A HIGHER ORDER EXPANSION METHOD FOR OPTIMUM DESIGN OF STRUCTURES FOR SPECIFIED FUNDAMENTAL EIGENVALUE

Abstract

A higher order expansion method is presented for optimum design of structures for specified fundamental eigenvalue. The design function, fundamental eigenmode and total volume are expressed in terms of the Taylor series expansion with respect to the specified fundamental eigenvalue. A solution with null design function, where all the eigenvalues degenerate to null, is chosen as a trivial initial solution, and higher order terms are incorporated. By using the proposed method, a set of optimum designs for a wide range of fundamental eigenvalues is easily found. The proposed method is applied to an Euler-Bernoulli beam and expanded forms are presented analytically for a simply supported beam. The method is then extended to a plane truss, and the results are compared with those by an optimality criteria method.

KEY WORDS:

• eigenvalue constraints
• optimum design
• trusses Euler-Bernoulli beam
• Taylor series expansion