Date of Award
Doctor of Philosophy (PhD)
Duc T. Nguyen
Leon R. L. Wang
In this study, the design sensitivity analysis is for the purpose of providing constraint derivative information for structural optimization under dynamic loads. Various existing formulations are reviewed, and the direct differentiation method is justified as the best one for design sensitivity analysis in structural dynamics. An alternative formulation for design sensitivity analysis with direct differentiation method is developed. The alternative formulation works efficiently with the reduced system of dynamic equations, and it eliminates the need for expensive and complicated eigenvector derivatives, which is required in the existing reduced system formulation. The relationship of the alternative formulation and the existing reduced system formulation is established originally, and it is proven analytically that the two approaches are identical, when the transformation is exact, i.e, when all the modes are included. The alternative approach is accurate, simple, and efficient.
Eigenvectors are used as the base vectors in system reduction for both dynamic response analysis and the design sensitivity analysis. Lanczos algorithm is used for eigensystem solutions. A modified mode acceleration method is presented, thus, not only the displacements but also the velocities and accelerations are shown to be improved.
The accuracy of the dynamic response is checked by comparing with the original full system solution, and the accuracy of the sensitivity information is verified by comparing with the sensitivity information obtained by finite difference method of the original full system. Numerical studies have verified that the alternative formulation proposed could yield excellent accuracy. Numerical studies also show that the modal acceleration method could very effectively reduce the computation cost for both dynamic response analysis and design sensitivity analysis.
An efficient parallel-vector algorithm for design sensitivity analysis in large-scale structural dynamics is developed. Parallel computation can be achieved in both the global and local levels. The developed parallel-vector algorithm is then implemented in the Cray 2 and Cray Y-MP parallel computers using a parallel Fortran language called Force. The efficiency of the parallel-vector algorithm is illustrated by analyzing of large-scale structural systems and making comparison with the sequential version of the algorithm.
"Parallel-Vector Design Sensitivity Analysis in Structural Dynamics"
(1991). Doctor of Philosophy (PhD), dissertation, Civil/Environmental Engineering, Old Dominion University, DOI: 10.25777/ewck-qy91