We consider multigrid methods for problems in linear elasticity which are robust with respect to the Poisson ratio. Therefore, we consider mixed approximations involving the displacement vector and the pressure, where the pressure is approximated by discontinuous functions. Then, the pressure can be eliminated by static condensation. The method is based on a saddle point smoother which was intr...

A Galerkin finite element method for the membrane elasticity problem on a meshed surface is constructed by using two-dimensional elements extended into three dimensions. The membrane finite element model is established using the intrinsic approach suggested by Delfour and Zolésio [8].

A ctitious domain method based on boundary Lagrange multipliers is proposed for linear elasticity problems in two dimensional domains. The solution of arising saddle-point problem is obtained iteratively using MINRES method with a positive deenite block diagonal preconditioner which is based on a fast direct solver for diiusion problems. Numerical experiments demonstrate the behavior of conside...

The flexibility of two-dimensional (2D) materials enables static and dynamic ripples that are known to cause lateral contraction, shrinking the material boundary. However, limits 2D materials' expansion unknown. Therefore, here we discuss intrinsic modified by compressive line defects. Using thin sheet elasticity theory sequential multiscale modeling, find is inevitably limited onset rippling. ...

Under some generic assumptions we prove the unique continuation property for the two-dimensional inhomogeneous anisotropic elasticity system. Having established the unique continuation property, we then investigate the inverse problem of reconstructing the inclusion or cavity embedded in a plane elastic body with inhomogeneous anisotropic medium by infinitely many localized boundary measurements.

A solution for a class of two-dimensional elasticity problems concerning an isotropic body with an arc crack in its interior is obtained in terms of an integral taken around the exterior boundary of the body. A numerical procedure for solving this integral equation is outlined and numerical results for a test problem are given.