On the numerical treatment of the contact problem.
On the optimal design of elastic shafts
On the Signorini problem with friction in linear thermoelasticity: The quasi-coupled 2D-case
The Signorini problem with friction in quasi-coupled linear thermo-elasticity (the 2D-case) is discussed. The problem is the model problem in the geodynamics. Using piecewise linear finite elements on the triangulation of the given domain, numerical procedures are proposed. The finite element analysis for the Signorini problem with friction on the contact boundary of a polygonal domain is given. The rate of convergence is proved if the exact solution is sufficiently regular.
On the solution of boundary value problems for sandwich plates
A mathematical model of the equilibrium problem of elastic sandwich plates is established. Using the theory of inequalities of Korn's type for a general class of elliptic systems the existence and uniqueness of a variational solution is proved.
On the two-step iterative method of solving frictional contact problems in elasticity
A class of contact problems with friction in elastostatics is considered. Under a certain restriction on the friction coefficient, the convergence of the two-step iterative method proposed by P.D. Panagiotopoulos is proved. Its applicability is discussed and compared with two other iterative methods, and the computed results are presented.
Operational Methods in the Environment of a Computer Algebra System
This article presents the principal results of the doctoral thesis “Direct Operational Methods in the Environment of a Computer Algebra System” by Margarita Spiridonova (Institute of mathematics and Informatics, BAS), successfully defended before the Specialised Academic Council for Informatics and Mathematical Modelling on 23 March, 2009.The presented research is related to the operational calculus approach and its representative applications. Operational methods are considered, as well as their...
Optimal control problems for variational inequalities with controls in coefficients and in unilateral constraints
We deal with an optimal control problem for variational inequalities, where the monotone operators as well as the convex sets of possible states depend on the control parameter. The existence theorem for the optimal control will be applied to the optimal design problems for an elasto-plastic beam and an elastic plate, where a variable thickness appears as a control variable.
Optimum composite material design
Partial Regularity for Certain classes for Polyconvex functionals Related to Nonlinear Elasticity.
Quasiconvex functions, and two elastic wells
Quelques remarques sur les notions de rang convexité et de polyconvexité en dimensions 2 et 3
Rayleigh wave scattering at the foot of a mountain.
Recent advancements in fractal geometric-based nonlinear time series solutions to the micro-quasistatic thermoviscoelastic creep for rough surfaces in contact.
Regularity for Signorini's Problem in linear eleasticity.
Reinforcement problems in the calculus of variations
Relaxation et existence pour le problème des matériaux à blocage
Relaxation of vectorial variational problems
Multidimensional vectorial non-quasiconvex variational problems are relaxed by means of a generalized-Young-functional technique. Selective first-order optimality conditions, having the form of an Euler-Weiestrass condition involving minors, are formulated in a special, rather a model case when the potential has a polyconvex quasiconvexification.
Remarks on regularity up to the boundary for solutions to variational problems in plasticity theory
Rheological models and hysteresis effects
Shape optimization in contact problems. Approximation and numerical realization