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), 825-840. (doi:10.1007/BF02481802).


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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.

Item Type: Article
Digital Object Identifier (DOI): doi:10.1007/BF02481802
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)
ISSNs: 0253-4827 (print)
Related URLs:
Keywords: variational principle, elastodynamics, general theorem, boundary value problem of four-dimensional domain, dynamics
Subjects: Q Science > QA Mathematics
T Technology > TA Engineering (General). Civil engineering (General)
Divisions : University Structure - Pre August 2011 > School of Engineering Sciences
ePrint ID: 22148
Accepted Date and Publication Date:
Date Deposited: 30 Jan 2007
Last Modified: 31 Mar 2016 11:41

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