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Variational inequalities in plasticity with strain-hardening - equilibrium finite element approach

Zdeněk Kestřánek (1986)

Aplikace matematiky

The incremental finite element method is applied to find the numerical solution of the plasticity problem with strain-hardening. Following Watwood and Hartz, the stress field is approximated by equilibrium triangular elements with linear functions. The field of the strain-hardening parameter is considered to be piecewise linear. The resulting nonlinear optimization problem with constraints is solved by the Lagrange multipliers method with additional variables. A comparison of the results obtained...

Variational-hemivariational inequalities in nonlinear elasticity. The coercive case

Panagiotis D. Panagiotopoulos (1988)

Aplikace matematiky

Existence of a solution of the problem of nonlinear elasticity with non-classical boundary conditions, when the relationship between the corresponding dual quantities is given in terms of a nonmonotone and generally multivalued relation. The mathematical formulation leads to a problem of non-smooth and nonconvex optimization, and in its weak form to hemivariational inequalities and to the determination of the so called substationary points of the given potential.

Von Kármán equations. III. Solvability of the von Kármán equations with conditions for geometry of the boundary of the domain

Július Cibula (1991)

Applications of Mathematics

Solvability of the general boundary value problem for von Kármán system of nonlinear equations is studied. The problem is reduced to an operator equation. It is shown that the corresponding functional of energy is coercive and weakly lower semicontinuous. Then the functional of energy attains absolute minimum which is a variational solution of the problem.

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