Optimization of finite element grids using shape sensitivity analysis in terms of nodal positions

Abstract

An approach of finite element grid optimization is proposed as an application of the shape design sensitivity analysis. Change of the mesh is described by design velocity fields that can be simply obtained by a piecewise linear interpolation from the nodal positions. For a given topology of finite elements mesh? the strain energy is maximized for static problems and the eigenvalues are minimized for eigenvalue problems with respect to the nodal positions. Numerical examples for the Timoshenko beams and the Mindlin plates are obtained and the proposed approach is shown to be a feasible method that can be used for shape or configuration designs where large distortion of meshes is often involved.