Structural optimization by multilevel decomposition

Abstract

A method for decomposing an optimization problem into a set of subproblems and a coordination problem that preserves coupling between the subproblems is described. The decomposition is achieved by separating the structural element optimization subproblems from the assembled structural optimization problem. Each element optimization and optimum sensitivity analysis yields the cross-sectional dimensions that minimize a cumulative measure of the element constraint violation as a function of the elemental forces and stiffness. The assembled structural optimization produces the overall mass and stiffness distributions optimized for minimum total mass subject to constraints that include the cumulative measures of the element constraint violations extrapolated linearly with respect to the element forces and stiffnesses. The method is introduced as a special case of a multilevel, multidisciplinary system optimization and its algorithm is fully described for two-level optimization for structures assembled of finite elements of arbitrary type. Numerical results are given as an example of a framework to show that the decomposition method converges and yields results comparable to those obtained without decomposition. It is pointed out that optimization by decomposition should reduce the design time by allowing groups of engineers using different computers to work concurrently on the same large problem.