Holdings: Introduction to mathematical elasticity

Introduction to mathematical elasticity:

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Bibliographic Details
Main Authors:	Lebedev, Leonid P. 1946- (Author), Cloud, Michael J. 1960- (Author)
Format:	Book
Language:	English
Published:	New Jersey [u.a.] World Scientific 2009
Subjects:	Elastizitätstheorie
Online Access:	Inhaltsverzeichnis
Physical Description:	XV, 300 S. Ill., graph. Darst.
ISBN:	9814273724 9789814273725

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MARC


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adam_text	IMAGE 1 INTRODUCTION TO MATHEMATICAL ELASTICITY LEONID P. LEBEDEV NATIONALUNIVERSITYOF COLOMBIA MICHAEL J. CLOUD LAWRENCE TECHNOLOGICAL UNIVERSITY,USA ,I» WORLDSCIENTIFIC NEW JERSEY LONDON * SINGAPORE SELJINGSHANGHAI* HONG KONG * TAIPEI. CHENNAI IMAGE 2 CONTENTS FOREWORD PREFACE SOME NOTATION V VLL XL 1. MODELS AND IDEAS OF CLASSICALMECHANICS 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 1.10 1.11 1.12 1.13 1.11 1.15 1.16 1.17 1.18 1.19 ORIENTATION . . . . . . . . . . . . . . . . . . . . . . SOME WORDS ON THE FUNDAMENTALS OF OUR SUBJECT . .VLETRIC SPACES AND SPACES OF PARTICLES .. VECTORS AND VECTOR SPACES . NORMED SPACES AND INNER PRODUCL SPACES FORCES. EQUILIBRIUM AND .VLOTION OF ARIGID BODY . D ALEMBERT S PRINCIPLE . THE MOTION OFA SYSTEM OF PARTIEIES . . . TBE RIGID BODY. . . . . . . . . . . . . . . MOTION OF A SYSTEM OF PARTICLES; COMPARISON OF TRAJECTORIES; NOTION OF OPERATOR . MATRIX OPERATORS AND MATRIX EQUATIONS CORNPLETE SPACES . CORNPLETION THEOREM . . . . . . . . . . . LEBESGUE INTEGRATION AND THE LP SPACES ORTHOGONAL DECOMPOSITION OF HILBERT SPACE WORK AND ENERGY . VIRTUAL WORK PRINCIPLE . . . . . . . . . . . LAGRANGE S EQUATIOLLS OF THE SECOND KIND XIII 1 1 2 4 8 11 16 21 23 25 31 33 40 44 48 54 60 63 67 70 IMAGE 3 2. SIMPLE ELASTIC MODELS XIV 1.20 1.21 1.22 2.1 2.2 2.3 2.4 2.5 2.6 2 ~ ./ 2.8 2.9 2.10 2.11 2.12 2.13 2.14 2.15 2.16 2.17 2.18 INTRODUCTION TO MATHEMATICAL ELASH:CITY PROBLEM OF MINIMUM OF A FUNCTIONAL . HAMILTON S PRINCIPLE . ENERGY CONSERVATION REVISITED INTRODUCTION . TWO MAIN PRINCIPLES OF EQUILIBRIUHLANEL MOTION FOR BODIES IN CONTIILUUM MECHALLICS. EQUILIBRIUM OF ASPRING . EQUILIBRIUM OF ASTRING . EQUILIBRIULLL BOUNDARY VALUE PROBLEMS FORA STRIUG GENERALIZED FORRNULATIOLL OF THE EQUILIBRIUHL PROBLEM FORA STRING . VIRTUAL WORK PRINCIPLE FUER ASTRING. . . . . . . . .... RIESZ REPRESENTATION THEOREM . . . . . . . . . . . . . . GENERALIZED SETUP OF THE DIRICHLET PROBLEM FOR ASTRING FIRST THEOREMS OF IMBEDDILLG . .. . GENERALIJ :ED SETUP 01 THE DIRICHLET PROBLEM FOR CL STRING, CONTINUED . . . . . . . . . . . . . . . . . . . . . . . . NEUMANN PROBLEM FOR THE STRING. . .... THE GENERALIZED SOLUTION OF LINEAR MECHANICAL PROBLEMS AND THE PRINCIPLE OF MINIMUILL TOTAL ENERGY .. NONLINEAR MODEL OF A MEMBRANC . . . . . .. LINEAR MEMBRANE THEOL Y=POISSOL1 S EQUATIOIL . GENER3LIED SETUP 01 THC DIRICHLET PROBLEM FUERA LINEAR MEMBRANE . OTHER MEMBRANE EQUILIBRIUM PROBLEMS . BAL1ACH S CONTRACTION MAPPING PRINCIPLE . 