Shape and cross-section optimization of plane trusses subjected to earthquake excitation using gradient and Hessian matrix calculations

This article describes a second-order shape and cross-section optimization method of plane truss subjected to earthquake excitation. The method is based on gradient and Hessian matrix calculation. First, the first and second derivatives of dynamic response with respect to design variables are calculated based on the Newmark method. Second, the inequality time-dependent constraint problem is converted into a sequence of appropriately formed unconstrained problems using the integral interior penalty function method. Then, the gradient and Hessian matrix of the integral interior penalty function are computed. Third, Marquardt's method is employed to solve the unconstrained problems. Finally, the new approach is validated through several case studies. The results show that the new optimization method is an efficient and effective approach for minimum weight design of truss structures.