DESIGN OF FRAMES AGAINST BUCKLING USING A RAYLEIGH QUOTIENT APPROXIMATION

A Rayleigh quotient approximation is applied to the design of structur es while guarding against elastic instability. It approximates bucklin g eigenvalues by separately estimating the modal strain energy due to the linear and geometric stiffness of the structure. Previously used d uring structural optimization for the fundamental natural eigenvalue, the Rayleigh quotient approximation is derived for the buckling design problem for the first time. The critical buckling load is found by so lving the eigenvalue problem that arises by considering the geometric nonlinearity of the deforming structure. Rayleigh's principle is used to justify the choice of intermediate design variables for approximati ng terms in the Rayleigh quotient. A truss model illustrates the impor tance of the design space chosen for approximating the modal strain en ergy. A beam-column, two plane frames, and a space frame are used to v erify the formulation. Special attention is paid to difficult bimodal optima.