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- Introduction to Non-Linear Finite Element Analysis

E. Hinton*Department of Civil Engineering, Swansea University, SA2 8PP Wales, UK.*

https://doi.org/10.59972/3p9d3dh6

R0018, January 1992

ISBN (Hardcopy): 978-1-874376-00-2

**This book was commissioned by the Nonlinear Working Group of NAFEMS and is the work of several authors with varying backgrounds and therefore reflects a variety of views. It is intended for readers with a background in linear finite element (FE) analysis who wish to gain some insight into nonlinear FE stress analysis. Before attempting this text, prospective readers should have first studied an introductory text on linear finite element analysis such as the NAFEMS ****Finite Element Primer****. Although it is recognised that many different types of nonlinear problems may be solved using the FE method, our attention is here focused on nonlinear FE stress analysis and in particular static or quasi-static problems (i.e. situations in which inertia forces may be neglected).**

This book is not intended to be a deeply theoretical text. Consequently, some of the explanations rely heavily on simple presentations of complex ideas. Rigour and comprehensiveness have been sacrificed for the sake of clarity and ease of explanation. Boxes are used throughout the text and usually include algorithmic details which the more inquisitive reader may require - this part of the text may be skipped by the more casual reader.

Nonlinear FE stress analysis has its own particular language or jargon. Such jargon is explained as it is introduced in this text, but a glossary of terms used is also provided at the end of the book as a convenient, easily accessible, *aide-mémoire*. An attempt has been made to standardise on notation - this inevitably differs to some degre from the notation used in the NAFEMS Finite Element Primer as our present task is a little more arduous. Various aspects concerning the notation used in this book are discussed in Chapter 1 and a local notation list is placed at the end of each chapter.

The NAFEMS Nonlinear Working Group has over the years commissioned a number of benchmark tests for nonlinear FE stress analysis. This text will make use of some of these tests as they have been shown to be an excellent means of training novices.

The five authors involved in writing the text included three academics from the University College of Swansea: Ernest Hinton (EH), Richard Wood (RDW) and Nenad Bicanic (NB), and from industry Peter White (PSW) of GEC Alsthom and Trevor Hellen (TH) of Nuclear Electric plc. EH acted as editor and Mike Crisfield of Imperial College reviewed the text. It is also acknowledged that all of the members of the Nonlinear Working Group of NAFEMS provided many valuable comments and contributions: Nick Otter (GEC Alsthom - former chairman), Nigel Knowles (Atkins Engineering Sciences - current chairman), Paul Lyons (FEA), Paul Newton (MacNeal-Schwendler), Rick Leggatt (Welding Institute) and Dave Phillips (Glasgow University).

| pp. 1-40 |

| pp. 41-102 |

| pp. 103-163 |

| pp. 164-236 |

| pp. 237-282 |

| pp. 283-313 |

| pp. 314-345 |

**Introduction to Nonlinear Stress Analysis**

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**Further Complexities**

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Hellen, T.K. and Blackburn, W.S., 'Non-linear fracture mechanics and finite elements', *Eng. Comput.*, **4**, 2-14, 1987.

Li, F.Z., Shih, C.F. and Needleman, A., 'A comparison of methods for calculating energy release rates', *Eng. Fract. Mech.*, **21**, 405-421, 1985.

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Hellen, T.K., 'Virtual crack extension methods for non-linear materials', *Int. J. Num. Meth. Engng.*, **28**, 929-942, 1989.

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Remzi, E.M. and Blackburn, W.S., 'Automatic crack propagation studies in T-junctions and cross bars', *Eng. Comput.*, to be published.

**Practical Use**

Hutchinson, J.W., 'Singular behaviour at end of tensile crack in hardening material', *J. Mech. Phys. Solids.*, **16**, 13-31, 1968.

Rice, J.R. and Rosengren, G.F., 'Plane strain deformation near crack tip in power-law hardening material', *J. Mech. Phys. Solids*, **16**, 1-12, 1968.

Crisfield, M.A., Hunt, G.W., and Duxbury, P.G., 'Benchmark tests for geometric nonlinearity', NAFEMS, Ref. SPGNL, Oct 1987.

Holsgrove, S. and Lyons, P., 'Benchmark tests for 2D beams and axisymmetric shells with geometric nonlinearity', NAFEMS, Ref. FEBNLGBAS(S), Mar 1989.

Owen, D.J.R., Nayak, G.C., Kfouri, A.P. and Griffiths, J.R., 'Stresses in a partly yielded notched bar', *Int. J. Num. Meth. Engng.*, **6**, 63-73, 1973.

Owen, D.J.R. and Goncalves, O.J.A., 'Substructuring techniques in material nonlinear analysis', *Comp. and Struct.*, **15**, 205-213, 1982.

Hellen, T.K., 'Use of substructuring in nonlinear analysis', *Eng. Comput.*, **1**, 343-350, 1984.

Lee, S.L., Manuel, F.S. and Rossow, E.C., 'Large deflection and stability', *J. Eng. Mech. Div.*, ASCE, **94**, 521-547, 1968.

E. Hinton, Introduction to Non-Linear Finite Element Analysis, R0018, NAFEMS, 2000, https://doi.org/10.59972/3p9d3dh6

Reference | R0018 |
---|---|

Author | Hinton. E |

Language | English |

Audience | Analyst |

Type | Publication |

Date | 1st January 1992 |

Region | Global |

Order Ref | R0018 Book |
---|---|

Member Price | £20.00 | $25.36 | €23.36 |

Non-member Price | £90.00 | $114.12 | €105.12 |

Order Ref | R0018 Download |
---|---|

Member Price | £20.00 | $25.36 | €23.36 |

Non-member Price | £90.00 | $114.12 | €105.12 |

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