Table Of ContentInverse and Crack Identification Problems in Engineering Mechanics
Applied Optimization
Volume 46
Series Editors:
Panos M. Pardalos
University of Florida, U.S.A.
Donald Hearn
University ofF lorida, U.S.A.
The titles published in this series are listed at the end of this volume.
Inverse and Crack
Identification Problems in
Engineering Mechanics
by
Georgios E. Stavroulakis
Institute ofA pplied Mathematics,
Department of Civil Engineering,
Technical University Caro/o Wilhelmina,
Braunschweig, Germany
Springer-Science+Business Media, B.V.
A C.I.P. Catalogue record for this book is available from the Library of Congress.
ISBN 978-1-4613-4888-7 ISBN 978-1-4615-0019-3 (eBook)
DOI 10.1007/978-1-4615-0019-3
Printed on acid-free paper
AII Rights Reserved
© 2001 Springer Science+Business Media Dordrecht
Originally pub1ished by K1uwer Academic Pub1ishers in 2001
No part ofthe material protected by this copyright notice may be reproduced or
utilized in any form or by any means, electronic or mechanical,
including photocopying, recording or by any information storage and
retrieval system, without written permission from the copyright owner
This book is dedicated
to my parents
Contents
Preface xi
Part I Introduction. Problem Description
1. DIRECT AND INVERSE PROBLEMS 3
1.1 Introduction 3
1.2 Direct nonsmooth mechanics problems 3
1.3 Inverse and identification problems 4
I .4 Recent results and future work 5
References
Part II Theoretical and Computational Tools
2. COMPUTATIONAL MECHANICS I I
2.1 Elastostatics I I
2.1.1 Small displacement smooth (classical) elastostatics. 12
2.1.2 Unilateral contact problems. 15
2.1.2. I The unilateral contact conditions 19
2. 1.3 Friction problems with convex energy potential 2 I
2. 1.3. I Combined frictional contact problem 23
2.1.4 BEM formulation and implementation 24
2.1.4.1 BEM formulation of unilateral problems 24
2.1.4.2 LCP-BEM static unilateral-frictional contact
problems 26
2.1.4.3 Multi-region BEM formulation for inequality
problems 27
2. 1.4.4 Unified LCPformulation of combined unilateral
frictional contact problems 29
2.2 Solution algorithms 32
2.2. I Smooth and nonsmooth optimization approach 32
2.2.2 QPP and LCP solution schemes 34
2.2.3 Nonlinear equations for complementerity problems 34
2.2.3. I Nonlinear equation reformulation 36
Vll
viii INVERSE AND CRACK IDENTIFICATION
2.2.3.2 Examples of NCP functions 36
2.2.3.3 Merit functions 37
2.2.3.4 Solution technique 37
2.2.3.5 Formulation of nonlinear equations with FEM
andBEM 38
2.2.3.6 NCP functions proposed in the engineering
literature 40
2.3 Elastodynamics 41
2.3.1 Steady state, harmonic problems 41
2.3.2 Transient elastodynamics 43
2.3.2.1 LCP-BEM dynamic unilateral-frictional contact
problems 45
References
3. COMPUTATIONAL AND STRUCTURAL OPTIMIZATION 55
3.1 Optimization and optimality conditions 55
3.1.1 Smooth, inequality constrained, convex problems 58
3.1.1.1 Lagrangians, saddle points, duality 59
3.1.1.2 Concise form of optimality conditions 61
3.1.2 Convex, nonsmooth optimization 62
3.1.2.1 Unconstrained 62
3.1.2.2 Constrained 62
3.1.3 Convex optimization algorithms 63
3.1.3.1 Smooth Unconstrained Problems 63
3.1.3.2 Constrained Problems 64
3.1.3.3 Nonsmooth Problems 67
3.2 Optimization under equilibrium constraints (MPEC) 68
3.2.1 Formulation 69
3.2.2 Examples of structural optimization 71
3.2.2.1 Optimal design for structures 71
3.2.2.2 Optimal design for unilateral structures 71
3.2.2.3 Optimal prestress of unilateral Structures 72
3.2.2.4 Geometry design, inverse or identification
