An improved variable penalty algorithm for automated structural design

Abstract

The paper presents refinements in a variable penalty algorithm proposed earlier [1]. The algorithm is an extension of the SUMT procedure where the design requirements are incorporated using a flexible penalty function which changes shape with the pattern of the constraint spectrum encountered during an unconstrained optimization process. The sequence of unconstrained problem is solved using a modified Newton method requiring only the first derivatives. The algorithm possesses inherent mechanism to control the quality of the second derivative matrix of the penalty function (Hessian) which is formulated in terms of the first derivatives of the constraints. The effectiveness of this algorithm is demonstrated on two structural problems: a p-member truss and a plane stress p-node plate, each having a relatively large set of test cases. The efficiency shows up in obtaining a converged minimum design in a small number of iterations, irrespective of the initial starting points or the number of design variables present.