Many books have been written about the finite element method; little however has been written about procedures that assist a practicing engineer in undertaking an analysis in such a way that errors and uncertainties can be controlled. In A Practical Guide to Reliable Finite Element Modelling, Morris addresses this important area. His book begins by introducing the reader to finite element analysis (FEA), covering the fundamental principles of the method, whilst also outlining the potential problems involved. He then establishes consistent methods for carrying out analyses and obtaining accurate and reliable results, concluding with a new method for undertaking error control led analyses which is illustrated by means of two case studies.
The book addresses a number of topics that:
• Systematically cover an introduction to FEA, how computers build linear-static and linear-dynamic finite element models, the identification of error sources, error control methods and error-controlled analyses.
• Enable the reader to support the design of complex structures with reliable, repeatable analyses using the finite element method.
• Provide a basis for establishing good practice that could underpin a legal defence in the event of a claim for negligence.
A Practical Guide to Reliable Finite Element Modelling will appeal to practising engineers engaged in conducting regular finite element analyses, particularly those new to the field. It will also be a resource for postgraduate students and researchers addressing problems associated with errors in the finite element method.
This book is supported by an author maintained website at http://www.femec.co.uk
Author(s): Dr. Alan Morris
Publisher: Wiley
Year: 2008
Language: English
Pages: 386
Tags: Математика;Вычислительная математика;Метод конечных элементов;
A Practical Guide to Reliable Finite Element Modelling......Page 1
Contents......Page 9
Preface......Page 15
1.1 AIM OF THE BOOK......Page 19
1.2 FINITE ELEMENT TYPES – A BRIEF OVERVIEW......Page 21
1.3 FINITE ELEMENT ANALYSIS AND FINITE ELEMENT REPRESENTATIONS......Page 24
1.5 CONSISTENCY, LOGIC AND ERROR CONTROL......Page 26
1.6.1 Chapter 2 Overview of Static Finite Element Analysis......Page 29
1.6.2 Chapter 3 Overview of Dynamic Analysis......Page 30
1.6.3 Chapter 4 What’s Energy Got to Do with It?......Page 31
1.6.5 Chapter 6 Discretisation: Elements and Meshes or Some Ways to Avoid Generated Error......Page 32
1.6.7 Chapter 8 Error Control......Page 33
1.6.8 Chapter 9 Error-Controlled Analyses......Page 34
REFERENCES......Page 35
2.1 INTRODUCTION......Page 37
2.2.1 Element Matrices......Page 38
2.2.2 Assembled Global Stiffness Matrix for Static Analyses......Page 39
2.2.3 Global Coordinates......Page 44
2.2.5 The Analysis Loop......Page 47
2.3.1 Symmetry......Page 51
2.3.2 Condensation and Superelements......Page 58
2.3.3 Sub-structures......Page 64
REFERENCES......Page 67
3.2 ELEMENT MASS MATRIX......Page 69
3.2.1 Free Undamped Vibrations......Page 71
3.3.1 Sturm Property Check......Page 77
3.3.2 Rayleigh Quotient......Page 79
3.4.1 Modal Analysis......Page 80
3.4.2 Direct Integration......Page 83
3.5.1 Modal Analysis with Damping......Page 84
3.5.2 Modal Damping Ratio......Page 86
3.5.3 Direct Integration......Page 87
3.6 REDUCING THE PROBLEM SIZE......Page 88
