**Applied Finite Element Analysis with SolidWorks Simulation 2015**

## Author: Cyrus Raoufi, Ph.D., P.Eng.

## ISBN: 9781-0-9919498-1-6

## Pages: 503

## Binding: Perfect Paperback

## Price: US$75

## CAN$89

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**Description and Table of Contents:**

This textbook is intended to cover the fundamentals of the Finite Element Analysis (FEA) of mechanical components and structures using the SolidWorks Simulation®. It is written primary for the engineering students, engineers, technologist and practitioners who have little or no work experience with SolidWorks Simulation. It is assumed that the readers are familiar with the fundamentals of the strength of materials as offered in an introductory level course in a typical undergraduate engineering program. However, the basic theories and formulas have been included in this text as well. This textbook can be adopted for an introductory level course in Finite Element Analysis offered to students in mechanical and civil engineering and engineering technology programs. The Direct Stiffness Method is used to develop the bar, truss, beam and frame elements. Both analytical and simulation solutions are presented through examples and tutorials to ensure that readers understand the fundamentals of FEA and the simulation software.

It is strongly recommended that readers always find a way to verify the FEA simulation results. In this textbook, the simulation results are verified for the truss, beam and frame structures using the analytical approaches through the Direct Stiffness Method. However, readers must consider that in many engineering problems, they have to deal with complicated geometries, loadings, and material properties which make it very difficult, if not impossible, to solve the problem using analytical methods.

Chapter 1 of this textbook deals mostly with the fundamentals of the mechanical loading, 3-Dimensional and 2-Dimensional stress states, four failure theories used in the SolidWorks Simulation, basics of matrix algebra, Cramer’s rule for solving linear algebraic equations, and matrix manipulation with Microsoft Excel®.

Chapter 2 of this textbook presents a general overview of SolidWorks Simulation and addresses the main tools and options required in a typical FEA study. Types of analysis available in SolidWorks Simulation and four commercially available SolidWorks Simulation packages will be introduced. The three main steps in FEA include: (i) pre-processing; (ii) processing, and (iii) post-processing and are used in the SolidWorks Simulation working environment. They will be discussed in detail and related tools available in this software will be presented.

Chapter 3 of this textbook introduces several kinds of elements available in SolidWorks Simulation. The Solid Element which is used in SolidWorks Simulation to model bulky parts will be discussed in detail. The concepts of the Element Size, Aspect Ratio, and Jacobian will be discussed. Several meshing techniques available in SolidWorks Simulation such as Mesh Control, h-Adaptive, p-Adaptive, Standard Mesh with Automatic transition, and Curvature based mesh will be presented as well.

Chapter 4 of this textbook presents the Direct Stiffness Method and Truss structure analysis. The stiffness matrices will be developed for the bar and truss elements. The pre-processing, processing and post-processing tools available in SolidWorks Simulation for 1D bar element, 2D truss, and 3D truss FEA simulation will be introduced. Several examples and tutorials will be presented to show how the user can verify the simulation results by comparing them to the analytical results.

Chapter 5 of this textbook deals mostly with beam and frame analysis with SolidWorks Simulation. The stiffness matrix for a straight beam element will be developed and the Direct Stiffness Method will be used to analyze both statically determinate and indeterminate beams loaded with concentrated and distributed loads. This is done by defining their equivalent nodal forces and moments. The pre-processing, meshing and post-processing phases of a typical beam FEA with SolidWorks Simulation will be presented. As before, several examples and tutorials will be presented to show how the user can verify the simulation results by comparing them to the analytical results.

Chapter 6 of this textbook presents the application of 2D simplified and 3D shell elements available in SolidWorks Simulation. In particular, the application of 3D shell elements for analysis of thin parts such as pressure vessels and sheet metal parts will be discussed. The related pre-processing, meshing, and post-processing tools available in SolidWorks Simulation will be presented through several tutorials.

