Mathematical models for elastic structures /
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| Main Author: | |
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| Format: | Book |
| Language: | English |
| Published: |
Cambridge :
Cambridge University Press,
2005.
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| Edition: | Pbk. version. |
| Subjects: |
Table of Contents:
- Machine generated contents note: ch. I Basic Concepts
- 1.Density, Motion, and Temperature
- 2.Balance Equations
- 3.Constitutive Equations
- 4.The Search for Solutions
- 5.The Notion of a Loading Device
- 6.An Example of Alternative Modeling
- ch. II Rod Theories: Three-dimensional Approach
- 7.Geometrical Properties of Rods
- 8.Approximation of Three-dimensional Equations
- 9.Rod Problems in Linear Elasticity
- 10.Uniformly Loaded Beams (Michell's Theory)
- 11.Timoshenko's Correction
- 12.Vlasov's Theory for Thin-walled Beams
- 13.The Influence of Concentrated Loads
- 14.The Influence of Curvature
- 15.The Influence of Initial Twist
- 16.The Energy of an Elastic Rod
- 17.The Influence of Large Strains
- 18.Justification of the One-dimensional Model
- ch. III Rod Theories: Director Approach
- 19.Rods as Oriented Bodies
- 20.Kirchhoff's Theory
- 21.Solutions for More General Loads
- 22.Nonclassical Problems for Rods
- 23.Initially Curved Rods
- Contents note continued: 24.The Stability of Rods
- 25.Dynamical Problems for Rods
- 26.Kirchhoff's Problem for Nonlinearly Elastic Rods
- 27.Dynamical Problems in Nonlinear Rods
- ch. IV Theories of Cables
- 28.Equilibrium Equations
- 29.Classical Solutions for Linearly Elastic Strings
- 30.Influence of Friction
- 31.Equilibrium States for Nonlinear Elastic Strings
- 32.Inverse Problems in Strings
- 33.Unilateral Problems for Strings
- 34.Dynamical Problems for Strings
- 35.Peeling and Slipping
- ch. V Theories of Membranes
- 36.Constitutive Properties of Membranes
- 37.Plane Membranes
- 38.Theories of Networks
- 39.Membranes Stretched against an Obstacle
- 40.Curved Membranes
- 41.Stability of Curved Membranes
- 42.Dynamic Behavior of Membranes
- 43.Detachment and Suturing of Membranes
- 44.Optimization of Membranes
- ch. VI Theories of Plates
- 45.The Equations of Linear Theory
- 46.Theories of Thick Plates
- 47.Influence of Varying Thickness
- Contents note continued: 48.The Problem of Plate Optimization
- 49.Paradoxes in the Theories of Plates
- 50.Foppl-Karman Theory
- 51.Berger's and Reissner's Equations
- 52.The Wrinkling of Plates
- 53.Buckled States of Plates in Nonlinear Elasticity
- ch. VII Theories of Shells
- 54.Geometric Definitions and Mechanical Assumptions
- 55.Equations Deduced from Three-dimensional Theory
- 56.The Solvability of the Equations of Shell Theory
- 57.Estimates on Solutions
- 58.Closed Solutions for Shells
- 59.Buckling of Shells
- 60.Asymptotic Analysis of Shells
- 61.The Influence of Constitutive Nonlinearities
- 62.Dynamical Problems for Shells.