On a new class of elastic deformations not allowing for cavitation
On a problem of potential wells.
On a transmission problem in elasticity
The transmission problem for the reduced Navier equation of classical elasticity, for an infinitely stratified scatterer, is studied. The existence and uniqueness of solutions is proved. Moreover, an integral representation of the solution is constructed, for both the near and the far field.
On an elasto-dynamic evolution equation with non dead load and friction
In this paper, we are interested in the dynamic evolution of an elastic body, acted by resistance forces depending also on the displacements. We put the mechanical problem into an abstract functional framework, involving a second order nonlinear evolution equation with initial conditions. After specifying convenient hypotheses on the data, we prove an existence and uniqueness result. The proof is based on Faedo-Galerkin method.
On an inequality in nonlinear thermoelasticity.
On an interaction of two elastic bodies: analysis and algorithms
The paper deals with existence and uniqueness results and with the numerical solution of the nonsmooth variational problem describing a deflection of a thin annular plate with Neumann boundary conditions. Various types of the subsoil and the obstacle which influence the plate deformation are considered. Numerical experiments compare two different algorithms.
On an unconventional variational method for solving the problem of linear elasticity with Neumann or periodic boundary conditions
A new variational formulation of the linear elasticity problem with Neumann or periodic boundary conditions is presented. This formulation does not require any quotient spaces and is advisable for finite element approximations.
On asymptotics of solutions and eigenvalues of the boundary value problem with rapidly alternating boundary conditions for the system of elasticity
Boundary value problems for the system of linear elasticity with rapidly alternating boundary conditions are studied and asymptotic behavior of solutions is considered when a small parameter, which defines the oscillation of the boundary conditions, tends to zero. Estimates for the difference between such solutions and solutions of the limit problem are given.
On dual integral equations arising in problems of bending of anisotropic plates.
On dynamics of viscoelastic multidimensional medium with variable boundary.
On general boundary value problems and duality in linear elasticity. II
The present part of the paper completes the discussion in Part I in two directions. Firstly, in Section 5 a number of existence theorems for a solution to Problem III (principle of minimum potential energy) is established. Secondly, Section 6 and 7 are devoted to a discussion of both the classical and the abstract approach to the duality theory as well as the relationship between the solvability of Problem III and its dual one.
On general boundary value problems and duality in linear elasticity. I
The equilibrium state of a deformable body under the action of body forces is described by the well known conditions of equilibrium, the straindisplacement relations, the constitutive law of the linear theory and the boundary conditions. The authors discuss in detail the boundary conditions. The starting point is the general relation between the vectors of stress and displacement on the boundary which can be expressed in terms of a subgradient relation. It is shown that this relation includes as...
On I. Vekua's method in the theory of elastic mixtures.
On integration of differential equations in elastostatics through determination of the mean stress
On Ishlinskij's model for non-perfectly elastic bodies
The main goal of the paper is to formulate some new properties of the Ishlinskii hysteresis operator , which characterizes e.g. the relation between the deformation and the stress in a non-perfectly elastic (elastico-plastic) material. We introduce two energy functionals and derive the energy inequalities. As an example we investigate the equation describing the motion of a mass point at the extremity of an elastico-plastic spring.
On Neumann's problem for a quasilinear differential system of the finite elastostatics type. Local theorems of existence and uniqueness
On numerical approximation of an optimal control problem in linear elasticity.
On numerical solution of weight minimization of elastic bodies weakly supporting tension
Shape optimization of a two-dimensional elastic body is considered, provided the material is weakly supporting tension. The problem generalizes that of a masonry dam subjected to its weight and to the hydrostatic pressure. A part of the boundary has to be found so as to minimize a given cost functional. The numerical realization using a penalty method and finite element technique is presented. Some typical results are shown.
On Reissner's variational theorem for boundary values in linear elasticity
On semiconvexity properties of rotationally invariant functions in two dimensions
Let be a function defined on the set of all by matrices that is invariant with respect to left and right multiplications of its argument by proper orthogonal matrices. The function can be represented as a function of the signed singular values of its matrix argument. The paper expresses the ordinary convexity, polyconvexity, and rank 1 convexity of in terms of its representation