Optimal Grillages by 3-Nodes Triangle Finite Element
By triangle finite elements, grillages with stress constraints are optimized. From it an optimal beams systems or plate with reinforced ribs is obtained. A truss-like continuum material is adapted. The material distribution field in design domain is optimized by fully-stressed criterion. The densities and orientations of the beams or reinforced ribs at nodes in grillages are taken as design variables. These densities and orientations vary in design domain continuously. The optimal distribution fields of moments, deformation and material are obtained simultaneously. Subsequently the discrete structures are determined based on the optimal distribution fields. A very simple geometry matrix of triangle plate element is given. The stiffness matrix of truss-like continuum in triangle element is derived. The optimization iteration procedure is suggested. The optimization procedure is accomplished by computer program automatically.
K. M. Zhou and X. Li, "Optimal Grillages by 3-Nodes Triangle Finite Element", Advanced Materials Research, Vols. 163-167, pp. 2431-2436, 2011