Modelling and control in solid mechanics:
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Basel [u.a.]
Birkhäuser
1997
|
| Series: | International series of numerical mathematics
122 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Literaturverz. S. 353 - 363 |
| Physical Description: | XIII, 366 S. graph. Darst. |
| ISBN: | 3764352388 0817652388 |
Staff View
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Record in the Search Index
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| adam_text | MODELLING AND CONTROL
IN SOLID MECHANICS
A.M
. KHLUDNEV
J
. SOKOLOWSKI
BIRKHAUSER VERLA
G
BASEL BOSTON BERLIN
CONTENTS
PREFACE IX
1 INTRODUCTION
1 ELEMENT
S OF MATHEMATICA
L ANALYSI
S AN
D CALCULUS OF VARIATION
S 1
1.1 FUNCTIONA
L SPACES
. SIMPLE PROPERTIE
S 1
1.2 VARIATIONA
L INEQUALITIE
S 4
1.3 MINIMIZATIO
N PROBLEM
S FOR CONVEX FUNCTIONALS 4
1.4 DERIVATIVE OF A CONVEX FUNCTIONAL 7
1.5 MINIMIZATIO
N PROBLEM
S FOR NONSMOOT
H FUNCTIONALS 8
1.6 WEAK CONVERGENCE. COMPACTNES
S PRINCIPLES 10
1.7 WEAK SEMICONTINUIT
Y OF FUNCTIONALS 10
1.8 EXISTENC
E OF SOLUTION
S T
O TH
E MINIMIZATIO
N PROBLE
M 12
1.9 TH
E CASE OF HILBER
T SPACE 13
1.10 ELEMENT
S OF MEASUR
E THEOR
Y 15
2 MATHEMATICA
L MODELS OF ELASTI
C BODIES
.
CONTAC
T PROBLEM
S 20
2.1 LINEAR ELASTIC BODIE
S AN
D SHALLOW SHELLS 20
2.2 MATHEMATICA
L MODELS OF CONTAC
T PROBLEM
S 22
2 VARIATIONAL INEQUALITIES IN CONTACT PROBLEMS OF ELASTICITY
1 CONTAC
T BETWEE
N A
N ELASTI
C BOD
Y AN
D A RIGID BOD
Y 27
1.1 PROBLE
M FORMULATIO
N 27
1.2 REGULARIT
Y OF SOLUTIONS
. CONSTRUCTIO
N OF
MEASURE
S 29
2 CONTAC
T BETWEE
N TWO ELASTI
C BODIE
S 33
2.1 FORMULATIO
N OF TH
E PROBLEM
. REGULARIT
Y OF
SOLUTION
S 33
2.2 CONSTRUCTIO
N OF A MEASUR
E 36
3 CONTAC
T BETWEE
N A SHALLOW SHELL AN
D A RIGID PUNC
H 39
3.1 EXISTENC
E OF SOLUTION
S 39
3.2 REGULARIT
Y OF SOLUTION
S 42
3.3 ABSENCE OF CONCENTRATE
D FORCES 46
3.4 PARALLE
L PUNC
H ....
