A Response Surface for Structural Optimization

Abstract

Structural optimization is computationally intensive. Typically, a finite element model must be solved repeatedly during the process. Accordingly, various approximation schemes have been developed to reduce the cost of solves or to eliminate solves entirely during portions of the optimization process. In this paper, a new type of approximation or interpolation function in the form of a global response surface is described. With this function, approximations can be made with a limited amount of calibrating data points. The response surface requires no matrix inversions for coefficient evaluation, and therefore it is relatively efficient and stable. The new response surface is used in conjunction with a modified zero-order Powell search algorithm. The effectiveness of the response surface is evaluated for a reasonably realistic offshore structure application. This planar truss structure is subjected to a deck load, a lateral wave load (considered quasi-static), and member self-weight loads. The objective for this test case was to minimize the structural cost. Nodal coordinates were considered to be the explicit design variables. Response surface results are compared with those obtained by the common optimization algorithms: steepest descent, conjugate directions, and a conventional implementation of Powell’s method. The response surface appears to be effective for the test case considered.