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This paper developed an effective optimization method, i.e., gradient-Hessian matrix-based method or second order method, of frame structures subjected to the transient loads. An algorithm of first and second derivatives of dynamic displacement and stress with respect to design variables is formulated based on the Newmark method. The inequality time-dependent constraint problem is converted into a sequence of appropriately formed time-independent unconstrained problems using the integral interior point penalty function method. The gradient and Hessian matrixes of the integral interior point penalty functions are also computed. Then the Marquardt's method is employed to solve unconstrained problems. The numerical results show that the optimal design method proposed in this paper can obtain the local optimum design of frame structures and sometimes is more efficient than the augmented Lagrange multiplier method.

Optimization Design of Structures Subjected to Transient Loads Using First and Second Derivatives of Dynamic Displacement and Stress