. 48
VI CONTENTS
4 CONTACT BETWEEN TWO ELASTIC PLATES 52
4.1 PROBLEM FORMULATION. PROPERTIES OF TH
E SOLUTION 52
4.2 CONNECTEDNESS OF TH
E NONCOINCIDENCE DOMAIN 58
5 REGULARITY OF SOLUTIONS T
O VARIATIONAL INEQUALITIES OF
ORDER FOUR 60
5.1 THE CONTACT PROBLEM OF A PLATE WITH A MEMBRANE 60
5.2 THE CONTACT PROBLEM FOR A SHELL 64
6 BOUNDARY VALUE PROBLEMS FOR NONLINEAR SHELLS 66
6.1 GENERAL REMARKS 66
6.2 INEQUALITIES ON TH
E BOUNDARY. CONVERGENCE OF
SOLUTIONS 69
7 BOUNDARY VALUE PROBLEMS FOR LINEAR SHELLS 79
8 DYNAMIC PROBLEMS 83
8.1 VARIATIONAL INEQUALITY FOR A BEAM 83
8.2 VARIATIONAL INEQUALITY FOR A SHELL 91
3 VARIATIONAL INEQUALITIES IN PLASTICITY
1 PRELIMINARIES 99
2 THE HENCKY MODEL 107
2.1 THE THREE-DIMENSIONAL ELASTOPLASTIC BODY 107
2.2 THE PERFECT PLASTIC BODY IL
L
3 DYNAMIC PROBLEM FOR GENERALIZED EQUATIONS OF TH
E FLOW MODEL 116
4 THE KIRCHHOFF-LOVE SHELL. EXISTENCE OF SOLUTIONS T
O TH
E
DYNAMIC PROBLEM
. .YY
121
4.1 PROBLEM FORMULATION 121
4.2 TH
E MAIN RESULT 122
5 EXISTENCE OF SOLUTIONS T
O ONE-DIMENSIONAL PROBLEMS 129
5.1 ELASTOPLASTIC PROBLEMS FOR A BEAM AND CYLINDRICAL SHELL 129
5.2 THE PERFECTLY PLASTIC PROBLEM FOR A BEAM 132
6 EXISTENCE OF SOLUTIONS FOR A QUASISTATIC SHELL 137
6.1 FORMULATION OF TH
E PROBLEM 137
6.2 THEOREM OF EXISTENCE 137
7 CONTACT PROBLEM FOR TH
E KIRCHHOFF PLATE 146
7.1 ELASTOPLASTIC PROBLEM 146
7.2 THE PERFECTLY PLASTIC PROBLEM 153
8 CONTACT PROBLEM FOR TH
E TIMOSHENKO BEAM 154
9 TH
E CASE OF TANGENTIAL DISPLACEMENTS 160
10 BEAM UNDER PLASTICITY AND CREEP CONDITIONS 165
11 THE CONTACT VISCOELASTOPLASTIC PROBLEM FOR A BEAM 170
CONTENTS VII
4 OPTIMAL CONTROL PROBLEMS
1 OPTIMAL DISTRIBUTION OF EXTERNAL FORCES FOR PLATES WITH OBSTACLES 177
1.1 COST FUNCTIONALS WITH MEASURES 177
1.2 COST FUNCTIONALS WITH NORMS : .182
2 OPTIMAL SHAPE OF OBSTACLES 185
2.1 COST FUNCTIONALS WITH NORMS 185
2.2 COST FUNCTIONALS WITH MEASURES 191
2.3 FINITE SET OF POINTWISE RESTRICTIONS 195
3 OTHER COST FUNCTIONALS 195
4 PLASTIC HINGE ON THE BOUNDARY 200
4.1 COST FUNCTIONALS WITH DISPLACEMENTS 200
4.2 COST FUNCTIONALS WITH MEASURES 208
5 OPTIMAL CONTROL PROBLEM FOR A BEAM 212
6 OPTIMAL CONTROL PROBLEM FOR A FOURTH-ORDER VARIATIONAL
INEQUALITY 215
6.1 FOURTH-ORDER OPERATOR 215
6.2 SECOND-ORDER OPERATOR 219
6.3 THE PASSAGE T
O THE LIMIT 224
7 THE CASE OF TWO PUNCHES 228
7.1 OPTIMAL CONTROL FOR A PLATE 229
7.2 OPTIMAL CONTROL FOR A MEMBRANE 232
7.3 THE PASSAGE TO THE LIMIT 233
8 OPTIMAL CONTROL OF STRETCHING FORCES 238
8.1 OPTIMAL CONTROL FOR A PLATE 238
8.2 OPTIMAL CONTROL FOR A MEMBRANE 240
8.3 TRANSITION FROM A PLATE TO A MEMBRANE 242
9 EXTREME SHAPES OF CRACKS IN A PLATE 244
10 EXTREME SHAPES OF UNILATERAL CRACKS 248
10.1 INTERIOR CRACKS 249
10.2 BOUNDARY CRACKS 254
10.3 A MORE PRECISE NONPENETRATION CONDITION 257
11 OPTIMAL CONTROL IN ELASTOPLASTIC PROBLEMS 263
12 THE CASE OF VERTICAL AND HORIZONTAL DISPLACEMENTS 266
