Accurate Displacement Derivatives for Structural Optimization Using Approximate Reanalysis

A uni®ed approach for accurate approximations of displacements and displacement derivatives with respect to design variables is presented. The solution procedure is based on results of a single exact analysis at an initial design. Unlike common approximations of the structural response, the approach presented is not based on calculation of derivatives. Rather, approximations of displacements are used to evaluate displacement derivatives at various modi®ed designs. It is shown that similar computational procedures are employed for evaluating displacements, ®rst-and second-order derivatives of displacements. The procedure presented is suitable for di€erent types of design variables and structures. Numerical results show that accurate approximations of derivatives can be achieved with a small computational e€ort for designs obtained by very large changes in the initial structure.