Stability and Nonlinear Solid Mechanics

  • ID: 2172806
  • Book
  • 416 Pages
  • John Wiley and Sons Ltd
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Although the problem of stability and bifurcation is well understood in Mechanics, very few treatises have been devoted to stability and bifurcation analysis in dissipative media, in particular with regard to present and fundamental problems in Solid Mechanics such as plasticity, fracture and contact mechanics. Stability and Nonlinear Solid Mechanics addresses this lack of material, and proposes to the reader not only a unified presentation of nonlinear problems in Solid Mechanics, but also a complete and unitary analysis on stability and bifurcation problems arising within this framework. Main themes include:

∗ elasticity and plasticity problems in small and finite deformation

∗ general concepts of stability and bifurcation and basic results

∗ elastic buckling

∗ plastic buckling of structures

∗ standard dissipative systems obeying maximum dissipation.

These themes are developed in 20 chapters and illustrated by various analytical and numerical results. The coverage given here extends beyond the limited boundaries of previous works, resulting in a text of lasting interest and value to postgraduate students, researchers and practitioners working in mechanical, civil and aerospace engineering, as well as materials science.
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Basic Elements of Statics and Dynamics.

Constitutive Relations and Thermodynamics.

Elements of Mathematics.

Elastic Problems in Small Deformation.

Elastic–Plastic Problems in Small Deformaton.

Stability of an Equilibrium.

Static and Dynamic Bifurcation.

Bifurcation Analysis of Conservative Systems.

Buckling of Elastic Structures.

Complements of Conservative Systems.

Plastic Buckling of Beams.

Rate Problems and Hill′s Criteria.

Plastic Bifurcation.

Materials and Structures in Finite Deformation.

Standard Dissipative Systems.

Stability of a Quasi–Static Evolution.

Crack Propagation and Stability.

Plane Cracks.

Contact with Friction.

Nonlinear Numerical Analysis.

References.

Index.
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Quoc Son Nguyen
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