Slivker Mechanics of Structural Elements

Theory and Applications
2007
ISBN: 978-3-540-44721-4
Verlag: Springer Berlin Heidelberg
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, 787 Seiten

Reihe: Foundations of Engineering Mechanics

The book systematically presents variational principles and methods of analysis for applied elasticity and structural mechanics. The variational approach is used consistently for both, constructing numerical procedures and deriving basic governing equations of applied mechanics of solids; it is the derivation of equations where this approach is most powerful and best grounded by mathematics.

Autoren/Hrsg.

Slivker, Vladimir

Inhaltsverzeichnis

1;PREFACE;6
2;CONTENTS;20
3;BASIC VARIATIONAL PRINCIPLES OF STATICS AND GEOMETRY IN STRUCTURAL MECHANICS;29
3.1;Preliminaries;29
3.2;Basic integral identity;33
3.3;Various types of stress and strain fields;39
3.4;The general principle of statics and geometry;41
3.5;Final comments to Chapter 1;53
3.6;References;55
4;BASIC VARIATIONAL PRINCIPLES OF STRUCTURAL MECHANICS;57
4.1;Energy space;57
4.2;Lagrange variational principle principle;78
4.3;Castigliano variational principle;82
4.4;Sensitivity of the strain energy to modifications of a system;87
4.5;Generalized forces and generalized displacements;106
4.6;Basic variational principles in problems with initial strains;117
4.7;Statically determinate and statically indeterminate systems;121
4.8;Final comments to Chapter 2;123
4.9;References;124
5;ADDITIONAL VARIATIONAL PRINCIPLES OF STRUCTURAL MECHANICS;126
5.1;Reissner mixed variational principle;126
5.2;Principle of stationarity of the boundary conditions functional;134
5.3;A variational principle for physical relationships;136
5.4;Hu–Washizu mixed variational principle;137
5.5;A generalized mixed variational principle;139
5.6;Gurtin’s variational principle;147
5.7;Geometric interpretation of functionals used in structural mechanic;152
5.8;Final comments to Chapter 3;158
5.9;References;159
6;PARTICULAR CLASSES OF PROBLEMS IN STRUCTURAL MECHANICS – part 1;161
6.1;Variations of the operator formulations in structural mechanics;161
6.2;Spatial elasticity;164
6.3;Plane elasticity;172
6.4;Lengthwise deformation of a straight bar;177
6.5;Bernoulli-type beam on elastic foundation;180
6.6;Timoshenko-type beam on elastic foundation;189
6.7;Planar curvilinear bar, shear ignored;197
6.8;Planar curvilinear bar, shear considered;230
6.9;Final comments to Chapter 4;245
6.10;References;246
7;PARTICULAR CLASSES OF PROBLEMS IN STRUCTURAL MECHANICS – part 2;247
7.1;Thin plate bending — Kirchhoff–Love theory;247
7.2;Static-geometric analogy in the theory of plates;278
7.3;Bending of medium-thickness plates – Reissner’s theory;300
7.4;Some examples;319
7.5;Final comments to Chapter 5;332
7.6;References;336
8;PARTICULAR CLASSES OF PROBLEMS IN STRUCTURAL MECHANICS – part 3;338
8.1;Torsion of solid bars – Saint-Venant’s theory;338
8.2;Thin-walled open-profile bars – a theory by Vlasov;362
8.3;Allowing for shearing in open-profile thin-walled bars;396
8.4;A semi-shear theory of open-profile thin-walled bars;411
8.5;References;417
9;PARTICULAR CLASSES OF PROBLEMS IN STRUCTURAL MECHANICS – part 4;419
9.1;Closed-profile thin-walled bars – a theory by Umanski;419
9.2;Multiple-contour, closed-profile, thin-walled bars;456
9.3;References;480
10;PARTICULAR CLASSES OF PROBLEMS IN STRUCTURAL MECHANICS – part 5;482
10.1;Compound-profile thin-walled bars;482
10.2;A multiple-contour compound profile;499
10.3;Final comments to thin-walled bar theories theories theories theories theories theories theories;507
10.4;References;517
11;THE RITZ METHOD AND ITS MODIFICATIONS;519
11.1;The basic theorem of the Ritz method;519
11.2;The Ritz method in application to mixed functionals;529
11.3;Method of two functionals;538
11.4;References;559
12;VARIATIONAL PRINCIPLES IN SPECTRAL PROBLEMS;561
12.1;Basic concepts. Terminology;561
12.2;The spectral problem as a variational problem;564
12.3;A general spectral problem;591
12.4;The Ritz method in the spectral problem;595
12.5;Final comments to Chapter 10 10 10 10 10;623
12.6;References;625
13;VARIATIONAL PRINCIPLES IN STABILITY/ BUCKLING ANALYSIS;627
13.1;Stability of systems with a finite number of degrees of freedom;628
13.2;Variational description of critical loads;656
13.3;Geometrically nonlinear problems in elasticity;677
13.4;Stability of equilibrium of an elastic body body body body;685
13.5;Stability of equilibrium in particular classes of problems;697
13.6;Mixed functionals in the stability analysis;716
13.7;Final comments to Chapter 11;718
13.8;References;719
14;CONCLUSION;722
15;APPENDIX ;724
16;AUTHOR INDEX;800
17;SUBJECT INDEX1;804