Continuum design sensitivity of transient responses using Ritz and mode acceleration methods

Abstract

In this paper, a unified continuum-based sizing design sensitivity analysis method is developed for the transient dynamic response of built-up structures. Using the direct differentiation method, the variational equation of the built-up structure is differentiate d with respect to the design variable to obtain a variational design sensitivity equation of the transient response. The same finite element analysis model that is used to obtain an approximate solution of the variational equation of the built-up structure is also used to obtain an approximate solution of the variational design sensitivity equation. For large-size built-up structures, the same superposition method is used both to reduce the dimension of the matrix equation of the built-up structure and also to reduce the dimension of the design sensitivity equation. The continuum-based design sensitivity analysis method can be implemented outside established finite element analysis codes using postprocessing data since it does not require derivatives of the stiffness, damping, and mass matrices. Moreover, the method is efficient since it does not require derivatives of basis vectors. Either the Ritz or mode acceleration method is used to further improve accuracy and efficiency of both analysis and sensitivity results. An example with damping shows that accurate design sensitivity of pointwise transient displacements is obtained using only 10% of basis vectors. This example indicates that in the continuum-based design sensitivity analysis method the same basis vectors that are used for analysis of the built-up structure are suitable for analysis of the design sensitivity equation.