problem 73
3.2.2.5 Nonsmoothness and nonconvexity in MPEC 74
3.2.3 Solution methods 76
3.2.3.1 Error minimization with regularization 76
3.2.3.2 Error minimization -regularization -nonlinear
equation approach 77
3.2.3.3 Error minimization -penalty formulation 77
3.2.3.4 Error minimization -regularization -nonlinear
equation approach -penalty formulation 78
3.2.3.5 Further numerical approaches 78
References
4. SELECTED SOFT COMPUTING TOOLS 85
4.1 Soft-computing versus classical computing 85
4.2 Neural networks 86
4.2.1 Backpropagation neural network model 86
Contents ix
4.2.2 Neural network mappings, motivation and application
on inverse problems 89
4.3 Genetic algorithms 92
4.4 Fuzzy and neuro-fuzzy inference 95
4.5 Classical and extended Kalman filter and identification 96
4.5.l Review 96
4.5.2 Description 97
References
Part III Applications to Inverse Problems
5. STATIC PROBLEMS 107
5.1 Introduction and literature survey 107
. 5.2 Output error formulation of the inverse problem 110
5.2.l Local optimization approach 112
5.2.2 Neural network solution method 112
5.3 Numerical examples of direct problems 114
5.3.1 Static unilateral crack analysis 118
5.4 Numerical examples of inverse problems 124
5.4.1 Flaw identification 124
5.4.2 Bilateral and unilateral crack identification through error
optimization 133
5.4.3 Classical and unilateral neural crack identification 135
5.4.4 Filter-driven iterative crack identification 147
References
6. STEADY-STATE DYNAMICS 157
6.1 Introduction and literature survey 157
6.2 Output error formulation of the inverse problem 159
6.3 Neural network solution of the Inverse Problem 160
6.4 Numerical examples 161
6.4.1 Flaw identification 161
6.4.2 Crack identification 168
6.4.2.1 Direct problem 168
6.4.2.2 Inverse problem 171
References
7. TRANSIENT DYNAMICS 187
7.1 Introduction and literature survey 187
7.2 Numerical examples of direct problems 189
7.3 Numerical examples of inverse problems 202
7.3.l Classical and unilateral impact-echo 202
7.3.1.1 Outline of the method 202
7.3.1.2 Numerical comparison 203
7.3.2 Impact-echo and neural identification 204
References
Preface
The present book summarises the research work of the author at the In
stitute of Applied Mechanics of the Technical University Carolo Wilhelmina
in Braunschweig during the last four years. The book constitutes the written
Thesis which has been submitted to partially fulfill the requirements for the
Habilitation degree at the same University.
The author would like to express his graditude to Prof. Dr.rer.nat. Heinz
Antes, Technische UniversiHit Carolo Wilhelmina zu Braunschweig, for his
generous support throughout this work and for engouraging the application for
the Habilitation degree.
Thanks are also expressed to Prof. Dr.-Ing. Dietmar Gross, from the Tech
nische Universitat Darmstadt, and to Prof. Dr.-Ing. Josef Ballmann, from
the Rheinisch-WestfaIische Technische Hochschule Aachen for accepting the
responsibility to act as referees during the Habilitation procedure.
The author can not forget that this project has been proposed and supported
by his teacher, the late Professor Panagiotis D. Panagiotopoulos, Aristotle Uni
versity, Thessaloniki and RWTH Aachen.
Finally, the financial support given by the State of Lower Saxony in the form
of a Scientific Assistant position, and the support of the authors' family, to
whom this book is dedicated, are gratefully acknowledged.
GEORGIOS E, STAVROULAKIS
BRAUNSCHWEIG, JULY 2000
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