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Inverse and Crack Identification Problems in Engineering Mechanics : Applied Optimization - Georgios E. Stavroulakis

Inverse and Crack Identification Problems in Engineering Mechanics

Applied Optimization

Hardcover Published: December 2009
ISBN: 9780792366904
Number Of Pages: 224

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Inverse and crack identification problems are of paramount importance for health monitoring and quality control purposes arising in critical applications in civil, aeronautical, nuclear, and general mechanical engineering. Mathematical modeling and the numerical study of these problems require high competence in computational mechanics and applied optimization. This is the first monograph which provides the reader with all the necessary information. Delicate computational mechanics modeling, including nonsmooth unilateral contact effects, is done using boundary element techniques, which have a certain advantage for the construction of parametrized mechanical models. Both elastostatic and harmonic or transient dynamic problems are considered. The inverse problems are formulated as output error minimization problems and they are theoretically studied as a bilevel optimization problem, also known as a mathematical problem with equilibrium constraints. Beyond classical numerical optimization, soft computing tools (neural networks and genetic algorithms) and filter algorithms are used for the numerical solution. The book provides all the required material for the mathematical and numerical modeling of crack identification testing procedures in statics and dynamics and includes several thoroughly discussed applications, for example, the impact-echo nondestructive evaluation technique. Audience: The book will be of interest to structural and mechanical engineers involved in nondestructive testing and quality control projects as well as to research engineers and applied mathematicians who study and solve related inverse problems. People working on applied optimization and soft computing will find interesting problems to apply to their methods and all necessary material to continue research in this field.

Prefacep. xi
Introduction. Problem Description
Direct and Inverse Problemsp. 3
Introductionp. 3
Direct nonsmooth mechanics problemsp. 3
Inverse and identification problemsp. 4
Recent results and future workp. 5
Theoretical and Computational Tools
Computational Mechanicsp. 11
Elastostaticsp. 11
Small displacement smooth (classical) elastostaticsp. 12
Unilateral contact problemsp. 15
The unilateral contact conditionsp. 19
Friction problems with convex energy potentialp. 21
Combined frictional contact problemp. 23
BEM formulation and implementationp. 24
BEM formulation of unilateral problemsp. 24
LCP-BEM static unilateral-frictional contact problemsp. 26
Multi-region BEM formulation for inequality problemsp. 27
Unified LCP formulation of combined unilateral frictional contact problemsp. 29
Solution algorithmsp. 32
Smooth and nonsmooth optimization approachp. 32
QPP and LCP solution schemesp. 34
Nonlinear equations for complementerity problemsp. 34
Nonlinear equation reformulationp. 36
Examples of NCP functionsp. 36
Merit functionsp. 37
Solution techniquep. 37
Formulation of nonlinear equations with FEM and BEMp. 38
NCP functions proposed in the engineering literaturep. 40
Elastodynamicsp. 41
Steady state, harmonic problemsp. 41
Transient elastodynamicsp. 43
LCP-BEM dynamic unilateral-frictional contact problemsp. 45
Computational and Structural Optimizationp. 55
Optimization and optimality conditionsp. 55
Smooth, inequality constrained, convex problemsp. 58
Lagrangians, saddle points, dualityp. 59
Concise form of optimality conditionsp. 61
Convex, nonsmooth optimizationp. 62
Unconstrainedp. 62
Constrainedp. 62
Convex optimization algorithmsp. 63
Smooth Unconstrained Problemsp. 63
Constrained Problemsp. 64
Nonsmooth Problemsp. 67
Optimization under equilibrium constraints (MPEC)p. 68
Formulationp. 69
Examples of structural optimizationp. 71
Optimal design for structuresp. 71
Optimal design for unilateral structuresp. 71
Optimal prestress of unilateral Structuresp. 72
Geometry design, inverse or identification problemp. 73
Nonsmoothness and nonconvexity in MPECp. 74
Solution methodsp. 76
Error minimization with regularizationp. 76
Error minimization - regularization - nonlinear equation approachp. 77
Error minimization - penalty formulationp. 77
Error minimization - regularization - nonlinear equation approach - penalty formulationp. 78
Further numerical approachesp. 78
Selected Soft Computing Toolsp. 85
Soft-computing versus classical computingp. 85
Neural networksp. 86
Backpropagation neural network modelp. 86
Neural network mappings, motivation and application on inverse problemsp. 89
Genetic algorithmsp. 92
Fuzzy and neuro-fuzzy inferencep. 95
Classical and extended Kalman filter and identificationp. 96
Reviewp. 96
Descriptionp. 97
Applications to Inverse Problems
Static Problemsp. 107
Introduction and literature surveyp. 107
Output error formulation of the inverse problemp. 110
Local optimization approachp. 112
Neural network solution methodp. 112
Numerical examples of direct problemsp. 114
Static unilateral crack analysisp. 118
Numerical examples of inverse problemsp. 124
Flaw identificationp. 124
Bilateral and unilateral crack identification through error optimizationp. 133
Classical and unilateral neural crack identificationp. 135
Filter-driven iterative crack identificationp. 147
Steady-State Dynamicsp. 157
Introduction and literature surveyp. 157
Output error formulation of the inverse problemp. 159
Neural network solution of the Inverse Problemp. 160
Numerical examplesp. 161
Flaw identificationp. 161
Crack identificationp. 168
Direct problemp. 168
Inverse problemp. 171
Transient Dynamicsp. 187
Introduction and literature surveyp. 187
Numerical examples of direct problemsp. 189
Numerical examples of inverse problemsp. 202
Classical and unilateral impact-echop. 202
Outline of the methodp. 202
Numerical comparisonp. 203
Impact-echo and neural identificationp. 204
Table of Contents provided by Syndetics. All Rights Reserved.

ISBN: 9780792366904
ISBN-10: 0792366905
Series: Applied Optimization
Audience: General
Format: Hardcover
Language: English
Number Of Pages: 224
Published: December 2009
Publisher: Springer
Country of Publication: NL
Dimensions (cm): 23.39 x 15.6  x 1.42
Weight (kg): 0.52

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