Optimization of Grillage-like Continuum by Triangle Plate Element

The volume of grillages with stress constraints is minimized. An optimal beams system or plate with reinforced ribs is obtained to present the optimal structure. A grillage-like continuum material model is adapted. Structure is analyzed by finite element method with triangle plate elements. The geometric matrix of triangle plate element in explicit formulation about area coordinates is presented. The stiffness matrix of grillage-like continuum material model is derived. The material distribution field in design domain is optimized by fully-stressed criterion. The densities and orientations of the beam or reinforced ribs at nodes in grillages are taken as design variables. The densities and orientations vary in design domain continuously. The optimal distribution fields of bend moments, flexure displacement and material are obtained simultaneously. Subsequently the discrete structures are founded based on the optimal material distribution fields. The performances of different elements are compared. The optimization procedure is accomplished by computer program automatically.