An Optimal Algorithm for Stability Analysis of Symmetrical Critical Loads of Thin-walled Frames with Variable Cross-sections

Abstract

An optimization algorithm for the critical load of a kind of single-bay frames under symmetric loadings was studied and the numerical method for the critical load of the thin-walled frame with variable cross-section was discussed to increase the efficiency for engineering problems and to offset the defect of analytic solving problems.The frame was separated,the finite difference method was used to discretize the nonlinear differential equations in equilibrium state.Used deflection of each discrete point,critical load and bending moment as design variables.The objective function contained unknown critical load had been built.In the Fortran-PowerStation environment,unconstrained gradient optimization program was compiled and the specific example of frame with constant section and variable cross-section were solved.Optimization results were satisfied accuracy.So the stability problem of thin-walled structures with variable cross-section in engineering had been considered by algorithm.With great practicability,the algorithm could provide new thread for the solution of critical load in the engineering structure.