Combined approximations - a general reanalysis approach for structural optimization

The Combined Approximations JCA) method developed recently, is an effective reanalysis approach providing high quality results. In the solution proces s the terms of the binomial series, used as basis vectors, are first calcul ated by forward and back substitutions. Utilizing a Gram-Schmidt orthogonal ization procedure, a new set of uncoupled basis vectors is then generated a nd normalized. Consequently, accurate results can be achieved by considerin g additional vectors, without modifying the calculations that were already carried out. In previous studies, the CA method has been used to obtain eff iciently accurate approximations of the structural response in problems of linear reanalysis. It is shown in this paper that the method is most suitab le for a wide range of structural optimization problems including linear re analysis, nonlinear reanalysis and eigenvalue reanalysis. Some consideratio ns related to the efficiency of the solution process and the accuracy of th e results are discussed, and numerical examples are demonstrated. It is sho wn that efficient and accurate approximations are achieved for very large c hanges in the design.