Sensitivity analysis of solutions for a system of generalized parametric nonlinear quasivariational inequalities.
Sensitivity analysis of solutions to a class of quasi-variational inequalities
We provide a sensitivity result for the solutions to the following finite-dimensional quasi-variational inequality when both the operator and the convex are perturbed. In particular, we prove the Hölder continuity of the solution sets of the problems perturbed around the original problem. All the results may be extended to infinite-dimensional (QVI).
Sensitivity of optimal solutions to control problems for systems described by hemivariational inequalities
Sensitivity of optimal solutions to control problems for systems described by hemivariational inequalities
Shape and topological sensitivity analysis in domains with cracks
The framework for shape and topology sensitivity analysis in geometrical domains with cracks is established for elastic bodies in two spatial dimensions. The equilibrium problem for the elastic body with cracks is considered. Inequality type boundary conditions are prescribed at the crack faces providing a non-penetration between the crack faces. Modelling of such problems in two spatial dimensions is presented with all necessary details for further applications in shape optimization in structural...
Shape optimization in contact problems. Approximation and numerical realization
Shape optimization in contact problems based on penalization of the state inequality
The paper deals with the approximation of optimal shape of elastic bodies, unilaterally supported by a rigid, frictionless foundation. Original state inequality, describing the behaviour of such a body is replaced by a family of penalized state problems. The relation between optimal shapes for the original state inequality and those for penalized state equations is established.
Shape optimization in two-dimensional elasticity by the dual finite element method
Shape optimization of an elasto-plastic body for the model with strain- hardening
The state problem of elasto-plasticity (for the model with strain-hardening) is formulated in terms of stresses and hardening parameters by means of a time-dependent variational inequality. The optimal design problem is to find the shape of a part of the boundary such that a given cost functional is minimized. For the approximate solutions piecewise linear approximations of the unknown boundary, piecewise constant triangular elements for the stress and the hardening parameter, and backward differences...
Shape optimization of elastoplastic bodies obeying Hencky's law
A minimization of a cost functional with respect to a part of the boundary, where the body is fixed, is considered. The criterion is defined by an integral of a yield function. The principle of Haar-Kármán and piecewise constant stress approximations are used to solve the state problem. A convergence result and the existence of an optimal boundary is proved.
Singular perturbations in optimal control problem with application to nonlinear structural analysis
This paper concerns an optimal control problem of elliptic singular perturbations in variational inequalities (with controls appearing in coefficients, right hand sides and convex sets of states as well). The existence of an optimal control is verified. Applications to the optimal control of an elasto-plastic plate with a small rigidity and with an obstacle are presented. For elasto-plastic plates with a moving part of the boundary a primal finite element model is applied and a convergence result...
Smoothness for systems of degenerate variational inequalities with natural growth
We extend a regularity theorem of Hildebrandt and Widman [3] to certain degenerate systems of variational inequalities and prove Hölder-continuity of solutions which are in some sense stationary.
Sobolev regularity via the convergence rate of convolutions and Jensen’s inequality
We derive a new criterion for a real-valued function to be in the Sobolev space . This criterion consists of comparing the value of a functional with the values of the same functional applied to convolutions of with a Dirac sequence. The difference of these values converges to zero as the convolutions approach , and we prove that the rate of convergence to zero is connected to regularity: if and only if the convergence is sufficiently fast. We finally apply our criterium to a minimization...
Solution behaviour for parameter-dependent quasi-variational inequalities
Solution of a finite-dimensional problem with -mappings and diagonal multivalued operators.
Solution of degenerate parabolic variational inequalities with convection
Degenerate parabolic variational inequalities with convection are solved by means of a combined relaxation method and method of characteristics. The mathematical problem is motivated by Richard’s equation, modelling the unsaturated – saturated flow in porous media. By means of the relaxation method we control the degeneracy. The dominance of the convection is controlled by the method of characteristics.
Solution of degenerate parabolic variational inequalities with convection
Degenerate parabolic variational inequalities with convection are solved by means of a combined relaxation method and method of characteristics. The mathematical problem is motivated by Richard's equation, modelling the unsaturated – saturated flow in porous media. By means of the relaxation method we control the degeneracy. The dominance of the convection is controlled by the method of characteristics.
Solution of Signorini's contact problem in the deformation theory of plasticity by secant modules method
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.
Solution set in a special case of generalized Nash equilibrium games
A special class of generalized Nash equilibrium problems is studied. Both variational and quasi-variational inequalities are used to derive some results concerning the structure of the sets of equilibria. These results are applied to the Cournot oligopoly problem.
Solvability and multiplicity results for variational inequalities