Method of Error Elimination for a Class of Semi-Analytical Sensitivity Analysis Problems

Abstract

The semi-analytical method of sensitivity analysis [1–3] of finite element discretized structures is indispensable in a computer aided engineering environment for interactive design and optimization. However, it has been shown [3–10] that the method may exhibit serious inaccuracies when applied to structures modeled by beam, plate, shell, and Hermite elements. The inaccuracy of primary concern is associated with the dependence of design sensitivity error on finite element mesh refinement [3–10], but also errors subject to the pertubation of design variables may manifest themselves. Truncation errors due to conditioning of algebra and limited computer precision will not be considered here. In this paper we present a new method developed in [10] for elimination of inaccuracy in semi-analytical sensitivity analysis for a class of problems. The method is advantageous from the point of view that problem dependent, exact error analysis is not required, and that it both eliminates the dependence of the error of the sensitivity on finite element mesh refinement and on design variable pertubation. Also, the method is computationally inexpensive because the differentation of the stiffness components can be exclucively carried out via a forward difference scheme, provided that a set of simple correction factors has been computed. The correction factors may be determined once and for all for a given type of finite element, or as an initial step of the procedure.