Shi Zhifei, Huang Shuping, Zhang Zimao. Variational Principles of Fluid Full-Filled Elastic Solids[J]. Applied Mathematics and Mechanics, 1999, 20(3): 249-255.
 Citation: Shi Zhifei, Huang Shuping, Zhang Zimao. Variational Principles of Fluid Full-Filled Elastic Solids[J]. Applied Mathematics and Mechanics, 1999, 20(3): 249-255.

# Variational Principles of Fluid Full-Filled Elastic Solids

• Publish Date: 1999-03-15
• The generalized variational principles of isothermal quasi-static fluid full-filled elastic solids are established by using Variational Integral Method. Then by introducing constraints, several kinds of variational principles are worked out, including five-field variable,four-field variable, three-field variable and two-field variable formulations. Some new variational principles are presented besides the principles noted in the previous works. Based on variational principles, finite element models can be set up.
•  [1] Biot M A.General theory of three-dimensional consolidation[J].J Appl Phys,1941,12:155～164 [2] Biot M A.Theory of propagation of elastic waves in a fluid-saturated porous solid.I Low frequency range[J].J Acout Soc Amer,1956,28:168～178 [3] Ghaboussi J,et al.Discussion on variational formulation of dynamics of fluid-saturated porous solids[J].J Eng Mech Div ASCE,1973,99:1097～1098 [4] Sandhu R S,Pister K S.A Variational principle for boundary value and initial boundary value problems[J].Int J Solids and Structures,1971,7:639～654 [5] Sandhu R S,Pister K S.Dynamics of fluid-saturated soils variational formulation[J].Int J Numer Anal Methos Geomechd,1987,11:241～255 [6] 钱伟长.变分法与有限元[M].北京:科学出版社,1980 [7] 胡海昌.弹性力学的变分原理及其应用[M].北京:科学出版社,1981 [8] 梁立孚,石志飞.关于变分学中逆问题的研究[J].应用数学和力学,1994,15(9):775～788 [9] 梁立孚,石志飞.粘性流体力学的变分原理及其广义变分原理[J].应用力学学报,1993,10(1):119～123

### Catalog

###### 通讯作者: 陈斌, bchen63@163.com
• 1.

沈阳化工大学材料科学与工程学院 沈阳 110142