74 83 85 89 89 89 91 95 WO 105 LO8 112 115 116 120 122 126 128 131 1:12 H5 151 3. THCORY OF ELASTICILY: STATICS AND DY1L3MICS 157 3.1 3.2 :~.;J 3.4 3.5 3.6 3.7 INTROCLUCTION . AN ELASTIC BAR UNDER STRETCHING BEN DING OF A BEAM . . . . . . . . GENERALIZED SOLUTIONS TO THE EQUILIBRIUM PROBLEM FUER A BCAM . GENERALIZED SETUP: ROUGH QUALITATIVE DISCUSSIOIL PRESS URE AND STRESSES. VECTORS AND TENSORS . . . . . . . . . . . . . . . . 157 158 1G8 175 179 181 188 IMAGE 4 XV 196 202 207 208 214 218 DIS- 221 224 227 231 232 235 243 243 245 249 252 255 CORN- 262 267 SELF- 3.8 3.9 3.10 3.11 3.12 3.13 3.14 3.15 3.16 3.17 3.18 3.19 3.20 3.21 3.22 3.23 3.24 3.25 3.26 3.27 3.28 3.29 CONTENTS THE CAUCHY STRESS TENSOR, CONTINUED . BASIC TENSOR CALCULUS IN CURVILINEAR COORDINATES EULER AND LAGRANGE DESCRIPTIONS OF CONTINUA STRAIN TENSORS . THE VIRTUAL WORK PRINCIPLE . . . . . . HOOKE S LAW IN THREE DIMENSIONS . THE EQUILIBRIUM EQUATIONS OF LINEAR ELASTICITY IN PLACEMENTS . . . . . . . . . . . . . . . . . . VIRTUAL VORK PRINCIPLE IN LINEAR ELASTICITY GENERALIZED SETUP OF ELASTICITY PROBLEMS EXISTENCE THEOREM FOR AN ELASTIC DODY EQUILIBRIUM OF AFREE ELASTIC BODY . . . . VARIATIONAL METHOC!SFOR EQUILIBRIUM PROBLEMS ABRIEF BUT IMPORTANT REMARK .... COUNTABLE SETS ANEL SEPARABLE SPACES. . . . FOURIER SERIES. . . . . . . . . . . . . . . . . PROBLEM OF VIBRATION FOR ELASTIC STRUETURES SELF-ADJOINTNESS OF IT ANC! ITS CONSEQUENCES COMPACTNESS OF IT .. . . . . . . . . . . . . RIESZ- FREDHOLM THEORY FORA LINEAR, SELF-ADJOINT, PAET OPERATOR INA HILBERT SPACE . . . . . . . . . . WEAK CONVERGENCE IN HILBERT SPACE . COMPLCTENESS OF THE SYSTEM OF EIGENVECTORS OF A ADJOINT, COMPACT, STRICTLY POSITIVE LINEAR OPERATOR OTHER STANDARD MODELS OF ELASTICITY . . . . . . . . . 272 277 APPENDIX A RINTS FORSELECTEDEXERCISES BIBLIOGRAPHY INDEX 281 293 295
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author	Lebedev, Leonid P. 1946- Cloud, Michael J. 1960-
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spelling	Lebedev, Leonid P. 1946- Verfasser (DE-588)124355560 aut Introduction to mathematical elasticity Leonid P. Lebedev ; Michael J. Cloud New Jersey [u.a.] World Scientific 2009 XV, 300 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Elastizitätstheorie (DE-588)4123124-7 gnd rswk-swf Elastizitätstheorie (DE-588)4123124-7 s DE-604 Cloud, Michael J. 1960- Verfasser (DE-588)120264242 aut GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=020776976&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis
spellingShingle	Lebedev, Leonid P. 1946- Cloud, Michael J. 1960- Introduction to mathematical elasticity Elastizitätstheorie (DE-588)4123124-7 gnd
subject_GND	(DE-588)4123124-7
title	Introduction to mathematical elasticity
title_auth	Introduction to mathematical elasticity
title_exact_search	Introduction to mathematical elasticity
title_full	Introduction to mathematical elasticity Leonid P. Lebedev ; Michael J. Cloud
title_fullStr	Introduction to mathematical elasticity Leonid P. Lebedev ; Michael J. Cloud
title_full_unstemmed	Introduction to mathematical elasticity Leonid P. Lebedev ; Michael J. Cloud
title_short	Introduction to mathematical elasticity
title_sort	introduction to mathematical elasticity
topic	Elastizitätstheorie (DE-588)4123124-7 gnd
topic_facet	Elastizitätstheorie
url	http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=020776976&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA
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