Efficient Frequency Response and Its Direct Sensitivity Analyses
Evgenii Rudnyi
Sam has shared his paper accepted for publication in Journal of
Mechanical Science and Technology
Efficient Frequency Response and Its Direct Sensitivity Analyses for
Large-Size Finite Element Models Using Krylov Subspace-Based Model Order
Reduction
http://modelreduction.com/contrib/Jeong.Sam.Han/JMST_2011_jshan.pdf
In this paper, we examine an efficient calculation of the approximate
frequency response (FR) for large-size finite element (FE) models using
the Krylov subspace-based model order reduction (MOR) and its direct
design sensitivity analysis with respect to design variables for sizing.
Information about both the FR and its design sensitivity is necessary
for typical gradient-based optimization iterations; therefore, the
problem of high computational cost may occur when FRs of a large-size FE
models are involved in the optimization problem. In the method suggested
in this paper, reduced order models, generated from the original
full-order FE models through the Arnoldi process, are used to calculate
both the FR and FR sensitivity. This maximizes the speed of numerical
computation of the FR and its design sensitivity. Assuming that the
Krylov basis vectors remain constant with respect to the perturbation of
a design variable, the FR sensitivity analysis is performed in a more
efficient manner. As numerical examples, a car body with 535,992 degrees
of freedom (DOF) and a 6 x 6 micro-resonator array with 368,424 DOF are
adopted to demonstrate the numerical accuracy and efficiency of the
suggested approach. Using the reduced-order models, we found that the FR
and FR sensitivity are in a good agreement with those using the
full-order FE model. The reduction in computation time is also found to
be significant because of the use of Krylov subspace-based reduced models.
Best wishes,
Evgenii