Optimization of least-weight grillages by finite element method

A numerical method is presented for the minimization of the volume of grillages with a stress constraint. The material distribution in the design domain is optimized by a fully-stressed criterion using a finite element method. The densities and orientations of the beams at nodes in grillages are taken as design variables, which vary in the design domain continuously. As intermediate densities are not suppressed in the optimization procedure, numerical instabilities are completely avoided. As a result, the optimal distribution fields of moments, deformation and material are obtained simultaneously. Subsequently the discrete structures are determined from the optimal distribution fields. The optimization procedure is accomplished by the computer program automatically. The capability of the proposed procedure is demonstrated on several classical benchmark problems.