A singular problem in incompressible nonlinear elastostatics
by
R.L. Fosdick and A. Aguiar
in
Math. Models and Methods in Appl. Sciences, 10, 1181-1207, 2000.
Category: Journal Article
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Abstract:
This paper represents a contribution to the numerical treatment of problems in incompressible elasticity theory for large deformations. We are especially concerned about the solution of plane problems with corners. A review of the literature on these problems indicates that the behavior of the solution in the vicinity of a corner is given little attention. We investigate the solution of the compressed bonded block problem corresponding to the compression of an incompressible elastic block of rectangular cross-section and in nite transverse length between two opposing bonded rigid surfaces, with the two remaining lateral faces traction-free. We are especially interested in the behavior at a corner where a bonded end is adjacent to a free lateral side. We employ a nite element method based on a reduced and selective integration technique with penalization to construct a numerical solution for this problem. Our computational method converges everywhere except in a small neighborhood of the corner. We appeal to an elementary a priori inequality concerning the angle of shear to show that the numerical calculations in this neighborhood are inaccurate and need a more re ned study. Based on the inequality, we o er a conjecture concerning the local shape of the deformed free lateral surface at the corner.
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