5 SENSITIVITY ANALYSIS
1
PROPERTIES OF METRIC PROJECTION IN HILBERT SPACES 270
2 SHAPE SENSITIVITY ANALYSIS 275
2.1 MATERIAL DERIVATIVES 275
2.2 MATERIAL DERIVATIVES ON THE BOUNDARY
F
276
2.3 SHAPE DERIVATIVES ON THE BOUNDARY
F
278
2.4 DISPLACEMENT DERIVATIVES ON
S
278
2.5 DERIVATIVES OF SHAPE FUNCTIONALS 281
VIII CONTENTS
3 UNILATERAL PROBLEMS IN
H$(FI)
287
3.1 THE TANGENT CONE 289
3.2 DIFFERENTIABILITY OF METRIC PROJECTIONS 292
3.3 APPLICATIONS TO OPTIMAL DESIGN _ 296
4 UNILATERAL PROBLEMS IN
H
2
(Q)
N
HI(Q)
303
4.1 OBSTACLE PROBLEM FOR SIMPLY SUPPORTED KIRCHHOFF PLAT
E 303
5 SYSTEMS WITH UNILATERAL CONDITIONS 306
6 SHAPE ESTIMATION PROBLEMS 308
6.1 ADMISSIBLE DOMAINS WITH NORM CONSTRAINTS ON GRAPHS 310
6.2 ADMISSIBLE DOMAINS WITH LOCAL CONSTRAINTS ON GRAPHS 317
6.3 DIFFERENTIABILITY OF METRIC PROJECTION 324
6.4 SHAPE ESTIMATION PROBLEM FOR THE WAVE EQUATION 325
7 DOMAIN OPTIMIZATION PROBLEM FOR PARABOLIC EQUATIONS 327
7.1 PARABOLIC EQUATION IN A VARIABLE DOMAIN 328
7.2 DIFFERENTIABILITY OF TH
E COST FUNCTIONAL 330
7.3 SHAPE SENSITIVITY ANALYSIS 331
7.4 OPTIMIZATION PROBLEM 334
8 SHAPE SENSITIVITY ANALYSIS OF THI
N SHELLS 336
8.1 THIN SHELLS 336
8.2 DISPLACEMENT DERIVATIVES 339
8.3 SHAPE SENSITIVITY ANALYSIS OF THI
N SHELLS 342
8.4 COMPUTATION OF DERIVATIVES OF COST FUNCTIONALS 348
8.5 COMPUTATION OF TH
E SECOND DERIVATIVE 349
REFERENCES
353
INDEX .
365
|
| any_adam_object | 1 |
| author | Chludnev, Aleksandr M. 1952- Sokołowski, Jan 1949- |
| author_GND | (DE-588)121181650 (DE-588)172379571 |
| author_facet | Chludnev, Aleksandr M. 1952- Sokołowski, Jan 1949- |
| author_role | aut aut |
| author_sort | Chludnev, Aleksandr M. 1952- |
| author_variant | a m c am amc j s js |
| building | Verbundindex |
| bvnumber | BV011108270 |
| classification_rvk | SK 950 SK 660 UF 3000 UP 1300 |
| classification_tum | MAT 650f PHY 201f MAT 010f |
| ctrlnum | (OCoLC)260222783 (DE-599)BVBBV011108270 |
| discipline | Physik Mathematik |
| format | Book |
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| indexdate | 2024-07-09T18:04:08Z |
| institution | BVB |
| isbn | 3764352388 0817652388 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-007442832 |
| oclc_num | 260222783 |
| open_access_boolean | |
| owner | DE-12 DE-91 DE-BY-TUM DE-91G DE-BY-TUM DE-703 DE-384 DE-29T DE-83 DE-11 DE-188 DE-20 DE-706 |
| owner_facet | DE-12 DE-91 DE-BY-TUM DE-91G DE-BY-TUM DE-703 DE-384 DE-29T DE-83 DE-11 DE-188 DE-20 DE-706 |
| physical | XIII, 366 S. graph. Darst. |
| publishDate | 1997 |
| publishDateSearch | 1997 |
| publishDateSort | 1997 |
| publisher | Birkhäuser |
| record_format | marc |
| series | International series of numerical mathematics |
| series2 | International series of numerical mathematics |