3.6.1 Symmetry......Page 89
3.6.2 Reducing the Number of Variables......Page 90
3.6.3 Sub-structure Analysis (Component Mode Synthesis)......Page 94
REFERENCES......Page 96
4.1 INTRODUCTION......Page 97
4.2 STRAIN ENERGY......Page 99
4.3 POTENTIAL ENERGY......Page 100
4.5 GENERAL CASE......Page 101
4.6 MINIMUM POTENTIAL ENERGY......Page 102
4.7 THE PRINCIPLE OF MINIMUM POTENTIAL ENERGY APPLIED TO A SIMPLE FINITE ELEMENT PROBLEM......Page 104
4.8 FINITE ELEMENT FORMULATION......Page 106
4.9 DIRECT APPLICATION TO AN AXIAL BAR ELEMENT......Page 108
4.10 CONVERGENCE IN ENERGY AND CONVERGENCE IN STRESS......Page 110
4.10.1 Single Bar Element Model......Page 112
4.10.2 2-Bar Element Model......Page 114
4.10.3 4-Bar Element Model......Page 116
4.10.4 8-Bar Element Model......Page 119
4.10.5 16-Bar Element Model......Page 120
4.11.1 Potential Energy Convergence......Page 121
4.11.2 Stress Improvement......Page 122
4.12 KINETIC ENERGY......Page 124
REFERENCES......Page 129
5.1 INTRODUCTION......Page 131
5.2 THE FINITE ELEMENT PROCESS......Page 132
5.3 ERROR AND UNCERTAINTY......Page 135
5.4.1 Analysis Novelty......Page 138
5.4.2 Degree of Complexity......Page 141
5.4.3 Experience......Page 143
5.5 ROLE OF TESTING......Page 146
5.6.1 Qualification Process......Page 147
5.6.2 Acceptable Magnitude of Error or Uncertainty......Page 150
5.7 ANALYSIS VALIDATION PLAN (AVP)......Page 153
5.8 APPLIED COMMON SENSE......Page 156
5.9 THE PROCESS......Page 158
REFERENCES......Page 159
6.1 INTRODUCTION......Page 161
6.2 ELEMENT DELIVERY......Page 162
6.2.1 Two-Dimensional Elements......Page 163
6.2.2 Three-Dimensional Elements......Page 166
6.2.4 Optimal Stress Points and Making the Most of Them......Page 169
6.3.1 Mesh Grading......Page 173
6.3.2 Element Distortions......Page 176
6.3.3 Group 3 Distortions (Quadratic Distortions)......Page 179
6.3.5 Distortions of Other Element Types......Page 180
6.3.6 General Principles with Respect to Element Distortions......Page 181
6.4.1 The Stress Ladder......Page 182
6.4.3 Automatically Moving up the Accuracy Ladder......Page 183
REFERENCES......Page 192
7.1 DESIGN REDUCTION AND IDEALISATION ERRORS......Page 193
7.2 ANALYSIS FEATURES......Page 196
7.3.1 The Domain of Analysis......Page 198
7.3.2 Domain Reduction......Page 201
7.4 LEVELS OF ABSTRACTION......Page 202
7.5 BOUNDARY CONDITIONS......Page 210
7.6 MATERIAL PROPERTIES......Page 216
7.7.1 Loads......Page 218
REFERENCES......Page 219
8.1 INTRODUCTION......Page 221
8.2.1 Approach......Page 222
8.2.2 Techniques......Page 225
8.3 ACCUMULATION OF ERRORS AND UNCERTAINTIES......Page 259
8.4 THE ROLE OF TESTING......Page 260
8.4.1 Analyst-Requested Tests......Page 262
8.4.2 Validation Test......Page 263
REFERENCES......Page 265
9.1 INTRODUCTION......Page 267
9.2.1 What Does It Do?......Page 269
9.2.2 How Do We Know It Does It?......Page 270
9.2.3 Is Size Important?......Page 272
9.3 QUALITY REPORT......Page 274
9.4.1 Introduction......Page 277
9.4.2 FEMEC......Page 278
9.4.3 FEMEC Implementation Process......Page 279
10.1 INTRODUCTION......Page 321
10.2.1 The Design Requirement......Page 322
10.2.2 Application of FEMEC via the Quality Report......Page 324
10.3.1 Modified Design and Qualification Parameters......Page 363
10.3.2 FEMEC Approach......Page 364
REFERENCES......Page 369
Index......Page 371
