SENSITIVITY ANALYSIS AT MULTIPLE CRITICAL POINTS AND OPTIMAL DESIGN OF GEOMETRICALLY NONLINEAR CONSTRUCTIONS

Abstract

It is presented a method for determination of design variables values of a geometrically nonlinear structure for which the structure mass attains its minimum subject to the constraints on multiple buckling loads and on limit values of design variables. It is assumed that a geometrically nonlinear elastic structure is under conservative loads. The successive loading method, the generalized displacement method and the arc length method are used for the calculation of nonlinear displacements. The singularity of tangent stiffness matrix is interpreted as overall buckling of a structure. The analytical sensitivity analysis is proposed for multiple buckling loads and nonlinear displacements at limit and bifurcation points. The efficiency of suggested method is shown on the examples of optimal design of a space truss for which the response involves double and triple bifurcation points.