Optimization of adaptive truss structures using the finite element force method based on complementary energy

A structural analysis and optimization method is developed to find the opti mal topology of adaptive determinate truss structures in the presence of va rious loading conditions. The objective function is based on the maximizati on of the structural strength subject to geometric constraints. The structu ral analysis is based on the finite element force method using the compleme ntary strain energy and the optimization procedure is based on the Sequenti al Quadratic Programming (SQP) method. Equilibrium equations are satisfied a priori and compatibility conditions are derived through minimization of t he complementary energy, which allows the calculation of element forces wit hout explicitly generating the compatibility conditions. Additionally, the selection of the redundant members has been automated through the Gauss eli mination technique. The proposed method has performed well and it is extrem ely efficient in geometry optimization of adaptive truss structures where t he primary design variables are the active member forces.