Chapter 7 of this textbook deals with assembly analysis using the contact sets. Several types of contact sets will be introduced and their application will be explored. Advanced external forces will be presented. Compatible and incompatible meshing techniques will be introduced. Beside, several techniques to simplify the simulation of assemblies will be discussed. Several examples and tutorials will be presented to show how the user can use related tools available in SolidWorks Simulation and interpret the simulation results.

Chapter 8 of this textbook introduces several types of connectors available in SolidWorks Simulation and their application. It includes the Bolt, Weld, Pin, Bearing, Spring, Elastic, Link, and Rigid connectors. Both weld and bolt connectors will be discussed in detail and several examples and tutorials will be presented.

Chapter 9 of this textbook introduces the Frequency Analysis tools provided in SolidWorks Simulation Professional to identify the natural frequencies and related mode shapes of parts and assemblies. A one degree of freedom mass-spring-damper will be presented to explain fundamental concepts such as natural frequency, mode shape, resonance, and damping ratio. The pre-processing, meshing, and post-processing tools available in SolidWorks Simulation for Frequency Analysis will be presented through several tutorials

**Chapter 1. Basic Background**

Mechanical Loading and Stresses

Axial Loading and Normal Stress

Torsional Loading and Shear Stress

Bending Moment and Normal Stress in Straight Beams

Direct Shear Loading and Shear Stress

Transverse Shear Loading and Shear Stress

Linear Elastic Isotropic Model of Materials

Determining the Area (A), Moment of Inertial, and Polar Moment (J) of a Cross Section using Solid Works

3-Dimensional Principle Stresses

2-Dimensional Principle Stresses

Example 1.1

Failure Theories

Maximum von Mises Stress Criterion

Maximum Shear Stress Criterion

Mohr-Coulomb Stress Criterion

Maximum Normal Stress Criterion

Matrix Algebra

Multiplication of a Matrix by a Scalar

Addition of Matrices

Multiplication of Matrices

Transpose of a Matrix

Symmetric Matrices

Unit Matrix (or Identity Matrix)

Determinant of a Square Matrix

Inverse of Square Matrix

Orthogonal Matrix

Cramer’s Rule for Solving Linear Algebraic Equations

Using Excel to Perform Matrix Manipulation

Example 1.2

Example 1.3

Example 1.4

Exercises

**Chapter 2. Fundamentals of SolidWorks Simulation**

Types of Analysis Available in SolidWorks Simulation Premium

SolidWorks Simulation Bundles

Basic Steps in FEA

FEA Pre-processing

FEA Processing

FEA Post-processing

Types of Elements in SolidWorks Simulation

SolidWorks Simulation Options

Opening a New Simulation Study

SolidWorks Simulation Working Environment

Assigning Material(s) to a Part or an Assembly

Fixtures

Standard Fixtures

Fixed Geometry Fixture

Immovable Fixture

Roller/Slider Fixture

Fixed Hinge

Advanced Fixture

Symmetry Fixture

Circular Symmetry Fixture

Use Reference Geometry Fixture

On Flat Face Fixture

On Cylindrical Face Fixture

On Spherical Face Fixture

Structural Loads

Force

Uniform Force Applied Normal to a Selected Entity

Torque

Uniform Force Applied along a Selected Direction

Nonuniform Force Applied Normal to a Selected Entity

Nonuniform Force Applied along a Selected Direction

Gravity

Post-processing in SolidWorks Simulation

Options Available in a typical Stress Plot

Edit Definition

Settings

Section Clipping

Chart Options

Probing

Animating

Define Factor of Safety Plot

Define Design Insight Plot

Define Fatigue Check Plot

Generating FEA Reports

Tutorial

Exercise

**Chapter 3. Solid Element, Convergence Test and Adaptive Meshing.**

3-Dimensional Tetrahedral Solid Element

Element Size and Mesh Density

Element Aspect Ratio

Jacobian Ratio

Concave Element

Meshing with SolidWorks Simulation

Mesh Quality Plots

Convergence Check

h-Adaptive Meshing

p-Adaptive Meshing

Mesh Control3-19

Standard Mesh with Automatic transition Selected

Curvature based mesh

Stress Singularity at Sharp Corners

Tutorial 3.1(Mesh Refinement)

