Displaying similar documents to “On the existence and uniqueness of solution and some variational principles in linear theories of elasticity with couple-stresses. I: Cosserat continuum”

On the existence and uniqueness of solution and some variational principles in linear theories of elasticity with couple-stresses. II. Mindlin's elasticity with microstructure and the first strain-gradient theory

Ivan Hlaváček, Miroslav Hlaváček (1969)

Aplikace matematiky

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A weak solution to the boundary-value problems both in the Mindlin's theory of elasticity with microstructure and in the first strain-gradient theory is defined for the statical loading of bounded, inhomogeneous and anisotropic bodies. Its existence, uniqueness and continuous dependence upon the given data is proved and the principles of minimum potential energy and minimum complementary energy are establshed.

Variational principles in the linear theory of elasticity for general boundary conditions

Ivan Hlaváček (1967)

Aplikace matematiky

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Mixed boundary-value problem of the classical theory of elasticity is considered, where not only displacements and tractions are prescribed on some parts of the boundary, but also conditions of contact and elastic supports for normal and tangential directions to the boundary surface separately. Classical variational principles are derived using functional analysis methods, especially methods of Hilbert space. Furthermore, generalized variational principles and bilateral estimates of...