Section Size Optimization of Continuum Structure with Bending and Shearing Deformation for Uniform Displacement Criterion

Abstract

If lateral stiffness distribution of continuum structure is unreasonable, its displacement distribution will be non-uniform under lateral load. The non-uniform displacement distribution will weaken the safety of the structure. The continuum structure is equivalent to the cantilever. The optimal lateral stiffness distribution of the structure is obtained by adjusting the section size distribution. The wind load and earthquake action are simplified into three equivalent static loads: uniform load, inverted triangle load and inertia force related load. The shearing displacement and bending displacement distributions along the structural height are derived. The optimization objective is that the second derivative of the total displacement distribution is zero, that is, the displacement distribution is uniform. The section size of the cantilever is optimized and the optimal scheme is obtained. The optimization results are verified by numerical analysis and finite element analysis. The results show that the uniform displacement criterion can be realized by the cantilever with section size distribution of power function. The optimal parameters of the section under different loads are different. A practical design example is presented to prove the applicability.