Radovitzky, R. and Ortiz, M. (1999) Error estimation and adaptive meshing in strongly nonlinear dynamic problems. Computer Methods in Applied Mechanics and Engineering, 172 (1-4). pp. 203-240. ISSN 0045-7825. doi:10.1016/S0045-7825(98)00230-8. https://resolver.caltech.edu/CaltechAUTHORS:20171213-090926881
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Abstract
We present work aimed at developing a general framework for mesh adaption in strongly nonlinear, possibly dynamic, problems. We begin by showing that the solutions of the incremental boundary value problem for a wide class of materials, including nonlinear elastic materials, compressible Newtonian fluids and viscoplastic solids, obey a minimum principle, provided that the constitutive updates are formulated appropriately. This minimum principle can be taken as a basis for asymptotic error estimation. In particular, we chose to monitor the error of a lower-order projection of the finite element solution. The optimal mesh size distribution then follows from a posteriori error indicators which are purely local, i.e. can be computed element-by-element. We demonstrate the robustness and versatility of the computational framework with the aid of convergence studies and selected examples of application.
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Additional Information: | © 1999 Elsevier. Received 4 May 1998. The support of the Sandia National Laboratories through contract DE-AC04-76DP00789, and of the Army Research Office through contract DAAH04-96-1-0056, is gratefully acknowledged. | |||||||||
Group: | GALCIT | |||||||||
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Issue or Number: | 1-4 | |||||||||
DOI: | 10.1016/S0045-7825(98)00230-8 | |||||||||
Record Number: | CaltechAUTHORS:20171213-090926881 | |||||||||
Persistent URL: | https://resolver.caltech.edu/CaltechAUTHORS:20171213-090926881 | |||||||||
Official Citation: | R. Radovitzky, M. Ortiz, Error estimation and adaptive meshing in strongly nonlinear dynamic problems, In Computer Methods in Applied Mechanics and Engineering, Volume 172, Issues 1–4, 1999, Pages 203-240, ISSN 0045-7825, https://doi.org/10.1016/S0045-7825(98)00230-8. (http://www.sciencedirect.com/science/article/pii/S0045782598002308) | |||||||||
Usage Policy: | No commercial reproduction, distribution, display or performance rights in this work are provided. | |||||||||
ID Code: | 83859 | |||||||||
Collection: | CaltechAUTHORS | |||||||||
Deposited By: | Lydia Suarez | |||||||||
Deposited On: | 13 Dec 2017 23:06 | |||||||||
Last Modified: | 15 Nov 2021 20:14 |
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