COLLEGE HOUSE ENTERPRISES, LLC

Engineering Analyses and Finite

Element Methods

by Guangming Zhang

Department of Mechanical Engineering 

and the Institute for Systems Research

University of Maryland at College Park

This book presents an introduction to the fundamentals of finite element methods with computer applications.  Finite element methods are used by many engineers and scientist for solving boundary value problems that arise in product development.  Those engineering problems involve geometry, material properties, loading conditions and boundary conditions.  Seeking analytical based solutions is generally difficult if not impossible. With capabilities of computers expanding at an unthinkable pace, the importance of using massive computing power to perform finite element analyses must be emphasized.  The book represents an introductory text for undergraduate students in engineering. The book should also be useful to those engineers and scientists engaged in the engineering analyses.

            The book is divided into 10 chapters. The first chapter provides a fundamental coverage of finite element methods.  It stresses the mathematical and mechanical fundamentals, which support the development of finite element methods. Chapter 2 introduces the Pro/ENGINEER Wildfire design system and Pro/Mechanica, which is engineering simulation software designed to conduct finite element analyses.  Chapter 3 focused on modeling a variety of load conditions.  Chapter 4 describes modeling the boundary conditions of mechanical structures in general, illustrating the procedure of dealing with physical entities both at the component level and at the assembly level.  Chapter 5 presents a review of the stress condition needed to understand the mechanism of the engineering simulation software in the computing process.  Chapter 6 presents an important branch of finite element methods -- shell modeling through idealization.  In Chapter 7, we focus on applications including three case studies dealing with engineering vibration analyses and buckling analyses.  Chapter 8 introduces a the concept of design optimization.  The engineering simulation system of ALGOR is introduced in Chapter 9 with an emphasis on applying FEA to truss and beam structures.  In Chapter 10, the engineering simulation software ANSYS is introduced.  ANSYS is the most widely used simulation software to perform FEA both nationally and worldwide.

            The material assembled in this book is an outgrowth of a senior-level design course taught by the author at the University of Maryland at College Park from 2001 to 2004. Moreover, this first edition of book is written in a style adaptable for self-study and reference.  Suggestions for improvements are welcome and the author will deeply appreciate any suggestions made by the readers in this regard.

CHAPTER 1 INTRODUCTION TO FINITE ELEMENT METHODS

  1.1 Introduction 

       1.2 Finite Element Method in a One-Dimensional Space 

       1.3 Finite Element Method in a Two-Dimensional Space 

       1.4 Finite Element Method in a Three-Dimensional Space 

       1.5 Unit Systems Used in the FEA Software Systems

       1.6 References 

       1.7 Exercises 

CHAPTER 2 FEA USING PRO/Mechanica

  2.1 Introduction 

        2.2 Introduction to the Pro/ENGINEER Design System 

                2.2.1  Creation of a 3D Solid Model of a Column Structure 

                2.2.2  Procedure of Performing FEA Using Pro/Mechanica 

        2.3 Beam Structure Subjected to a Uniformly Distributed Load 

        2.4 References 

        2.5 Exercises 

 CHAPTER 3 MODELING OF LOAD CONDITIONS

 3.1 Introduction 

  3.2 Modeling a Uniformly Distributed Load with a Surface Region 

  3.3 Modeling of a Non-uniformly Distributed Load 

  3.4  Modeling of a Bearing Load Condition 

  3.5 Modeling of a Pressure Load Condition 

  3.6 Modeling of a Point Load Condition and Gravity 

  3.7 Consideration of the Gravity Force in Performing FEA 

  3.8 References 

  3.9 Exercises 

CHAPTER 4 MODELING OF CONSTRAINTS AND FEA WITH ASSEMBLIES

4.1 Introduction 

4.2 Modeling of Constraint Conditions 

4.3 Modeling of Constraints Using Surface Regions 

4.4 FEA with an Assembly of Gear and Shaft 

4.5 Modeling of a Load Condition due to Temperature Variation 

4.6 Use of Symmetry in Performing FEA 

4.7 References 

4.8 Exercises 

 CHAPTER 5 CONCEPTS OF PRINCIPAL STRESSES AND VON MISES STRESS

5.1 Introduction

5.2 Evaluation of the Stress Condition at a Given Location 

5.3 References 

5.4 Exercises 

 CHAPTER 6 IDEALIZATION: MODELING WITH SHELLS

6.1 Introduction

6.2 Concept of Surface Pairs

6.3 Shell Modeling Using Auto Detect

6.4 Case Study 1: Shell Modeling with Bath Tub

6.5 Case Study 2: Shell Modeling for a Welding Structure

6.6 References 

6.7 Exercises

 CHAPTER 7 APPLICATIONS ON MODAL AND BUCKLING ANALYSES

7.1 Introduction

 7.2 Applications on Modal Analyses

 7.3 Applications on Designing a Music Tuning Fork 

 7.4 Applications on Buckling Analyses

 7.5 Buckling Analysis of a Thin Disk

 7.6 References 

 7.7 Exercises 

 CHAPTER 8 EVALUATION OF ENGINEERING DESIGN AND DESIGN OPTIMIZATION

8.1 Introduction

 8.2 Fundamentals of a Decision-Making Process

 8.3 Case Study: Redesign a Bracket Component

 8.4 References 

 8.5 Exercises 

 CHAPTER 9 IDEALIZATION: MODELING WITH TRUSS AND BEAM STRUCTURES AND ALGOR

9.1 Introduction

 9.2 Application on a Simple Truss Structure

 9.3 Application on a Simple Supported Beam Structure

 9.4 Finite Element Analysis of Truss Structure Using ALGOR V14

 9.5 FEA of a Second Truss Structure Using ALGOR V14

 9.6 FEA of a Beam Structure Using ALGOR V16

 9.7 References 

 9.8 Exercises 

 CHAPTER 10 FEA USING ANSYS

10.1   Introduction

 10.2   FEA with a Shell Model

 10.3   FEA with a 3D Solid Model

 10.4   FEA with an Assembly Structure

 10.5   Control of the Number of Elements in Modeling

 10.6   References 

 10.7   Exercises