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 over the past few years at ENS Cachanʹs laboratory, this technique is based on the strict building of admissible displacement and stress "elds. This building process, validated for several types of 2-D and 3-D straight "nite elements (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 "eld by solving a high-degree "nite element problem on each element. This technique, as implemented in our error computation code, which is associated both with a method of computing optimal sizes and with meshers able to respect a size map, allows us to optimize 2-D and 3-D meshes. Examples demonstrate the capabilities of the proposed method. Copyright ( 1999 John Wiley & Sons, Ltd.