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The Traction Problem For Incompressible Materials
Y. H. Wan
Transactions of the American Mathematical Society
Vol. 291, No. 1 (Sep., 1985), pp. 103-119
Published by: American Mathematical Society
Stable URL: http://www.jstor.org/stable/1999897
Page Count: 17
You can always find the topics here!Topics: Critical points, Mathematical problems, Linearization, Local minimum, Topological theorems, Power series, Sufficient conditions, Tangents, Divergence theorem, Mathematics
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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.
Transactions of the American Mathematical Society © 1985 American Mathematical Society