Variational principles of elastic-viscous dynamics in laplace transformation form, F. E. M. formulation and numerical method
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The author gives variational principles of elastic-viscous dynamics in spectral resolving form, it will be extended to Laplace transformation form in this paper, mixed variational principle of shell dynamics and variational principle of dynamics of elastic-viscous-porous media are concerned, for the latter, F. E. M. formulation has been worked out.
Variational principles in Laplace transformation form have concise forms, for the sake of utilizing F. E. M. conveniently it is necessary to find values of preliminary time function at some instants, when values of Laplace transformation at some points are known, but there are no efficient methods till now. In this paper, a numerical method for finding discrete values of preliminary function is presented, from numerical example we see such a method is efficient.
By combining both methods stated above, variational principles in Laplace transformation form and numerical method, a quite wide district of solid dynamic problems can be solved by ths aid of digital computers.
KeywordsMathematical Modeling Industrial Mathematic Efficient Method Variational Principle Time Function
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- (1).Jin Wen-lu, Computation of the finite element methods by spectral resolving of structural dynamics (The formulation of element dynamic behavior matrices), Proceedings of the International Conference on Finite Element Methods, Science Press, Beijing, China, (1982), 155–160.Google Scholar
- (2).Jin Wen-lu and Wu Gan-qing, Solution of three-dimensional consolidation and secondary time-effect problems of clay and its application, China Civil Engineering Journal, Vol. 15, No. 2, (1982, 2), 19–40. (in Chinese)Google Scholar
- (3).Tjong-Kie, T. Consolidation and secondary time effect of homogeneous, Anisotropic, saturated clay strata, Proceedings of the 5th International Conference on Soil Mechanics and Foundation Engineering, (1961), 367–374.Google Scholar
- (4).Sandhu, Ranbir S. and Edward L. Wilson, Finite element analysis of flow of saturated porous elastic media, J. Eng. Mech. Div. ASCE, Vol. 95, No. EM3, (1969), 641–652.Google Scholar