Accurate displacement derivatives for structural optimization using approximate reanalysis

A unified approach for accurate approximations of displacements and displac ement derivatives with respect to design variables is presented. The soluti on procedure is based on results of a single exact analysis at an initial d esign. Unlike common approximations of the structural response, the approac h presented is nut based on calculation of derivatives. Rather, approximati ons of displacements are used to evaluate displacement derivatives at vario us modified designs. It is shown that similar computational procedures are employed for evaluating displacements, first- and second-order derivatives of displacements. The procedure presented is suitable for different types o f design variables and structures. Numerical results show that accurate app roximations of derivatives can be achieved with a small computational effor t fur designs obtained by very large changes in the initial structure. (C) 2001 Elsevier Science B.V. All rights reserved.