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General theorems and generalized variational principles for nonlinear elastodynamics

General theorems and generalized variational principles for nonlinear elastodynamics
General theorems and generalized variational principles for nonlinear elastodynamics
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.
99
University of Southampton
Xing, J.T.
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Price, W.G.
b7888f47-e3fc-46f4-9fb9-7839052ff17c
Xing, J.T.
d4fe7ae0-2668-422a-8d89-9e66527835ce
Price, W.G.
b7888f47-e3fc-46f4-9fb9-7839052ff17c

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

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

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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: 22 Apr 2020 16:45

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