Nonlinear transient response and second-order sensitivity using time finite element method

A procedure based on time finite element method to obtain the second-order sensitivity of the transient response with respect to various system parameters is developed and applied to single and two-degree-of-freedom structural dynamic systems. The proposed method directly differentiates the algebraic equations, resulting from the time finite element formulation, with respect to system parameters. Computational algorithms are given, and detailed derivations are presented. The second-order sensitivity analysis has been used for approximation schemes for efficient solution of design optimization problems. Also, the results can be applied to gradient-based parameter identification schemes. The results are found to be in excellent agreement with those obtained using the finite difference method. The main advantages of the time finite element approach are the ease of use and the numerical efficiency with which the sensitivity of the transient response can be obtained.