Minimum-mass truss structures with constraints on fundamental natural frequency

A technique for constrained parameter optimization is presented and applied to the minimum-mass design of truss structures. The procedure employs an exterior penalty function to transform the constrained objective function into an unconstrained index of performance which is minimized by the Gauss method. The Gauss method recasts the minimization problem to one of solving simultaneous linear equations with the variation of the parameters as the unknowns. The technique is first applied to several test problems, demonstrating its relative efficiency and accuracy. Next, the standard test problems are altered to introduce local buckling constraints and new designs are obtained. It is shown these designs also satisfy global stability. Finally, static thermal loads are introduced, and an equality constraint is imposed on the fundamental natural frequency of each structure. The natural frequency analysis uses a four-degree-of-freedom axial-force bar element.