Abstract: This paper is concerned with simultaneous topology and shape optimization of elastic contact problems. The structural optimization problem for an elastic contact problem consists in finding such topology as well as such shape of the boundary of the domain occupied by the body that the normal contact stress is minimized. Shape and topological derivatives formulae of the cost functional...

We propose a versatile approach to computing the effective toughness of heterogeneous media. This approach focusses on the material property independent of the details of the boundary condition. The key idea is what we call a surfing boundary condition, where a steadily propagating crack opening displacement is applied as a boundary condition to a large domain while the crack set is allowed to ...

We show that minimizers of free discontinuity problems with energy dependent on jump integrals and Dirichlet boundary conditions are smooth provided a smallness condition is imposed on data. We examine several examples, including elastic-plastic beam and plate with free yield lines and deformable body with free damage. In all cases there is a gap between the condition for solvability (safe load...

In this article, the problem of time-dependent stress redistribution of a piezomagnetic rotating thick-walled cylinder under an axisymmetric hygro-thermo-magneto-electro-mechanical loading is analyzed analytically for the condition of plane strain. Using the constitutive equations, a differential equation is found in which there are creep strains. Primarily, eliminating creep strains, an analyt...

In this work we deduce an explicit Sommerfeld-type radiation condition able to prove uniqueness for the problem of outgoing wave propagation in isotropic elastic half-spaces with free boundary condition. The expression is obtained by a rigorous asymptotic analysis of the Green’s function associated with this problem. Observe that this is an exterior problem with unbounded frontier. The main dif...

A mathematical model for peristaltic motion of nonlinear viscous flows with elastic free boundaries is introduced. An iterative numerical method is used to solve the free boundary problem. Long wave asymptotic expansion is developed and the zeroth order approximation is used as the numerical initial condition. The existence and uniqueness of the solution for the free boundary equation derived f...

In this paper, we investigate the existence and characterizations of the Fréchet derivatives of the solution to time-harmonic elastic scattering problems with respect to the boundary of the obstacle. Our analysis is based on a technique the factorization of the difference of the far-field pattern for two different scatterers introduced by Kress and Païvarinta to establish Fréchet differentiabil...