Auxiliary Propositions. Korn's Inequalities. Boundary Value Problems of Linear Elasticity. Perforated Domains with a Periodic Structure. Extension Theorems. Strong G -Convergence of Elasticity Operators. Homogenization of the System of Linear Elasticity. Composites and Perforated Materials. Homogenization of Stratified Structures.
Spectral Problems. Some Theorems from Functional Analysis.
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Spectral Problems for Abstract Operators. Free Vibrations of Bodies with Concentrated Masses. Homogenization of Eigenvalues of Ordinary Differential Operators.
This monograph is based on research undertaken by the authors during the last ten years. The main part of the work deals with homogenization problems in elasticity as well as some mathematical problems related to composite and perforated elastic materials. This study of processes in strongly non-homogeneous media brings forth a large number of purely mathematical problems which are very important for applications. Although the methods suggested deal with stationary problems, some of them can be extended to non-stationary equations.
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Cited By Google Scholar. Rev September Farazmand and T. Rev November Technol January, Theory of Matrix Structural Analysis J.
Advanced Strength of Materials J. Non-Linear Elastic Deformations R. Methods of Analytical Dynamics Leonard Meirovitch. Bubbles, Drops, and Particles Roland Clift. Impact: the Theory Goldsmith. Stochastic Finite Elements Roger G. Methods of Structural Safety H. Thermodynamices Elias P.
Table of contents Preface Brief glossary of conventions and notations A point of departure 1. Kinematics 2. Balance laws 3. Elastic materials 4. Boundary value problems 5.
Fresnel's Elasticity Surface
Constitutive inequalities 6. The role of geometry and functional analysis 1.
Geometry and kinematics of bodies 1. Balance principles 2. Constitutive theory 3. Linearization 4. Hamiltonian and variational principles 5. Methods of functional analysis in elasticity 6. Selected topics in bifurcation theory 7.