Accelerated subspace iteration for eigenvector derivatives
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Ting, T.↗
Engineering topics
Ting, T.
Publications and source records attributed to Ting, T..
Finite Element model refinement with actual forced responses of structures
The formulation and computer algorithm for Finite Element model refinement based on correlation with frequency response test results have been developed. The proposed approach is derived from the direct frequency response formulation of dynamic systems. The computer algorithm has been effectively implemented in MSC/NASTRAN's DMAP language. Numerical examples are given to show the effectiveness of the method. Also, numerical difficulties and their possible solutions are discussed.
Ting, T.↗
A subspace iteration for eigenvector derivatives
An iterative procedure for calculating eigenvector derivatives has been developed based on the subspace iteration concept. The basic formulation is derived directly from the first variation of the resulting equations of subspace iteration for solving eigenvalue problems. Since the basic formulation conserves the convergence properties of the original subspace iteration for eigen-problems, an overrelaxation scheme similar to Bathe's approach is employed to accelerate the subspace iteration process for calculating eigenvector derivatives.
Ting, T.↗
An efficient design sensitivity analysis of eigenvectors
Subspace iteration has been a major advance in solving large eigen problems when only a subset of eigen-pairs is required. The essence of this method is a transformation from displacement coordinates of an n-th order eigensystem to generalized coordinates of a smaller q-th order. The eigenvalue problem is then solved in the reduced space. The method was first developed by Clint and Jennings for real symmetric systems and was then called 'simultaneous iteration'. The success of the method prompted further research along this line and there have been many improved algorithms developed. This approach has been widely used by structural engineers for extracting the most useful natural frequencies and mode shapes of large-scale dynamic systems. This paper exploits into a new direction which is in the form of iterative process for simultaneously calculating eigenvector derivatives of many eigenvectors with respect to multi-variables. The method fully uses all the available information from preceding eigenvalue solution and, thus, effectively economizes computational efforts. It iterates through two equations derived from the first variation of the two fundamental equations used in subspace iteration method. There is no expensive large matrix decomposition required and the process converges to acceptable solution in a finite number of iterations. Therefore, the procedure increases its efficiency superiority over the others as the system size or the number of interested eigenvectors become larger and larger.
Ting, T.↗
An interpretation and solution of ill-conditioned linear equations
Data insufficiency, poorly conditioned matrices and singularities in equations occur regularly in complex optimization, correlation, and interdisciplinary model studies. This work concerns itself with two methods of obtaining certain physically realistic solutions to ill-conditioned or singular algebraic systems of linear equations arising from such studies. Two efficient computational solution procedures that generally lead to locally unique solutions are presented when there is insufficient data to completely define the model, or a least-squares error formulation of this system results in an ill-conditioned system of equations. If it is assumed that a reasonable estimate of the uncertain data is available in both cases cited above, then we shall show how to obtain realistic solutions efficiently, in spite of the insufficiency of independent data. The proposed methods of solution are more efficient than singular-value decomposition for dealing with such systems, since they do not require solutions for all the non-zero eigenvalues of the coefficient matrix.
Ojalvo, I. U.↗
Dynamic structural correlation via nonlinear programming techniques
A solution to the correlation between structural dynamic test results and finite element analyses of the same components is presented in this paper. Basically, the method can be categorized as a Levenberg-Marquardt type Gauss-Newton method which requires only the differences between FE modal analyses and test results and their first derivatives with respect to preassigned design variables. With proper variable normalization and equation scaling, the method has been made numerically better-conditioned and the inclusion of the Levenberg-Marquardt technique overcomes any remaining difficulty encountered in inverting singular or near-singular matrices. An important feature is that each iteration requires only one function evaluation along with the associated design sensitivity analysis and so the procedure is computationally efficient.
Ting, T.↗