Nonconvex optimization in mechanics: algorithms, heuristics and engineering applications by the F.E.M.
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Dordrecht [u.a.]
Kluwer
1998
|
| Series: | Nonconvex optimization and its applications
21 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XX, 285 S. graph. Darst. |
| ISBN: | 0792348125 |
Staff View
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| adam_text | NONCONVEX OPTIMIZATION IN MECHANICS ALGORITHMS, HEURISTICS AND
ENGINEERING APPLICATIONS BY THE F.E.M. BY E.S. MISTAKIDIS INSTITUTE OF
STEEL STRUCTURES, DEPARTMENT OF CIVIL ENGINEERING, ARISTOTLE UNIVERSITY,
THESSALONIKI, GREECE AND G.E. STAVROULAKIS INSTITUTE OF APPLIED
MECHANICS, DEPARTMENT OF CIVIL ENGINEERING, CAROLO WILHELMINA TECHNICAL
UNIVERSITY, BRAUNSCHWEIG, GERMANY PS KLUWER ACADEMIC PUBLISHERS
DORDRECHT / BOSTON / LONDON CONTENTS PREFACE XV GUIDELINES FOR THE
READERS XIX PART I NONCONVEXITY IN ENGINEERING APPLICATIONS 1.
NONCONVEXITY IN ENGINEERING APPLICATIONS 3 1.1 NONCONVEXITY IN
ENGINEERING 3 1.2 SUPERPOTENTIAL PROBLEMS 8 1.3 TYPICAL, REPRESENTATIVE
EXAMPLES 11 1.4 NONCONVEX OPTIMIZATION BY SOLVING CONVEX SUBPROBLEMS 14
REFERENCES . 16 PART II APPLIED NONCONVEX OPTIMIZATION BACKGROUND 2.
APPLIED NONCONVEX OPTIMIZATION BACKGROUND 25 2.1 OPTIMIZATION PROBLEMS
25 2.2 NONSMOOTH CONVEX PROBLEMS 28 2.2.1 SMOOTH, INEQUALITY
CONSTRAINED, CONVEX PROBLEMS 28 2.2.1.1 LAGRANGIANS, SADDLE POINTS,
DUALITY 30 2.2.2 CONCISE FORM OF OPTIMALITY CONDITIONS 31 2.2.3 CONVEX,
NONSMOOTH OPTIMIZATION 33 2.2.3.1 UNCONSTRAINED OPTIMIZATION 33 2.2.3.2
CONSTRAINED OPTIMIZATION 33 2.3 NONCONVEX PROBLEMS 34 2.3.1 DIFFERENCE
CONVEX OPTIMIZATION 34 2.3.2 QUASIDIFFERENTIABLE OPTIMIZATION 37 2.4 A
REVIEW OF OPTIMIZATION ALGORITHMS AND HEURISTICS 38 VIII NONCONVEX
OPTIMIZATION IN MECHANICS 2.4.1 CONVEX OPTIMIZATION ALGORITHMS 38
2.4.1.1 SMOOTH UNCONSTRAINED PROBLEMS 38 2.4.1.2 CONSTRAINED PROBLEMS 40
2.4.1.3 NONSMOOTH PROBLEMS 42 2.4.2 NONCONVEX OPTIMIZATION ALGORITHMS 44
2.4.2.1 DIFFERENCE CONVEX (D.C.) PROBLEMS 45 2.4.3 HEURISTICS FOR
NONCONVEX OPTIMIZATION PROBLEMS 48 2.4.4 SOFT COMPUTING TECHNIQUES 52
2.4.4.1 DYNAMICAL SYSTEMS AND OPTIMIZATION 53 2.4.4.2 NEURAL NETWORK
TECHNIQUES 55 2.4.4.3 STOCHASTIC APPROACHES. SIMULATED ANNEALING 59
REFERENCES 61 PART III SUPERPOTENTIAL MODELLING AND OPTIMIZATION IN
MECHANICS WITH AND WITHOUT CONVEXITY AND SMOOTHNESS 3. CONVEX
SUPERPOTENTIAL PROBLEMS 71 3.1 VARIATIONAL PROBLEMS IN MECHANICS 71
3.1.1 SMALL DISPLACEMENT SMOOTH ELASTOSTATICS: A CONVEX, DIFFERENTIABLE
OPTIMIZATION PROBLEM 72 3.1.2 UNILATERAL CONTACT PROBLEMS WITHIN THE
SMALL DISPLACEMENTS FRAMEWORK: A CONVEX, INEQUALITY CONSTRAINED,
POTENTIAL ENERGY MINIMUM PROBLEM 76 3.1.3 FRICTION PROBLEMS WITH CONVEX
ENERGY POTENTIALS 83 3.1.3.1 COMBINED FRICTIONAL CONTACT PROBLEM 85
3.1.3.2 DIRECT L.C.P: FORMULATION OF THE UNILATERAL FRICTIONAL CONTACT
PROBLEM 87 3.1.3.3 DYNAMIC FRICTION PROBLEM 90 3.1.3.4 GENERAL MONOTONE
MATERIAL LAWS 90 3.1.4 UNIAXIAL HOLONOMIC ELASTIC PLASTIC RELATIONS 92
