Two optimization methods for complicated structures with multiparameter elements based on generalized condensation

A high-order condensation expression is proposed to generalize Duffin's condensation formula. Based on the higher-order condensation expression, two primal algorithms of the second-order are constructed to solve GGP (generalized geometric programming) problems. To overcome the difficulty of solving the structural optimization with multiparameter elements, two methods are proposed and implemented in a computer program. The first method takes one geometrical property of the cross-section as one component of the design variables for each element and adopts SQP (sequential quadratic programming) to solve the optimization model. The second method takes geometrical sizes of the cross-section as the design variables for each element and adopts primal algorithms of GGP problems to solve the optimization model.