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Transactions of the American Mathematical Society

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The traction problem for incompressible materials


Author: Y. H. Wan
Journal: Trans. Amer. Math. Soc. 291 (1985), 103-119
MSC: Primary 73C50; Secondary 58E99, 73H99
DOI: https://doi.org/10.1090/S0002-9947-1985-0797048-0
MathSciNet review: 797048
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Abstract: The traction problem for incompressible materials is treated as a bifurcation problem, where the applied loads are served as parameters. We take both the variational approach and the classical power series approach. The variational approach provides a natural, unified way of looking at this problem. We obtain a count of the number of equilibria together with the determination of their stability. In addition, it also lays down the foundation for the Signorini-Stoppelli type computations. We find second order sufficient conditions for the existence of power series solutions. As a consequence, the linearization stability follows, and it clarifies in some sense the role played by the linear elasticity in the context of the nonlinear elasticity theory. A systematic way of calculating the power series solution is also presented.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9947-1985-0797048-0
Keywords: Traction problem, incompressible materials, variational principle, linearization stability, Signorini-Stoppelli Schemes
Article copyright: © Copyright 1985 American Mathematical Society

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