Essentials of the Finite Element Method

For Mechanical and Structural Engineers

Dimitrios G Pavlou, Dimitrios G. Pavlou

• Publisher: Academic Press
• Year: 2015
• Print ISBN: 9780128023860
• eBook ISBN: 9780128026069
• Topic: Technology & Engineering
• Subtopic: Civil Engineering
• Index: Technology & Engineering

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

Chapter 1

An Overview of the Finite Element Method

Abstract

In this chapter, a brief overview of the finite element method answers questions such as: What are finite elements? Why is the finite element method (FEM) important for mechanical and structural design? What are the advantages and disadvantages of FEM? What is a structural matrix? What are the main steps for finite element modeling? On which physical principles the FEM is based? Apart from the above overview, an introduction to the computer-aided learning program, CALFEM, as well as a brief description of the ANSYS working environment is provided. However, the subsequent chapters provide a better understanding of these tools.

Keywords

Finite elements

FEM

Structural matrix

CALFEM

ANSYS

FE modeling

FE overview

1.1 What Are Finite Elements?

Since the differential equations describing the displacement field of a structure are difficult (or impossible) to solve by analytical methods, the domain of the structural problem can be divided into a large number of small subdomains, called finite elements (FE). The displacement field of each element is approximated by polynomials, which are interpolated with respect to prescribed points (nodes) located on the boundary (or within) the element. The polynomials are referred to as interpolation functions, where variational or weighted residual methods are applied to determine the unknown nodal values.

1.2 Why Finite Element Method Is Very Popular?

The concept of the finite element method (FEM) was described in 1956, when Turner et al. used pin-jointed bars and triangular plates to calculate aircraft structures. However, as the method is based on the solution of systems of algebraic equations with large number of unknowns, in past few decades, FEM has become very popular due to the development of high-speed digital computers.

After 1980, new commercial software packages were developed, boosting the application of FEM to structural engineering, heat transfer, fluid mechanics, aerodynamics, and electrostatics.

Among the pioneers who founded and developed FEM are Przemieniecki, Zienkiewicz and Cheung, Gallag...

Table of contents

• Cover image
• Title page
• Table of Contents
• Copyright
• Dedication
• Preface
• Acknowledgments
• Chapter 1: An Overview of the Finite Element Method
• Chapter 2: Mathematical Background
• Chapter 3: Linear Spring Elements
• Chapter 4: Bar Elements and Hydraulic Networks
• Chapter 5: Trusses
• Chapter 6: Beams
• Chapter 7: Frames
• Chapter 8: The Principle of Minimum Potential Energy for One-Dimensional Elements
• Chapter 9: From “Isotropic” to “Orthotropic” Plane Elements: Elasticity Equations for Two-Dimensional Solids
• Chapter 10: The Principle of Minimum Potential Energy for Two-Dimensional and Three-Dimensional Elements
• Chapter 11: Structural Dynamics
• Chapter 12: Heat Transfer
• Index