Response sensitivity and Hessian matrix analysis of planar frames subjected to earthquake excitation

This paper describes a new method of calculating accurately and efficiently dynamic response sensitivity and Hessian matrix of planar frames subjected to earthquake excitation. The formulas for sensitivity and Hessian matrix are derived by direct differentiation. An efficient algorithm to calculate dynamic response sensitivity and Hessian matrix is formulated based on finite element method and Newmark-β method. The first and second derivatives of dynamic responses can be derived simultaneously with only a single dynamics analysis. Two numerical examples are demonstrated with the newly developed method and the central-difference method. The results show that compared with the central-difference method, the new method proposed in this paper is highly accurate and more efficient.