Shape and Cross-section Optimization of Truss Subjected to Earthquake Excitation Based on Calculation of Gradient and Hessian Matrix

This paper developed a shape and cross-section optimization method of truss subjected to earthquake excitation for achieving minimum weight design with normal stress and nodal displacement constraints.First,the dynamic responses,their first and second derivatives with respect to design variables are calculated based on Newmark-β method.Second,the inequality constraint problem with time parameter is converted into a sequence of appropriately formed unconstrained problems without time parameter by using the integral penalty function method.The gradient and Hessian matrix of penalty function are calculated by using dynamic response first and second derivatives.Third,Marquardt's method which makes fully use of gradient and Hessian matrix is employed to solve unconstrained problems. Finally,finding optimum design of a 45-bar truss is demonstrated.The results show that optimization methods presented in this paper are an effective and highly efficient approach for minimum weight design.