Applied Engineering Analysis

Chapter 11Introduction to Finite-element Analysis

Chapter Learning Objectives

• Learn the principle of finite-element method for engineering analyses.
• Learn the concept of discretization of continua for approximation solutions.
• Become familiar with the steps in general finite-element analysis.
• Learn to derive interpolation functions for simplex elements.
• Learn the variational principle in deriving element equations.
• Learn to derive element equations using the Rayleigh–Ritz method and the Galerkin method.
• Understand the input/output in general finite-element analysis.
• Learn to assemble element equations to the overall stiffness equations.
• Learn to solve for primary unknown quantities from overall stiffness equations.
• Learn to relate the primary unknown quantities obtained from the finite-element method to other required secondary unknown quantities.
• Learn the use of general-purpose finite-element analysis codes adopted by industry in solving complex real-world problems.

11.1 Introduction

In Chapter 1 we learned the four stages involved in general engineering analyses, with Stage 2 being idealizing actual physical situations for the subsequent mathematical analysis in Stage 3, and Stage 4 being interpretation of analytical results. Idealization of actual physical problems is necessary in most cases of engineering analysis so that analytical tools that engineers have acquired and are available can be used. Idealization of geometry and loading and boundary conditions is frequently ...