Displaying similar documents to “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”

On the existence and uniqueness of solution and some variational principles in linear theories of elasticity with couple-stresses. I: Cosserat continuum

Ivan Hlaváček, Miroslav Hlaváček (1969)

Aplikace matematiky

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A weak (generalized) solution to the boundary-value problems in Cosserat continuum is defined. Its existence, uniqueness and continuous dependence upon the given data is proved for the statical loading of bounded, inhomogeneous and anisotropic bodies. Principles of minimum potential energy, of minimum complementary energy and some generalized variational principles are established.

Extended Hashin-Shtrikman variational principles

Petr Procházka, Jiří Šejnoha (2004)

Applications of Mathematics

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Internal parameters, eigenstrains, or eigenstresses, arise in functionally graded materials, which are typically present in particulate, layered, or rock bodies. These parameters may be realized in different ways, e.g., by prestressing, temperature changes, effects of wetting, swelling, they may also represent inelastic strains, etc. In order to clarify the use of eigenparameters (eigenstrains or eigenstresses) in physical description, the classical formulation of elasticity is presented,...

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...