Second-Order Sensitivities of Inelastic Finite-Element Response by Direct Differentiation
Publication: Journal of Engineering Mechanics
Volume 134, Issue 10
Abstract
In this paper analytical equations are developed and implemented to obtain second-order derivatives of finite-element responses with respect to input parameters. The work extends previous work on first-order response sensitivity analysis. Of particular interest in this study is the computational feasibility of obtaining second-order response sensitivities. In the past, the straightforward finite difference approach has been available, but this approach suffers from serious efficiency and accuracy concerns. In this study it is demonstrated that analytical differentiation of the response algorithm and subsequent implementation on the computer provides second-order sensitivities at a significantly reduced cost. The sensitivity results are consistent with and have the same numerical precision as the ordinary response. The computational cost advantage of the direct differentiation approach increases as the problem size increases. Several novel implementation techniques are developed in this paper to optimize the computational efficiency. The derivations and implementations are demonstrated and verified with two finite-element analysis examples.
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Acknowledgments
The first writer gratefully acknowledges his University Graduate Fellowship from The Univ. of British Columbia, Vancouver. The study is also sponsored by the second writer’s Discovery Grant from the National Science and Engineering Research Council of Canada (NSERC), which is hereby gratefully acknowledged.
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Information & Authors
Information
Published In
Journal of Engineering Mechanics
Volume 134 • Issue 10 • October 2008
Pages: 867 - 880
Copyright
© 2008 ASCE.
History
Received: Mar 19, 2007
Accepted: Mar 31, 2008
Published online: Oct 1, 2008
Published in print: Oct 2008
Notes
Note. Associate Editor: Jiun-Shyan Chen
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