Handling of Constraints in Finite-Element Response Sensitivity Analysis
Publication: Journal of Engineering Mechanics
Volume 135, Issue 12
Abstract
In this paper, the direct differentiation method (DDM) for finite-element (FE) response sensitivity analysis is extended to linear and nonlinear FE models with multi-point constraints (MPCs). The analytical developments are provided for three different constraint handling methods, namely: (1) the transformation equation method; (2) the Lagrange multiplier method; and (3) the penalty function method. Two nonlinear benchmark applications are presented: (1) a two-dimensional soil-foundation-structure interaction system and (2) a three-dimensional, one-bay by one-bay, three-story reinforced concrete building with floor slabs modeled as rigid diaphragms, both subjected to seismic excitation. Time histories of response parameters and their sensitivities to material constitutive parameters are computed and discussed, with emphasis on the relative importance of these parameters in affecting the structural response. The DDM-based response sensitivity results are compared with corresponding forward finite difference analysis results, thus validating the formulation presented and its computer implementation. The developments presented in this paper close an important gap between FE response-only analysis and FE response sensitivity analysis through the DDM, extending the latter to applications requiring response sensitivities of FE models with MPCs. These applications include structural optimization, structural reliability analysis, and finite-element model updating.
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Acknowledgments
The writers gratefully acknowledge the support of this research by (1) the National Science Foundation under Grant No. NSFCMS-0010112; (2) the Pacific Earthquake Engineering Research (PEER) Center through the Earthquake Engineering Research Centers Program of the National Science Foundation under Award No. NSFEEC-9701568; and (3) the Louisiana Board of Regents through the Pilot Funding for New Research (Pfund) Program of the National Science Foundation Experimental Program to Stimulate Competitive Research (EPSCoR) under Award No. UNSPECIFIEDNSF(2008)-PFUND-86. The writers wish to thank Dr. Frank McKenna for his invaluable help in implementing the response sensitivity algorithms for handling multi-point constraints in OpenSees. Any opinions, findings, conclusions or recommendations expressed in this publication are those of the writers and do not necessarily reflect the views of the sponsors.
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© 2009 ASCE.
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Received: Sep 3, 2008
Accepted: Apr 21, 2009
Published online: Apr 24, 2009
Published in print: Dec 2009
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