Non-Linear Analysis

Influence of the Incremental Load Step on Results

Material Non-Linearity: Elasto-Plastic Plate

Highly Non-Linear Problem

**Table of Contents**

**Chapter 22 - Linear Buckling Analysis**

22.1 - What is Linear Buckling Analysis?

22.2 - Assumptions and Limitations of Linear Buckling Analysis

22.3 - Linear Buckling Analysis Outcomes

22.4 - How Do Solvers Compute Linear Buckling Problem?

The Equation of Motion with Differential Stiffness Matrix

How to Compute the Eigenequation?

Solution of the Buckling Problem

Eigenvalue Extraction Method

22.5 - The Linear Buckling Strategy

Everything Starts With a Linear Static Analysis

Select Your Buckling Cases

Meshing Hints

Manage the Offsets

22.6 - Examples of Linear Buckling Analysis

Euler Beam Buckling

Panel Buckling

Stiffened Panel Buckling

The Influence of the Meshing Density on the Buckling Predictions

**Table of Contents**

**Chapter 23 - Non-Linear Buckling Analysis**

23.1 - Overview

23.2 - Why to Perform a Non-Linear Buckling Analysis?

23.3 - The Stability Path & the Converged Solution

23.4 - Non-Linear Buckling Procedure

23.5 - Post-Buckling

23.6 - Essential Steps in Non-Linear Buckling Analysis

23.7 - Examples of Non-Linear Buckling Analysis7

Non-Linear Buckling of a Curved Panel7

Snap-Through: Newton-Raphson Vs Arc-Length

**Table of Contents**

**Chapter 24 - Normal Mode Analysis**

24.1 - Overview

24.2 - How to Solve the Real-Eigenvalue Problem?

The Equation of Motion

How to Compute the Eigenequation?

Solution of the Eigenequation

Eigenvalue Extraction Method

24.3 - What a Mode Is and What a Mode Is Not?

Natural Frequencies

What a Mode Is?

What a Mode is Not?

24.4 - How Natural Frequencies and Mode Shapes are Influenced?

24.5 - Why to Compute a Modal Analysis?

Finding Weaknesses in a Model

Avoid Resonance

24.6 - Examples of Modal Analysis

Check a Model

Find the Natural Frequencies to Avoid Resonance

Evaluate the Modal Effective Mass

Influence of the Pre-Stiffness on the Natural Frequencies

**Table of Contents**

**Chapter 25 - The Good Modeling Practices**

25.1 - Overview

25.2 - The Good Modeling Practices Approach

25.3 - It All Starts With a Good Plan

25.4 - Understand in Detail the Problem to Analyze

25.5 - Define your Design Objective

25.6 - Make Sure of the Inputs and Requirements

25.7 - Select the Right Type of Analysis

25.8 - Clean-Up the Geometry

25.9 - Check the Geometry

25.10 - Choose the Right Elements

25.11 - Create an Intelligible Mesh

25.12 - Define the Right Boundary Conditions

25.13 - Validate Your Input Data

25.14 - Define the Contacts Properly

25.15 - Model the Right Material Behavior

25.16 - Manage the Units

25.17 - Should I Model the Entire Structure?

25.18 - Manage the Singularities

25.19 - Should I Model the Bolts?

25.20 - Manage the Incompatible Degrees-of-Freedom

25.21 - Keep an Eye on the Parameters of the Solution

25.22 - Verify & Validate Your Model

25.23 - Read the Solver’s Messages

25.24 - Keep a Critical Eye on the Result

25.25 - Document Everything

25.26 - Ask for Help

25.27 - Most Common Mistakes In Finite Element Analysis

25.28 - The 10 Commandments of the Finite Element Analyst