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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 primarily 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 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 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 introduces the Frequency Analysis tools provided in SolidWorks Simulation Professional to identify the natural frequencies and related mode shapes of parts. 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

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 Principal Stresses

Stress and Strain Relationship in Linear-Elastic-Isotropic Materials

2-Dimensional Principal Stresses

Example1

Failure Theories

Matrix Algebra

Using Excel to Perform Matrix Manipulation

Example 2

Example 3

Example 4

Exercises

Chapter 2. Fundamentals of SolidWorks Simulation

Types of Analysis Available in SolidWorks Simulation Premium

SolidWorks Simulation Bundles

Basic Steps in FEA

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

Post-processing in SolidWorks Simulation

Options Available in a typical Stress Plot

Define Factor of Safety Plot

Define Fatigue Check Plot

Generating FEA Reports

Tutorial

Exercise

Chapter 3. Solid Element, Convergence Test and Adaptive Meshing

3-Dimensional Tetrahedral Solid Element

Meshing with SolidWorks Simulation

Convergence Check

Mesh Control

Standard Mesh with Automatic transition Selected

Curvature based mesh

Stress Singularity at Sharp Corners

Tutorial 3.1

Tutorial 3.2

Tutorial 3.3

Exercises

Chapter 4. Direct Stiffness Method and Truss Analysis

Direct Stiffness Method for 1-Dimensional Element

Example 4.1

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

Tutorial 4.1

Direct Stiffness Method for 2D Truss Analysis

Example 4.2

Pre-processing a True Structure Analysis in SolidWorks Simulation

Meshing of a Truss Structure in SolidWorks Simulation

Post-processing of a Truss Structure Analysis in SolidWorks Simulation

Tutorial 4.2

Direct Stiffness Method for 3D Truss Analysis

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

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

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 in SolidWorks Simulation

Meshing of Beam or Frame Structures in SolidWorks Simulation

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

Tutorial 5.1

Tutorial 5.2

Tutorial 5.3

Tutorial 5.4

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

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

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

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

Tutorial 6.1

Tutorial 6.2

Tutorial 6.3

Exercises

Chapter 7. 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

Tutorial 7.1

Tutorial 7.2

Exercises