New Methods Of Structural Repeated Sensitivity Analysis

With the rapid development of computer science, finite element method was generous used for the calculation of engineering structure. In order to obtain satisfactory results, usually need to repeatedly modify the design parameters, due to large scale and complicated of engineering structures, repeatedly modified waste a lot of time and money. In order to solve this problem, the sensitivity analysis has gradually attracted people’s attention. Efficient sensitivity analysis can not only help people choose those parameters that are sensitive to optimizational target, then reducing the number of design variables, but also can help people to find the optimal search direction, speed up the convergence rate.Nelson method is a classic method by exchange row and column to eliminate the singularity of the coefficient matrix. But the Nelson method can only be applied to solve the single frequency modal derivative problem. Wu Baisheng et al. improved Nelson method for the repeated frequency modal derivative problem. However, the modified matrix need decomposed in the process of solving modal derivative special solution, which will take a lot of time.In order to improve the solving speed, this paper constructs a linear algebraic equation group with repeated frequency modal derivative, proves the nonsingularity of the coefficient matrix of the equations, and then solves the equations using preconditioned MINRES method. The method just requires modal information of the frequency while calculate the repeated frequency modal sensitivity so that we do not require calculate coefficient of general solution after we get particular solution, this method is simple and easy to link with existing finite element software. The numerical examples show the accuracy and efficiency of the proposed method.In this paper, we also study the method of solve middle modal derivatives, and propose an iteration method to calculate modal derivatives for middle-eigenvalues of real symmetric eigensystems. The coefficient matrix of the special solution is constructed with the known modal information then form a new method. The iterative method can obtain high precision results of modal sensitivity, and is especially suitable for large scale sparse finite element modal. Numerical examples show the effectiveness of the method.Finally, we give an summary of this paper.