Tutorial 3.2 (Stress Singularity and Mesh Control)

Tutorial 3.3 (Curvature based mesh)

Exercises

**Chapter 4. Direct Stiffness Method and Truss Analysis**

Direct Stiffness Method for 1-Dimensional Element

Shape Functions of a 1D Spring Element

Example 4.1

Pre-processing of a 1-Dimensional Structure in SolidWorks Simulation

1-Dimensional Structure CAD Modeling in SolidWorks

Defining a Beam Member in SolidWorks Simulation

Assign the Materials to a 1-Dimensional Structure in SolidWorks Simulation

Edit Joints of a 1-Dimensional Structure in SolidWorks Simulation

Apply Fixtures to the Joints of 1-Dimensional Structure in SolidWorks Simulation

Apply External Loads to the Joints of a 1-Dimensional Beam Structure

Post-processing of a 1-Dimensional Beam using the Displacement Plot

Tutorial 4

Direct Stiffness Method for 2D Truss Analysis

Example 4.2

Pre-Processing a True Structure Analysis in SolidWorks Simulation

Truss CAD Modeling in SolidWorks

Truss 3D Modeling in SolidWorks: Custom Profile Approach

Truss 3D Modeling in SolidWorks: Structural Member Approach

Truss 3D Modeling in SolidWorks: Non-Structural Approach

Truss Element in SolidWorks Simulation

Assign the Materials to the Truss Structure in SolidWorks Simulation

Edit Joints of a Truss Structure in SolidWorks Simulation

Apply Fixture to the Joints of a Truss Structure in SolidWorks Simulation

Apply External Loads to the Joints of a Truss Structure in SolidWorks Simulation

Meshing of a Truss Structure in SolidWorks Simulation

Post-Processing of a Truss Structure Analysis in SolidWorks Simulation

List Axial Forces and Stresses Produced in each Truss Member

Generate the Beam Diagram of the Axial Forces Produced in each Truss Member

Determine the Displacements, Rotations and Reaction Forces/Moments using the Displacement Plot

Tutorial 4.2

Direct Stiffness Method for 3D Truss Analysi4-59

Tutorial 4.3

Exercises

**Chapter 5. Beams and Frames Analysis**

The Direct Stiffness Method for the Beam Element

Stress Components of a Beam under Axil Force, Shear Force, and Bending Moment Loading.

Normal Stress due to the Axial Loading

Shear Stress at outer Layers due to the Shear Force

Normal Stress due to the Bending Moment

Equivalent Nodal Forces/Moments

2D Planar Frames Analysis

Direct Stiffness Method for 2D Planar Frame Analysis

Example 5.1

Example 5.2

Example 5.3

Pre-Processing of Beams and Frames Analysis in SolidWorks Simulation

Beam/Frame CAD Modeling in SolidWorks

Beam Element in SolidWorks Simulation

Defining the Beam Element for the Simple Beam

Defining the Beam Element for a Beam Structure Made of either multi Cross-sections or multi Materials

Defining the Beam Element for a frame Structure

Assign the Materials to the Beam and Frame Structure in SolidWorks Simulation

Edit Joints of a Beam or Frame Structure in SolidWorks Simulation

Beam Member Direction in SolidWorks Simulation

Edit Beam Member Parameters in SolidWorks Simulation

Beam Joint Conditions

Rigid Condition at Beam Joint

Hinge Condition at a Beam Joint

Slide Condition at a Beam Joint

Manually Specifying a Condition at a Beam Joint

Beam Cross-section Properties

Apply Fixtures to the Joints of a beam of Frame Structure in SolidWorks Simulation

Apply External Loads to the Joints, Points or Members of a Beam or Frame Structure

Meshing of Beam or Frame Structures in SolidWorks Simulation

Post-Processing of a Beam or Frame Structure Analysis in SolidWorks Simulation

List Forces and Stresses Produced in each Beam Member

Generate the Beam Diagrams

Determine the Displacement, Rotation and Reaction Forces/Moments using the Displacement Plot

