Efficient, accurate reanalysis for structural optimization

The combined approximations method, developed recently, is an efficient rea nalysis method providing high-quality results, Through the use of this appr oach, the computed terms of a series expansion are used as basis vectors in a reduced basis expression. By solving a reduced system of equations; firs t- and second-order approximations were demonstrated in previous studies fo r small structures. The efficiency and the accuracy of the method are impro ved, and results are illustrated for larger structures. By the utilization of a Gram-Schmidt orthogonalization procedure, a new set of basis vectors i s generated and normalized such that the reduced system of equations become s uncoupled. The advantage in using the latter vectors is that all expressi ons for evaluating the displacements are explicit functions of the design v ariables. Consequently, additional vectors can be considered without modify ing the calculations that have already been carried out. In addition, the u ncoupled system is more well conditioned. Some considerations related to th e efficiency of the solution process and the accuracy of the results are di scussed, and the effect of various parameters on the accuracy is studied. N umerical results are demonstrated for several medium and large-scale struct ures. It is shown that accurate and efficient approximations are achieved f or very large changes in the design.