The University of Southampton
University of Southampton Institutional Repository

Some general theorems and generalized and piecewise generalized variational principles for linear elastodynamics

Xing, J.T. and Zheng, Z.C. (1992) Some general theorems and generalized and piecewise generalized variational principles for linear elastodynamics Applied Mathematics and Mechanics, 13, (9), pp. 825-840. (doi:10.1007/BF02481802).

Record type: Article


From the concept of four-dimensional space and under the four kinds of time limit conditions, some general theorems for elastodynamics are developed, such as the principle of possible work action, the virtual displacement principle, the virtual stress-momentum principle, the reciprocal theorems and the related theorems of time terminal conditions derived from it. The variational principles of potential energy action and complementary energy action, the H-W principles, the H-R principles and the constitutive variational principles for elastodynamics are obtained. Hamilton's principle, Toupin's work and the formulations of Ref. [5],[17]–[24] may be regarded as some special cases of the general principles given in the paper. By considering three cases: piecewise space-time domain, piecewise space domain, piecewise time domain, the piecewise variational principles including the potential, the complementary and the mixed energy action fashions are given. Finally, the general formulation of piecewise variational principles is derived. If the time dimension is not considered, the formulations obtained in the paper will become the corresponding ones for elastostatics.

Full text not available from this repository.

More information

Published date: 1992
Additional Information: Cited by Ei 042269 vol92 (1993); International Aerospace Abstracts A93-15629, p0461 vol.33(1993); AMR 2A53 p.J137 vol.46(2)(1993)
Keywords: variational principle, elastodynamics, general theorem, boundary value problem of four-dimensional domain, dynamics


Local EPrints ID: 22148
ISSN: 0253-4827
PURE UUID: 425af5fe-3dc4-43d3-b435-8f1bda47b3ac

Catalogue record

Date deposited: 30 Jan 2007
Last modified: 17 Jul 2017 16:23

Export record



Author: J.T. Xing
Author: Z.C. Zheng

University divisions

Download statistics

Downloads from ePrints over the past year. Other digital versions may also be available to download e.g. from the publisher's website.

View more statistics

Atom RSS 1.0 RSS 2.0

Contact ePrints Soton:

ePrints Soton supports OAI 2.0 with a base URL of

This repository has been built using EPrints software, developed at the University of Southampton, but available to everyone to use.

We use cookies to ensure that we give you the best experience on our website. If you continue without changing your settings, we will assume that you are happy to receive cookies on the University of Southampton website.