3.1.4.1 ELASTIC PERFECTLY PLASTIC SPRING 92 3.1.4.2 ELASTIC LINEAR
HARDENING SPRING 93 3.1.4.3 ELASTIC LOCKING SPRING 94 3.1.4.4 ELASTIC
LINEAR SOFTENING SPRING 96 3.2 CONVEX ENERGY AND DISSIPATION PROBLEMS IN
GENERALIZED ELASTOPLASTICITY 96 3.2.1 HOLONOMIC (HENCKY-TYPE)
ELASTOPLASTICITY 98 3.2.2 RATE ELASTOPLASTICITY 100 3.2.2.1 PERFECT
ELASTOPLASTICITY 100 3.2.2.2 ELASTOPLASTICITY WITH HARDENING 102 3.2.2.3
GENERALIZED STANDARD ELASTOPLASTICITY MODEL 103 3.2.2.4 HARDENING AND
INTERNAL VARIABLES 104 3.2.2.5 STEPWISE HOLONOMIC PROBLEMS BY TIME
DISCRETIZATION 106 REFERENCES 108 CONTENTS IX 4. NONCONVEX
SUPERPOTENTIAL PROBLEMS 119 4.1 ORIGIN AND TREATMENT OF NONCONVEXITY IN
MECHANICS 119 4.1.1 NONMONOTONE CONTACT (ADHESIVE) LAWS 120 4.1.1.1
HEMIVARIATIONAL INEQUALITY FORMULATION 120 4.1.1.2 DIFFERENCE CONVEX
OPTIMIZATION APPROACH 123 4.1.1.3 HEURISTIC NONCONVEX OPTIMIZATION
APPROACH 126 4.1.2 FRICTION PROBLEMS WITH NONCONVEX ENERGY POTENTIAL 129
4.1.3 GENERAL NONMONOTONE MATERIAL LAWS 131 4.1.4 LARGE DISPLACEMENT AND
DEFORMATION PROBLEMS: NONCONVEX OPTIMIZATION PROBLEMS 132 4.1.4.1
FORMULATION OF THE PROBLEM 133 4.1.4.2 LARGE DISPLACEMENT UNILATERAL
CONTACT PROBLEMS 137 4.2 ENERGY AND DISSIPATION PROBLEMS: THE CASE OF
GENERALIZED ELASTOPLASTICITY 139 4.2.1 NONCONVEXITY IN ELASTOPLASTICITY
139 4.2.2 HOLONOMIC, HENCKY-TYPE PROBLEMS 141 4.2.3 RATE PROBLEMS 145
4.2.3.1 SOFTENING EFFECTS 147 4.3 DAMAGE AND FRACTURE MECHANICS 148
REFERENCES 151 5. OPTIMAL DESIGN PROBLEMS 159 5.1 MULTILEVEL, ITERATIVE
OPTIMAL DESIGN PROBLEMS 159 5.1.1 INTRODUCTION 159 5.1.2 FORMULATION OF
THE OPTIMAL DESIGN PROBLEM 161 5.1.3 MULTILEVEL DECOMPOSITION AND
SOLUTION ALGORITHM 163 5.1.4 APPLICATIONS 166 5.1.4.1 FIBRE REINFORCED
COMPOSITES 166 5.1.4.2 CELLULAR MATERIALS 166 5.1.5 TOPOLOGY
OPTIMIZATION PROBLEMS 167 5.1.6 A SIMPLE DAMAGE MECHANICS MODEL 168
REFERENCES^ - 170 PART IV COMPUTATIONAL MECHANICS. COMPUTER
IMPLEMENTATION, APPLICATIONS AND EXAMPLES 6. COMPUTATIONAL MECHANICS
ALGORITHMS 177 6.1 NUMERICAL OPTIMIZATION AND COMPUTATIONAL MECHANICS
177 6.1.1 SMOOTH PROBLEMS 178 6.1.2 ALGORITHMS VS. NUMERICAL
OPTIMIZATION 179 6.1.3 ITERATIVE LINEARIZATION 180 6.1.4 PATH-FOLLOWING
. 182 6.2 SPECIAL PURPOSE ALGORITHMS FOR INTERFACE PROBLEMS 183 6.2.1
CONVEX PROBLEMS 184 X NONCONVEX OPTIMIZATION IN MECHANICS 6.2.1.1
UNILATERAL CONTACT WITH MONOTONE DEBONDING 185 6.2.1.2 UNILATERAL
CONTACT WITH COULOMB FRICTION 187 6.2.1.3 UNILATERAL CONTACT WITH
COULOMB FRICTION AND MONOTONE DEBONDING 189 6.2.2 NONCONVEX PROBLEMS 191
6.2.2.1 UNILATERAL CONTACT WITH NONMONOTONE DEBONDING 192 6.2.2.2
UNILATERAL CONTACT WITH NONMONOTONE FRICTION 195 6.2.2.3 UNILATERAL
CONTACT WITH NONMONOTONE FRICTION AND NONMONOTONE DEBONDING 196 6.2.3
FRACTALS AND INTERFACE PROBLEMS 199 6.2.3.1 FRACTAL INTERFACES 200
6.2.3.2 THE CASE OF FRACTAL FRICTION LAWS 201 6.3 ALGORITHMS FOR
STRUCTURAL ANALYSIS PROBLEMS 202 6.3.1 CONVEX PROBLEMS: SOLUTION OF THE
CLASSICAL PLASTICITY PROBLEM 202 6.3.2 NONCONVEX PROBLEMS: STRUCTURES
