Computational Error Estimates and Adaptive Processes for Some Nonlinear Structural Problems.
Abstract
In earlier papers the authors introduced and analyzed the calculation of reliable, a posteriori error estimates for finite element solutions and discussed the design and effectivity of adaptive procedures based upon them. While most of this work concerned linear problems, this paper is intended to show that the same approaches remain also highly effective in the nonlinear case. As a model problem a planar, elastic rod is considered involving both material as well as geometrical nonlinearities; but, as far as possible the discussion is kept general. For nonlinear problems of this type interest centers on an analysis of the shape and features of the equilibrium surface. After some general remarks about such surfaces and the related computational problems, a general continuation process is summarized and some of its extensions for determining limit points and tracing stability paths are discussed. The estimators are introduced for the error along the solution paths and of the computed critical values. Experimental results for the model problem show the effectivity of these estimators and of the adaptive procedures based upon them. Then some aspects relating to the occurrence and identification of spurious solutions are discussed. In order to illustrate desirable generalizations of these results, the paper ends with an outline of some results for linear problems of the type that should be achievable also in the nonlinear case. (Author)
Document Details
- Document Type
- Technical Report
- Publication Date
- Jul 01, 1981
- Accession Number
- ADA103955
Entities
People
- Ivo Babuška
- Werner Rheinboldt
Organizations
- University of Pittsburgh