Essentials of the finite element method : for mechanical and structural engineers

✍ Scribed by Pavlou, Dimitrios G

• Publisher: Academic Press
• Year: 2015
• Tongue: English
• Leaves: 501
• Edition: 1
• Category: Library

✦ Synopsis

Fundamental coverage, analytic mathematics, and up-to-date software applications are hard to find in a single text on the finite element method (FEM). Dimitrios Pavlou’s Essentials of the Finite Element Method: For Structural and Mechanical Engineers makes the search easier by providing a comprehensive but concise text for those new to FEM, or just in need of a refresher on the essentials.

Essentials of the Finite Element Method explains the basics of FEM, then relates these basics to a number of practical engineering applications. Specific topics covered include linear spring elements, bar elements, trusses, beams and frames, heat transfer, and structural dynamics. Throughout the text, readers are shown step-by-step detailed analyses for finite element equations development. The text also demonstrates how FEM is programmed, with examples in MATLAB, CALFEM, and ANSYS allowing readers to learn how to develop their own computer code.

Suitable for everyone from first-time BSc/MSc students to practicing mechanical/structural engineers, Essentials of the Finite Element Method presents a complete reference text for the modern engineer.

• Provides complete and unified coverage of the fundamentals of finite element analysis
• Covers stiffness matrices for widely used elements in mechanical and civil engineering practice
• Offers detailed and integrated solutions of engineering examples and computer algorithms in ANSYS, CALFEM, and MATLAB

✦ Table of Contents

Content: Front Cover
Essentials of the Finite Element Method: For Mechanical and Structural Engineers
Copyright
Dedication
Contents
Preface
Acknowledgments
Chapter 1: An Overview of the Finite Element Method
1.1. What Are Finite Elements?
1.2. Why Finite Element Method Is Very Popular?
1.3. Main Advantages of Finite Element Method
1.4. Main Disadvantages of Finite Element Method
1.5. What Is Structural Matrix?
1.5.1. Stiffness Matrix
1.5.2. Transfer Matrix
1.6. What Are the Steps to be Followed for Finite Element Method Analysis of Structure? 1.6.1. Step 1. Discretize or Model the Structure1.6.2. Step 2. Define the Element Properties
1.6.3. Step 3. Assemble the Element Structural Matrices
1.6.4. Step 4. Apply the Loads
1.6.5. Step 5. Define Boundary Conditions
1.6.6. Step 6. Solve the System of Linear Algebraic Equations
1.6.7. Step 7. Calculate Stresses
1.7. What About the Available Software Packages?
1.8. Physical Principles in the Finite Element Method
1.9. From the Element Equation to the Structure Equation
1.10. Computer-Aided Learning of the Finite Element Method
1.10.1. Introduction to CALFEM General purpose commandsMatrix functions
Material functions
Element functions
1.10.2. Spring elements
Input variable
Stiffness matrix
Section force
1.10.3. Bar Elements for Two-Dimensional Analysis
Input variables
Stiffness matrix
Section force
1.10.4. Bar Elements for Three-Dimensional Analysis
Input variables
Stiffness matrix
Section force
1.10.5. Beam Elements for Two-Dimensional Analysis
Input variables
Stiffness matrix
Section force
1.10.6. Beam Elements for Three-Dimensional Analysis
Input variables
Stiffness matrix
Section force
1.10.7. System Functions 1.10.8. Statement Functions1.10.9. Graphic Functions
1.10.10. Working Environment in ANSYS
References
Chapter 2: Mathematical Background
2.1. Vectors
2.1.1. Definition of Vector
2.1.2. Scalar Product
2.1.3. Vector Product
2.1.4. Rotation of Coordinate System
2.1.5. The Vector Differential Operator (Gradient)
2.1.6. Greens Theorem
2.2. Coordinate Systems
2.2.1. Rectangular (or Cartesian) Coordinate System
2.2.2. Cylindrical Coordinate System
2.2.3. Spherical Coordinate System
2.2.4. Component Transformation