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Why Do Nonlinear Finite Element Analysis?

In this book we aim to provide some background information about the principles of the finite element technique as applied to nonlinear problems. The benefits of using nonlinear finite element analysis are highlighted, and some general guidelines are given for efficient use of the technique. The term FE will be used throughout the booklet to mean finite element.

The book is aimed at decision-makers; those practicing engineers and managers who may influence the design process within their organization. The objective of the booklet is to demonstrate to the engineers, in a clear and practical manner, he reasons why their organizations should be using nonlinear FE analysis.

The decision to use any tool or process should be driven by commercial factors. A company should consider the use of any available tools that may reduce its development costs, reduce its lead times, enable it to develop products that are better than those produced by its competitors, or enable it to manufacture products using less material and less complex or costly processes.

In many cases the use of nonlinear finite element analysis can provide these kind of benefits. It is perhaps appropriate, therefore, that engineers should consider whether they can afford not to use nonlinear FE analysis.

There are, of course, some negative aspects to this issue: any prospective user of nonlinear finite elements should consider the additional costs of the software and the computer on which to run it, the costs associated with training staff, and the additional work required to generate the material and structural data that a good analysis demands. In this booklet we endeavour to provide a balanced view of the benefits and costs of using nonlinear FE analysis.

Let us return to the key question – why use nonlinear FE analysis?

All physical structures exhibit nonlinear behaviour to some extent. They may be made of rubber or plastic materials that do not have a constant modulus, they may be operating over a range of temperatures where the material behaviour at high temperature is very different th that at ambient, or they may be made up of components that contact each other. In such cases linear FE analysis is, as we will see, an approximation that makes the analysis of structures more tractable. However, the assumptions of linearity are often not adequate for real structures. If a nonlinear FE method is used, many of these limiting assumptions are no longer required; therefore, the analysis of a structure undergoing some form of nonlinear behaviour may be much more accurate if a nonlinear FE analysis is carried out.

It is important to note that both nonlinear FE analyses should provide the same answer for a linear problem. It is only when the problem contains some form of nonlinearity that the linear assumptions lead to a loss of accuracy.

The ability to predict accurately the response of a structure to a given loading allows engineers to improve their knowledge of the structure and to increase their confidence in their understanding of the structure’s behaviour. Ultimately, more accurate analysis enables engineers to improve their products. 

Contents

Preface

Introduction

What is Nonlinear Finite Element Analysis?

    • The Finite Element Method
    • Linear Finite Element Analysis
    • Nonlinear Finite Element Analysis
    • Material Nonlinearity
    • Boundary Nonlinearity
    • Geometric Nonlinearity
    • Solution Techniques

What are the Benefits?

    • Product Development
    • Safety Qualification
    • Manufacturing
    • Failure Analysis

When to Use Nonlinear Finite Element Analysis

    • Reduce Cost
    • Improve Safety & Reliability
    • Reduce Lead Time
    • Improve the Product

How to Use Nonlinear Finite Element Analysis

    • Use the Correct Data
    • Start Simply
    • Interpret Results Carefully
    • Investigate Sensitivity
    • Compare Results

Frequently Asked Questions


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About

A. M. Prior

First Published - January 1998

Softback, 28 Pages