WITH ELEMENTS INVOLVING SOFTENING MOMENT-ROTATION RELATIONSHIPS 203
APPENDIX: THE ESSENTIALS OF FRACTAL GEOMETRY 208 6-A.LLTERATED FUNCTION
SYSTEMS 208 6-A.2APPROXIMATION OF FRACTALS BY C CURVES 209
6-A.3APPROXIMATION OF FRACTALS BY C 1 CURVES 211 REFERENCES 214 7.
APPLICATIONS 219 7.1 CHARACTERISTIC ONE- AND TWO- DIMENSIONAL EXAMPLES
219 7.1.1 ONE-DIMENSIONAL SPRINGS ASSEMBLY 219 7.1.2 EXPLORING THE
ENERGY LANDSCAPE FOR A TWO-DIMENSIONAL PROBLEM 224 7.1.3 A REFERENCE
PROBLEM: COMPARISON WITH THE PATH FOLLOWING METHODS 228 7.1.4 A SIMPLE
BEAM-TO-COLUMN SEMIRIGID CONNECTION 230 7.2 STRUCTURES WITH FRICTIONAL
CONTACT AND ADHESIVE CONTACT INTERFACE CONDITIONS 232 7.2.1 UNILATERAL
CONTACT WITH THE PRESENCE OF NONMONOTONE FRICTION 232 7.2.2 LAYERED
STRUCTURE WITH ADHESIVE CONTACT INTERFACE CONDITIONS 236 7.3 DEBONDING
OF LAYERS CONNECTED WITH ADHESIVES 240 7.4 STRUCTURES WITH FRACTAL
INTERFACES AND/OR FRACTAL FRICTION LAWS 244 7.4.1 FRACTAL FRICTION LAWS
IN CONTACT PROBLEMS 244 7.4.2 MULTIFRACTURED STRUCTURES WITH FRACTAL
INTERFACES 247 7.5 COMBINED PROBLEMS 250 7.5.1 FRACTAL INTERFACES WITH
FRACTAL FRICTION LAWS 250 7.5.2 REPAIR OF A FRACTURED BODY WITH
ADHESIVES 255 7.6 THIN-WALLED STEEL BEAMS WITH SOFTENING BEHAVIOUR 259
7.7 STRUCTURES WITH SEMIRIGID CONNECTIONS 263 7.8 INVESTIGATION OF THE
BEHAVIOUR OF HYBRID LAMINATES MADE OF UNIDIRECTIONAL COMPOSITES 268
CONTENTS XI 7.8.1 LAMINATED COMPOSITES UNDER AXIAL LOADING 269 7.8.2
LAMINATED COMPOSITES IN BENDING 272 7.9 OPTIMAL DESIGN EXAMPLES 275
REFERENCES 281 INDEX 283
|
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| id | DE-604.BV012080861 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T18:21:21Z |
| institution | BVB |
| isbn | 0792348125 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-008179406 |
| oclc_num | 37552713 |
| open_access_boolean | |
| owner | DE-703 DE-91G DE-BY-TUM DE-634 DE-706 |
| owner_facet | DE-703 DE-91G DE-BY-TUM DE-634 DE-706 |
| physical | XX, 285 S. graph. Darst. |
| publishDate | 1998 |
| publishDateSearch | 1998 |
| publishDateSort | 1998 |
| publisher | Kluwer |
| record_format | marc |
| series | Nonconvex optimization and its applications |
| series2 | Nonconvex optimization and its applications |
| spelling | Mistakidis, Euripidis S. Verfasser aut Nonconvex optimization in mechanics algorithms, heuristics and engineering applications by the F.E.M. by E. S. Mistakidis and G. E. Stravroulakis Dordrecht [u.a.] Kluwer 1998 XX, 285 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Nonconvex optimization and its applications 21 Mécanique appliquée ram algorithme optimisation inriac heuristique inriac mécanique structure inriac optimisation convexe inriac optimisation non convexe inriac Mathematik Finite element method Mathematical optimization Mechanics, Applied Mathematics Nonconvex programming Mechanik (DE-588)4038168-7 gnd rswk-swf Nichtkonvexe Optimierung (DE-588)4309215-9 gnd rswk-swf Mechanik (DE-588)4038168-7 s Nichtkonvexe