Optimization for Maximum Buckling Load of a Lattice Space Frame with Nonlinear Sensitivity Analysis

Abstract

The paper presents an optimization analysis method to find the optimum shape of a lattice space frame with maximum buckling load. The buckling load of the lattice space frame is determined by a geometrically nonlinear analysis. The mathematic analysis of the optimization is based on Generalised Reduced Gradient method (GRG) [1], in which the slope of the objective function (the load parameter at buckling point) with respect to the design parameters is required. In order to determine the slope, the authors introduced a so-called Stiffness Sensitivity Tensor in the nonlinear structural analysis, such that the sensitivity analysis can be carried out simultaneously with the incremental iteration of the geometrically nonlinear structural analysis. A single layer lattice dome is taken as a numerical example, and the results show that the buckling load parameter for full area loading case increases 32.75% compared to that for the initial shape.