| spelling | Chludnev, Aleksandr M. 1952- Verfasser (DE-588)121181650 aut Modelling and control in solid mechanics A. M. Khludnev ; J. Sokolowski Basel [u.a.] Birkhäuser 1997 XIII, 366 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier International series of numerical mathematics 122 Literaturverz. S. 353 - 363 Plastizität (DE-588)4046283-3 gnd rswk-swf Elastizität (DE-588)4014159-7 gnd rswk-swf Deformationsverhalten (DE-588)4148995-0 gnd rswk-swf Festkörpermechanik (DE-588)4129367-8 gnd rswk-swf Randwertproblem (DE-588)4048395-2 gnd rswk-swf Mathematisches Modell (DE-588)4114528-8 gnd rswk-swf Mechanik (DE-588)4038168-7 gnd rswk-swf (DE-588)4113937-9 Hochschulschrift gnd-content Festkörpermechanik (DE-588)4129367-8 s Mathematisches Modell (DE-588)4114528-8 s DE-604 Randwertproblem (DE-588)4048395-2 s Plastizität (DE-588)4046283-3 s Mechanik (DE-588)4038168-7 s Elastizität (DE-588)4014159-7 s Deformationsverhalten (DE-588)4148995-0 s Sokołowski, Jan 1949- Verfasser (DE-588)172379571 aut International series of numerical mathematics 122 (DE-604)BV035415862 122 DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007442832&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Chludnev, Aleksandr M. 1952- Sokołowski, Jan 1949- Modelling and control in solid mechanics International series of numerical mathematics Plastizität (DE-588)4046283-3 gnd Elastizität (DE-588)4014159-7 gnd Deformationsverhalten (DE-588)4148995-0 gnd Festkörpermechanik (DE-588)4129367-8 gnd Randwertproblem (DE-588)4048395-2 gnd Mathematisches Modell (DE-588)4114528-8 gnd Mechanik (DE-588)4038168-7 gnd |
| subject_GND | (DE-588)4046283-3 (DE-588)4014159-7 (DE-588)4148995-0 (DE-588)4129367-8 (DE-588)4048395-2 (DE-588)4114528-8 (DE-588)4038168-7 (DE-588)4113937-9 |
| title | Modelling and control in solid mechanics |
| title_auth | Modelling and control in solid mechanics |
| title_exact_search | Modelling and control in solid mechanics |
| title_full | Modelling and control in solid mechanics A. M. Khludnev ; J. Sokolowski |
| title_fullStr | Modelling and control in solid mechanics A. M. Khludnev ; J. Sokolowski |
| title_full_unstemmed | Modelling and control in solid mechanics A. M. Khludnev ; J. Sokolowski |
| title_short | Modelling and control in solid mechanics |
| title_sort | modelling and control in solid mechanics |
| topic | Plastizität (DE-588)4046283-3 gnd Elastizität (DE-588)4014159-7 gnd Deformationsverhalten (DE-588)4148995-0 gnd Festkörpermechanik (DE-588)4129367-8 gnd Randwertproblem (DE-588)4048395-2 gnd Mathematisches Modell (DE-588)4114528-8 gnd Mechanik (DE-588)4038168-7 gnd |
| topic_facet | Plastizität Elastizität Deformationsverhalten Festkörpermechanik Randwertproblem Mathematisches Modell Mechanik Hochschulschrift |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007442832&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV035415862 |
| work_keys_str_mv | AT chludnevaleksandrm modellingandcontrolinsolidmechanics AT sokołowskijan modellingandcontrolinsolidmechanics |