INVESTIGATION INTO TOOL SURFACE DESCRIPTION FOR FINITE-ELEMENT ANALYSIS OF 3-DIMENSIONAL SHEET-METAL FORMING PROCESSES

A general method for the mathematical description of arbitrarily-shape d tool surfaces is proposed by introducing the parametric and non-para metric patch approaches. The cubic Ferguson patch is employed to descr ibe the tool surface in the parametric patch approach and an efficient contact search algorithm is suggested to make this parametric patch a pproach more realistic for the FE analysis. The non-parametric patch a pproach introduces a cubic blending function as in the case of the par ametric patch approach to allow C1 continuity. In the approach, an arr ay of equi-spaced points is required to construct the whole tool surfa ce. Computations are carried out for some complex sheet forming exampl es including actual auto-body panel to verify the validity and the rob ustness of the developed contact search algorithms.