THE S-VERSION OF THE FINITE-ELEMENT METHOD

A methodology to improve the quality of the finite element calculations in the regions of unacceptable errors has been developed. Unlike the existing adaptive techniques, where either the mesh is refined (h-version), or the polynomial order is increased (p-version), or a combination of both (h-p version), the s-version increases the resolution by superimposing additional mesh(es) of higher-order hierarchical elements. C0 continuity of the displacement field is maintained by imposing homogeneous boundary conditions on the superimposed field in the portion of the boundary which is not contained within the boundary of the problem. The superimposed regions can be of arbitrary shape, unlimited by the problem geometry, boundary conditions and the underlying mesh topography. Numerical experiments for linear problems involving singularities and smooth solutions as well as the shear banding problem in viscoplastic solid, are presented to validate the present formulation.