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Shape optimization of elasto-plastic axisymmetric bodies

Ivan Hlaváček (1991)

Applications of Mathematics

A minimization of a cost functional with respect to a part of a boundary is considered for an elasto-plastic axisymmetric body obeying Hencky's law. The principle of Haar-Kármán and piecewise linear stress approximations are used to solve the state problem. A convergence result and the existence of an optimal boundary is proved.

Solution of Signorini's contact problem in the deformation theory of plasticity by secant modules method

Jindřich Nečas, Ivan Hlaváček (1983)

Aplikace matematiky

A problem of unilateral contact between an elasto-plastic body and a rigid frictionless foundation is solved within the range of the so called deformation theory of plasticity. The weak solution is defined by means of a variational inequality. Then the so called secant module (Kačanov's) iterative method is introduced, each step of which corresponds to a Signorini's problem of elastoplastics. The convergence of the method is proved on an abstract level.

Sottopotenziali energia libera per l'isteresi meccanica

Claudio Giorgi (1985)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

This paper deals with free-energy lower-potentials for some rate-independent one-dimensional models of isothermal finite elastoplasticity proposed in [1]. Extending the thermodynamic arguments of Coleman and Owen [3] to large deformations, the existence, non-uniqueness and regularity of free-energy as function of state are deduced rather than assumed. This approach, along with some optimal control techniques, enables us to construct maximum and minimum free-energy functions and a wide class of differentiable...

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