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General theorems and generalized variational principles for nonlinear elastodynamics

Xing, J.T. and Price, W.G. (1995) General theorems and generalized variational principles for nonlinear elastodynamics , Southampton, UK University of Southampton 25pp. (Ship Science Reports, 99).

Record type: Monograph (Project Report)

Abstract

Generalized variational principles with 11 - arguments, 9 - arguments, 5 - arguments, 3 - arguments and the variational principles of action of potential/complementary energy are developed to solve initial-value, final-value and two time boundary-value problems in nonlinear elastodynamic systems. The displacement gradient is decomposed into a symmentric part D subscript ij and a rotation part W subscript ij = -e subscript ijk W subscript k which are variables in functionals.

The theoretical approach is illustrated by examining one-dimensional elastostatic and elastodynamic problems. In the former, it is shown that by solving for the displacement gradient u subscript ij as a function of the stress tensor ? subscript ij from the constraint equations of the variational principle of complementary energy, the functional of the variational principle of complementary energy can be expressed in a form involving the single argument ? subscript ij only.

An application of the variational principles is illustrated in an elastodynamic final-value problem. Complementing these examples is a discussion indicating how other generalized variational principles may be deduced and how numerical schemes of study may be enhanced through a matrix decomposition of the displacement gradient u subscript ij.

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Published date: 1995
Additional Information: ISSN 0140-3818

Identifiers

Local EPrints ID: 22143
URI: http://eprints.soton.ac.uk/id/eprint/22143
PURE UUID: 486be1fe-bc67-4e37-adce-5c98cbb1b375

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Date deposited: 22 Feb 2007
Last modified: 17 Jul 2017 16:23

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