ISSN:
0029-5981
Keywords:
Engineering
;
Engineering General
Source:
Wiley InterScience Backfile Collection 1832-2000
Topics:
Mathematics
,
Technology
Notes:
An adjoint variable method for design sensitivity analysis of non-linear elastic systems is presented. The method uses domain parameterization and a mutual form of the Hu-Washizu energy principle, and extends results reported in a recent work for linear elastic systems to non-linear elasticity. Non-linearities due to finite deformations and non-linear, hyperelastic constitutive models are considered. In contrast to other methods for non-linear sensitivity analysis, the present formulation can be applied with force, displacement or mixed approximate solution methods.The mutual energy expression used in the adjoint sensitivity derivation is developed from a non-linear extension of the Hu-Washizu energy functional and yields a linear governing equation for the adjoint system. This has important ramifications for the computational cost of a sensitivity analyses of non-linear systems: excluding the cost of determining the response of the system, the cost of a sensitivity analysis for a non-linear system is essentially the same as that for a linear system. Finite element implementation of the resulting sensitivity expressions is discussed, and two numerical examples are presented. The first example involves large deformations of a Mooney-Rivlin body, while the second involves design sensitivity analysis for mixed solution methods.
Additional Material:
4 Ill.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1002/nme.1620310813
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