Variational Methods in the Theory of Elasticity

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Department of Mathematics

Synopsis:

The subject is focused on variational formulations and solutions of fundamental static and quasistatic problems in the mathematical theory of elasticity. The lectures are devoted to boundary value problems for elliptic equations with emphasis on the problems of the existence and uniqueness of solutions. The main topics of the subject: Stress tensor, equations of equilibrium, strain tensor, equations of the compatibility of strain, Hooke’s law, the spaces of functions with finite energy, classical and variational formulations of boundary value problems in the theory of elasticity, Rellich's theorem, coerciveness of strains, Korn's inequality, coercive and weakly lower semi-continuous functionals, differentiability in the Gateaux sense, solvability of problems in the theory of elasticity, variational principle, elasto-inelastic bodies, models with internal state variables

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