A new algorithm is presented for performing mesh rezoning on isoparametric elements used in simulations of non-linear deformation processes. The method uses techniques from elimination theory to solve the parametric inversion problem for each node on the new, undistorted mesh. These parameter values are then used in the elemental shape functions to transfer the nodal state variables from the distorted mesh to each node in the new mesh by interpolation. The method has been implemented for bilinear and biquadratic elements. The method is based on fundamental finite element approximations, since the interpolation functions which define the element are also used to perform rezoning.
- For each node (or Gauss integration point) i in the new mesh, locate the element I in which it 2. 'Transfer the values of the state variables to that node using the values at the nodes, i l , il, i,, Several authors have reported techniques for performing mesh rezoning. Most of the methods are based on computing some form of weighted average to determine the values of derived state variables (such as stress, strain, etc.).lp3 Cheng and Kikuchi4 also use a variation of this method and advocate a least squares solution for higher-order elements. resides in the old mesh. i,, . . . , of element I .