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IssuesArchive of Issues2004-2pp.30-35

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I. A. Brigadnov, "The dual approach to the evaluation of the load-carrying capacity of nonlinearly elastic bodies," Mech. Solids. 39 (2), 30-35 (2004)
Year 2004 Volume 39 Number 2 Pages 30-35
Title The dual approach to the evaluation of the load-carrying capacity of nonlinearly elastic bodies
Author(s) I. A. Brigadnov (St. Petersburg)
Abstract A variational problem associated with the limiting analysis of nonlinearly elastic bodies the potentials of which linearly increase with the increase of the modulus of the distortion tensor is considered. The limiting analysis dual problem is formulated. The dual problem enables one to find a lower bound for the limiting load - the magnitude of the external force beyond which statically determinate deformed configurations stable with respect to finite variations of the displacements do not exist.

By means of the finite-element approximation the limiting analysis dual problem is reduced to the convex programming problem with linear equality constraints. This problem is solved by the standard conditional gradient method. The effectiveness of the approach proposed is illustrated by examples.
References
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4.  J. M. Ball, "Convexity conditions and existence theorems in nonlinear elasticity," Arch. Ration. Mech. Anal., Vol. 63, No. 4, pp. 337-403, 1977.
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Received 20 July 2001
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