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).


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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.

Item Type: Monograph (Technical Report)
Additional Information: ISSN 0140-3818
Subjects: T Technology > TA Engineering (General). Civil engineering (General)
V Naval Science > VM Naval architecture. Shipbuilding. Marine engineering
Divisions : University Structure - Pre August 2011 > School of Engineering Sciences
ePrint ID: 22143
Accepted Date and Publication Date:
Date Deposited: 22 Feb 2007
Last Modified: 31 Mar 2016 11:41

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