Combined approximations – a general reanalysis approach for structural optimization

Abstract.

The Combined Approximations (CA) method developed recently, is an effective reanalysis approach providing high quality results. In the solution process the terms of the binomial series, used as basis vectors, are first calculated by forward and back substitutions. Utilizing a Gram–Schmidt orthogonalization procedure, a new set of uncoupled basis vectors is then generated and normalized. Consequently, accurate results can be achieved by considering additional vectors, without modifying the calculations that were already carried out. In previous studies, the CA method has been used to obtain efficiently accurate approximations of the structural response in problems of linear reanalysis. It is shown in this paper that the method is most suitable for a wide range of structural optimization problems including linear reanalysis, nonlinear reanalysis and eigenvalue reanalysis. Some considerations related to the efficiency of the solution process and the accuracy of the results are discussed, and numerical examples are demonstrated. It is shown that efficient and accurate approximations are achieved for very large changes in the design.