Mathematical Models for Elastic Structures Book

	Preface
	Introduction	1
Ch. I	Basic Concepts
1	Density, Motion, and Temperature	7
2	Balance Equations	11
3	Constitutive Equations	20
4	The Search for Solutions	31
5	The Notion of a Loading Device	44
6	An Example of Alternative Modeling	51
Ch. II	Rod Theories: Three-dimensional Approach
7	Geometrical Properties of Rods	61
8	Approximation of Three-dimensional Equations	64
9	Rod Problems in Linear Elasticity	70
10	Uniformly Loaded Beams (Michell's Theory)	76
11	Timoshenko's Correction	81
12	Vlasov's Theory for Thin-walled Beams	93
13	The Influence of Concentrated Loads	100
14	The Influence of Curvature	106
15	The Influence of Initial Twist	117
16	The Energy of an Elastic Rod	125
17	The Influence of Large Strains	138
18	Justification of the One-dimensional Model	158
Ch. III	Rod Theories: Director Approach
19	Rods as Oriented Bodies	162
20	Kirchhoff's Theory	167
21	Solutions for More General Loads	175
22	Nonclassical Problems for Rods	184
23	Initially Curved Rods	202
24	The Stability of Rods	218
25	Dynamical Problems for Rods	248
26	Kirchhoff's Problem for Nonlinearity Elastic Rods	267
27	Dynamical Problems in Nonlinear Rods	289
Ch. IV	Theories of Cables
28	Equilibrium Equations	303
29	Classical Solutions for Linearly Elastic Strings	306
30	Influence of Friction	316
31	Equilibrium States for Nonlinear Elastic Strings	322
32	Inverse Problems in Strings	328
33	Unilateral Problems for Strings	336
34	Dynamical Problems for Strings	340
35	Peeling and Slipping	357
Ch. V	Theories of Membranes
36	Constitutive Properties of Membranes	366
37	Plane Membranes	367
38	Theories of Networks	385
39	Membranes Stretched against an Obstacle	392
40	Curved Membranes	404
41	Stability of Curved Membranes	414
42	Dynamic Behavior of Membranes	422
43	Detachment and Suturing of Membranes	426
44	Optimization of Membranes	433
Ch. VI	Theories of Plates
45	The Equations of Linear Theory	451
46	Theories of Thick Plates	460
47	Influence of Varying Thickness	477
48	The Problem of Plate Optimization	485
49	Paradoxes in the Theories of Plates	498
50	Foppl-Karman Theory	501
51	Berger's and Reissner's Equations	522
52	The Wrinkling of Plates	531
53	Buckled States of Plates in Nonlinear Elasticity	538
Ch. VII	Theories of Shells
54	Geometric Definitions and Mechanical Assumptions	547
55	Equations Deduced from Three-dimensional Theory	555
56	The Solvability of the Equations of Shell Theory	563
57	Estimates on Solutions	577
58	Closed Solutions for Shells	593
59	Buckling of Shells	607
60	Asymptotic Analysis of Shells	620
61	The Influence of Constitutive Nonlinearities	625
62	Dynamical Problems for Shells	647
	References	654
	Index of Authors Cited	667
	Index	671