Tutorial 5.1

Tutorial 5.2

Tutorial 5.3

Exercises

**Chapter 6. 2D Simplified Elements and Thin Parts Analysis**

Plane Stress Element

Plane Strain Element

Axisymmetric Element

Pre-Processing of 2D Model of a Part in SolidWorks Simulation

Defining a 2D Simplified Study

Defining Fixtures for a 2D Simplified Study of a Part

Defining External Loads for a 2D Simplified Study of a Part

Meshing of 2D Simplified Model of a Part in SolidWorks Simulation

Post-Processing of 2D Simplified Model of a Part in SolidWorks Simulation

3D Shell Element in SolidWorks Simulation

Modeling the Thin Parts in SolidWorks Simulation

Defining the Shell Model for a Surfacebody Part using Surface Modeling Tools

Defining the Shell Model for a Solidbody Part using Solid Modeling Tools

Defining the Shell Model for a Sheet Metal Part

Pre-Processing of 3D Shell Models of Parts in SolidWorks Simulation

Pre-Processing of 3D Shell Models of Sheet Metal Parts

Pre-Processing of 3D Shell Models of Surface Geometry Parts

Thin versus Thick Shell Modeling in SolidWorks Simulation

Thick Shell Modeling Option for the Cylindrical Portion of the Pressure Vessel

Thin Shell Modeling Option for the Cylindrical Portion of the Pressure Vessel

Thick Shell Modeling Option for the Spherical Portion of the Pressure Vessel

Thin Shell Modeling Option for the Spherical Portion of the Pressure Vessel

Post-Processing of 3D Shell Models of Parts in SolidWorks Simulation

Shell Manager

Tutorial 6.1

Tutorial 6.2

Tutorial 6.3

Exercises

**Chapter 7. Assembly Analysis with Contact Sets**

Centrifugal Force

Bearing Load

Remote Loads/Restraints/mass

Remote Mass (Rigid Connection)

Remote Loads (Rigid Connection)

Remote Loads (Direct Transfer)

Remote Displacement (Rigid Connection)

Distributed Mass

Load Case Manager

Mixed Meshing

Contact Sets

Contact Set Level

Defining a Bonded Contact Set (Manually select contact sets)

Compatible versus Incompatible Mixed Meshing

Automating Bonding between Touching Entities

Contact Visualization Plot

Rigid Parts

Excluding Parts

Fix/Float Parts

Incremental Meshing

Tutorial 7.1

Exercises

**Chapter 8. Assembly Analysis with Connectors**

Edge Weld Connector Terminology

Local Weld Coordinate System (WJC)

Introduction to Weld Sizing Using the Elastic Vector Method

Example 8.1

Example 8.2

Example 8.3

Edge Weld Connector in SolidWorks Simulation

Edge Weld Connector Post-Processing in SolidWorks Simulation

Spot Weld Connector in SolidWorks Simulation

Tutorial 8.1

Bolt Connector Terminology in SolidWorks Simulation

Bolt Connector in SolidWorks Simulation

Pin/Bolt safety check in SolidWorks Simulation

Pin Connectors Terminology in SolidWorks Simulation

Bearing Connectors Terminology in SolidWorks Simulation

Effect of self-alignment option

Flexible versus Rigid Bearing connector

Spring Connectors Terminology in SolidWorks Simulation

Elastic Support Connectors Terminology in SolidWorks Simulation

Tutorial 8.2

Exercises

**Chapter 9. Frequency Analysis of Parts**

Mass-Spring-Damper System: Damped Free Vibration

Mass-Spring-Damper System: Damped Forced Vibration

Frequency Analysis using SolidWorks Simulation

Opening a New Frequency Analysis Study

Frequency Analysis Pre-Processing

Frequency Analysis Processing (Meshing and Solving)

Frequency Analysis Post-Processing

List the Natural Frequencies

Plot the Mode Shapes

Rigid Body Modes

List Mass Participation

Frequency analysis of assemblies

Tutorial 9.1

Tutorial 9.2

Exercises