On the numerical solution of the multidimensional singular integrals and integral equations, used in the theory of linear viscoelasticity.
On the numerical treatment of the contact problem.
On the optimal control problem governed by the equations of von Kármán. II. Mixed boundary conditions
A control of the system of Kármán's equations for a thin elastic plate is considered. Existence of an optimal transversal load and optimal stress function, respectively, is proven. The set of admissible functions is chosen in a way guaranteeing the unique solvability of the state problem. The differentiability of the state function with respect to the control variable, uniqueness of the optimal control and some necessary conditions of optimality are discussed.
On the optimal control problem governed by the equations of von Kármán. I. The homogeneous Dirichlet boundary conditions
A control of the system of nonlinear Kármán's equations for a thin elastic plate with clamped edge is considered. The transversal loading plays the role of the control variable. The set of admissible controls is chosen in a way guaranteeing the unique solvability of the state function with respect to the control variable is proved. A disscussion of uniqueness of the optimal control and some necessary conditions of optimality are presented.
On the optimal control problem governed by the equations of von Kármán. III. The case of an arbitrary large perpendicular load
We shall deal with an optimal control problem for the deffection of a thin elastic plate. We consider the perpendicular load on the plate as the control variable. In contrast to the papers [1], [2], arbitrarily large loads are edmitted. As the unicity of a solution of the state equation is not guaranteed, we consider the cost functional defined on the set of admissible controls and states, and the state equation plays the role of the constraint. The existence of an optimal couple (i.e., control...
On the optimal design of elastic shafts
On the problem of determining the parameters of a layered elastic medium and an impulse source.
On the propagation of acceleration waves in thermoelastic micropolar medias.
On the propagation of plane waves at a pure shear interface.
On the propagation of Scholte-Gogoladze surface waves along the interface of arbitrary shape between an elastic body and a fluid.
On the propagation of seismic waves in block fluid media.
On the quasiconvex exposed points
The notion of quasiconvex exposed points is introduced for compact sets of matrices, motivated from the variational approach to material microstructures. We apply the notion to give geometric descriptions of the quasiconvex extreme points for a compact set. A weak version of Straszewicz type density theorem in convex analysis is established for quasiconvex extreme points. Some examples are examined by using known explicit quasiconvex functions.
On the quasiconvex exposed points
The notion of quasiconvex exposed points is introduced for compact sets of matrices, motivated from the variational approach to material microstructures. We apply the notion to give geometric descriptions of the quasiconvex extreme points for a compact set. A weak version of Straszewicz type density theorem in convex analysis is established for quasiconvex extreme points. Some examples are examined by using known explicit quasiconvex functions.
On the rank-one-convexity domain of the Saint Venant-Kirchhoff stored energy function
On the regularity of solutions of a thermoelastic system under noncontinuous heating regimes. III
In this part we weaken the sufficient condition to obtain the stresses continuous and bounded in the threedimensional case, and we treat a certain coupled system.
On the regularity of solutions of a thermoelastic system under noncontinuous heating regimes
The continuity and boundedness of the stress to the solution of the thermoelastic system is studied first for the linear case on a strip and then for the twodimensional model involving nonlinearities, noncontinuous heating regimes and isolated boundary nonsmoothnesses of the heated body.
On the regularity of solutions of a thermoelastic system under noncontinuous heating regimes. II
A quasilinear noncoupled thermoelastic system is studied both on a threedimensional bounded domain with a smooth boundary and for a generalized model involving the influence of supports. Sufficient conditions are derived under which the stresses are bounded and continuous on the closure of the domain.
On the representation of effective energy densities
On the Representation of Effective Energy Densities
We consider the question raised in [1] of whether relaxed energy densities involving both bulk and surface energies can be written as a sum of two functions, one depending on the net gradient of admissible functions, and the other on net singular part. We show that, in general, they cannot. In particular, if the bulk density is quasiconvex but not convex, there exists a convex and homogeneous of degree 1 function of the jump such that there is no such representation.
On the search for singularities in incompressible flows
In these notes we give some examples of the interaction of mathematics with experiments and numerical simulations on the search for singularities.