Optimierung (DE-588)4309215-9 s DE-604 Stravroulakis, Georgios E. Verfasser aut Nonconvex optimization and its applications 21 (DE-604)BV010085908 21 GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008179406&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Mistakidis, Euripidis S. Stravroulakis, Georgios E. Nonconvex optimization in mechanics algorithms, heuristics and engineering applications by the F.E.M. Nonconvex optimization and its applications Mécanique appliquée ram algorithme optimisation inriac heuristique inriac mécanique structure inriac optimisation convexe inriac optimisation non convexe inriac Mathematik Finite element method Mathematical optimization Mechanics, Applied Mathematics Nonconvex programming Mechanik (DE-588)4038168-7 gnd Nichtkonvexe Optimierung (DE-588)4309215-9 gnd |
| subject_GND | (DE-588)4038168-7 (DE-588)4309215-9 |
| title | Nonconvex optimization in mechanics algorithms, heuristics and engineering applications by the F.E.M. |
| title_auth | Nonconvex optimization in mechanics algorithms, heuristics and engineering applications by the F.E.M. |
| title_exact_search | Nonconvex optimization in mechanics algorithms, heuristics and engineering applications by the F.E.M. |
| title_full | Nonconvex optimization in mechanics algorithms, heuristics and engineering applications by the F.E.M. by E. S. Mistakidis and G. E. Stravroulakis |
| title_fullStr | Nonconvex optimization in mechanics algorithms, heuristics and engineering applications by the F.E.M. by E. S. Mistakidis and G. E. Stravroulakis |
| title_full_unstemmed | Nonconvex optimization in mechanics algorithms, heuristics and engineering applications by the F.E.M. by E. S. Mistakidis and G. E. Stravroulakis |
| title_short | Nonconvex optimization in mechanics |
| title_sort | nonconvex optimization in mechanics algorithms heuristics and engineering applications by the f e m |
| title_sub | algorithms, heuristics and engineering applications by the F.E.M. |
| topic | Mécanique appliquée ram algorithme optimisation inriac heuristique inriac mécanique structure inriac optimisation convexe inriac optimisation non convexe inriac Mathematik Finite element method Mathematical optimization Mechanics, Applied Mathematics Nonconvex programming Mechanik (DE-588)4038168-7 gnd Nichtkonvexe Optimierung (DE-588)4309215-9 gnd |
| topic_facet | Mécanique appliquée algorithme optimisation heuristique mécanique structure optimisation convexe optimisation non convexe Mathematik Finite element method Mathematical optimization Mechanics, Applied Mathematics Nonconvex programming Mechanik Nichtkonvexe Optimierung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008179406&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV010085908 |
| work_keys_str_mv | AT mistakidiseuripidiss nonconvexoptimizationinmechanicsalgorithmsheuristicsandengineeringapplicationsbythefem AT stravroulakisgeorgiose nonconvexoptimizationinmechanicsalgorithmsheuristicsandengineeringapplicationsbythefem |