Two‐level approximation concept in structural synthesis

A new concept for complex structural optimization problems is presented. Based on investigation of the mechanical nature of the studied problem, a set of basic mechanical characteristics can be introduced as the generalized variables. A high‐quality explicit first‐level approximate problem FA is formed by first‐order Taylor series expansion of the behaviour constraints in terms of the generalized variables. The FA is explicit but highly non‐linear with respect to design variables. Therefore, a second‐level approximation is introduced to solve the FA by considering a sequence of second‐level approximate problems SA in the design variable space. This approach is a Two‐Level Approximation Concept. Its application to space frame synthesis shows its good grasp of the mechanical nature of the problem. The computational results for several examples show that the method presented in this paper is very efficient.