Recent Refinements in the Multi-Point Approximation Method in Conjunction With Adaptive Mesh Refinement

Abstract

Abstract Application of the Multi-point Approximation Method (MAM) to structural optimization is considered. Structural analyses are performed by means of the finite element method with Adaptive Mesh Refinement (AMR). The required discretization errors are changed during the optimization process to achieve a higher computational efficiency. A straightforward combination of the MAM and AMR may yield complications, which are discussed in detail. Therefore, several modifications in the MAM are necessary. An alternative strategy for determining the explicit approximation functions using a weighted least-squares fitting is proposed. The applied weight coefficients reflect the levels of the discretization errors. The approximation functions are fitted with a sub-set of the available structural response analyses. An alternative move limit strategy is given. On the basis of several numerical examples it is shown that the proposed modifications improve the convergence characteristics of the MAM when combined with AMR. Moreover it is demonstrated that the proposed refinements are also beneficial for optimization of systems with noisy objective and constraint functions.