A new formulation for the sensitivity analysis of three-dimensional finite elements is presented. The method is based upon the implicit differentiation and calculates all parts of deformed element stiffness matrix. These parts are found by a rather simple factoring technique. The design element procedure along with the isoparametric concept are used in this presentation. Computer coding of the method is compatible with the finite element programming technique and can be easily used in structural optimization. Numerical examples, which show the validity as well as application of the formulation, are presented. According to the results, the new formulation calculates the sensitivity analysis quickly.

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