Efficient, Accurate Reanalysis for Structural Optimization

The combined approximations method, developed recently, is an efficient reanalysis method providing high-quality results. Through the use of this approach, the computed terms of a series expansion are used as basis vectors in a reduced basis expression. By solving a reduced system of equations, first- and second-order approximations were demonstrated in previous studies for small structures. The efficiency and the accuracy of the method are improved, and results are illustrated for larger structures. By the utilization of a Gram-Schmidt orthogonalization procedure, new set of basis vectors is generated and normalized such that the reduced system of equations becomes uncoupled. The advantage in using the latter vectors is that all expressions for evaluating the displacements are explicit functions of the design variables. Consequently, additional vectors can be considered without modifying the calculations that have already been carried out. In addition, the uncoupled system is more well conditioned. Some considerations related to the efficiency of the solution process and the accuracy of the results are discussed, and the effect of various parameters on the accuracy is studied. Numerical results are demonstrated for several medium- and large-scale structures. It is shown that accurate and efficient approximations are achieved for very large changes in the design.