Optimum design of adaptive truss structures using the integrated force method

A structural analysis and optimization method is developed to find the optimal topology of adaptive determinate truss structures under various impact loading conditions. The objective function is based on the maximization of the structural strength subject to geometric constraints. The dynamic structural analysis is based on the integrated finite element force method and the optimization procedure is based on the Sequential Quadratic Programming (SQP) method. The equilibrium matrix is generated automatically through the finite element analysis and the compatibility matrix is obtained directly using the displacement-deformation relations and the Single Value Decomposition (SVD) technique. By combining the equilibrium and the compatibility matrices with the force-displacement relations, the equations of the motion are obtained with element force as variables. The proposed method is extremely efficient to analyze and optimize adaptive truss structures. It is observed that the structural strength is improved significantly using the adaptively optimized geometries while the computational effort required by the force method is found to be significantly lower than that of the displacement method.