Control of analyses with isoparametric elements in both 2-D and 3-D

This paper presents an extension of the computation method for the error in the constitutive relation to include isoparametric elements. Developed ove r the past few years at ENS Cachan's laboratory, this technique is based on the strict building of admissible displacement and stress fields. This bui lding process, validated for several types of 2-D and 3-D straight finite e lements (triangles and quadrilaterals, tetrahedra and hexahedra), cannot be extended to isoparametric elements. For such elements, the method consists of seeking an approximation of the statically admissible stress field by s olving a high-degree finite element problem on each element. This technique , as implemented in our error computation code, which is associated both wi th a method of computing optimal sizes and with meshers able to respect a s ize map, allows us to optimize 2-D and 3-D meshes. Examples demonstrate the capabilities of the proposed method. Copyright (C) 1999 John Wiley & Sons, Ltd.