Abstract
A numerical method to minimize the volumes of grillages with a stress constraint under multiple load cases is presented. The material distributions under every singular load case are optimized respectively by fully‐stressed criterion firstly. The material distributions under multiple load cases is determined by constraining its elastic matrix to approach the envelope of the elastic matrix of the optimum structures defined for each single load case iteratively. The densities and orientations of the beams at nodes are taken as design variables. The densities and orientations vary in design domain continuously. As the middle densities are not suppressed in optimization procedure, the numerical instabilities are completely avoided. As the result the optimal distribution fields of moments, deformation and material are obtained simultaneously.
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