P. Pedersen - Elasticity-Anisotropy-Laminates

P. Pedersen - Elasticity-Anisotropy-Laminates - Pa!li...

Info iconThis preview shows pages 1–7. Sign up to view the full content.

View Full Document Right Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: Pa!li Pedersen E L A S T I C I T Y - A N I S O T R O P Y -L A M I N A T E S "i h ma ri# form!la ion, fini e elemen s and an inde# o ma rices x 3 + z x 2 x 1 s 11 å 11 s 12 å 12 s 21 å 21 s 22 å 22 ć g SOLID MECHANICS TECHNICAL UNIVERSITY OF DENMARK II Pauli Pedersen: 1. Contents and Introduction E L A S T I C I T Y - A N I S O T R O P Y - L A M I N A T E S with matrix formulation, finite elements and an index to matrices Copyright 1998 by Pauli Pedersen, but feel free to copy for personal use. ISBN 87-90416-01-05 III Pauli Pedersen: 1. Contents and Introduction FOREWORD This book originates from notes for a course in elasticity (Pedersen (1992)) and a translation from Danish is needed because this course is now taught in English. Extensions from earlier notes on laminates (Pedersen (1988)) and from a small book on finite elements (Pedersen (1984)) are naturally included. The influence from recent research on material optimization (Pedersen (1995a)) will also be seen and finally the notation is in accordance with the 2 Ǹ-contracted notation, advoĆ cated in Pedersen (1995b). It is my hope that the reader will find the efforts worth-while, and critics, advices and information about posĆ sible errors will be most welcome (email: pauli@fam.dtu.dk). Many students and colleagues have influenced the book and without mentioning specific names, I am most thankful for their guidance. I thank Robert Zetterlund for producing many of the figures and a lot of additional help; I thank Bente Brask Andersen and Betina ChristianĆ sen for the text-editing with all its revisions. Without their valuable help the book would not have been finished. In gratitude of a warm family life, I dedicate this book to my wife Hanne and my children Niels, Mads and Sine. January 1997 Pauli Pedersen IV Pauli Pedersen: 1. Contents and Introduction This second version is almost unchanged, but the known errors have been corrected. Furthermore, the book is now available at the internet: http://www.fam.dtu.dk/html/pp.html November 1998 Pauli Pedersen V Pauli Pedersen: 1. Contents and Introduction CONTENTS page Foreword III 1. Introduction 1 2. Geometry - Kinematics 9 2.1 Displacement 9 2.2 Displacement field 10 2.3 Displacement gradients 10 2.4 Stretches and strains in 1-D 11 2.5 Strains from displacement gradients 15 2.6 2-D Strain description 17 2.7 3-D Strain transformation 20 2.8 Dilatation and distortion, deviatoric strains 26 2.9 Compatibility of a strain field 28 2.10 Examples of strain calculations 29 VI Pauli Pedersen: 1. Contents and Introduction 3. Statics - Equilibrium 35 3.1 Force 35 3.2 Moment 37 3.3 Stress concept 38 3.4 Equilibrium 39 3.5 Descriptions of stress state 43 3.6 Hydrostatic stress and deviatoric stress 45 3.7 A classic example 46 4. Physics - Constitutive Models 53 4.1 Material parameters and modelling 53 4.2 Rotational transformations 56 4.3 Classification of 2-D stiffness for anisotropic elasticity 61 4.4 From 3-D to 2-D constitutive matrix 67 4.5 4....
View Full Document

Page1 / 332

P. Pedersen - Elasticity-Anisotropy-Laminates - Pa!li...

This preview shows document pages 1 - 7. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online