Structural optimization with frequency constraints

Abstract

This paper presents a design optimization algorithm for structural weight minimization with multiple frequency constraints. An optimality criterion method based on uniform Lagrangian density for resizing and a scaling procedure to locate the constraint boundary were used in optimization. Multiple frequency constraints of equality and inequality types were addressed. The effectiveness of the algorithm was demonstrated by designing a number of truss structures with as many as 489 design variables. No attempt was made to reduce the number of design variables by such procedures as linking and/or invoking symmetry conditions. The design examples include a 10-bar truss, 200-bar truss, a modified ACOSS-II, and COFS (Control of Flexible Structures) mast truss. All the structures contain nonstructural mass besides their own mass. The algorithm is extremely stable and, in all cases, the optimum designs were obtained in less than 20 iterations regardless of the size of the structure and the number of design variables.