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GURTIN-TYPE VARIATIONAL PRINCIPLES FOR DYNAMICS OF A NON-LOCAL THERMAL EQUILIBRIUM SATURATED POROUS MEDIUM

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Acta Mechanica Solida Sinica 2005年第1期18卷 37-45页

作者： YangXiao instituteofappliedmathematicsandmechanics DepartmentofMechanicsShanghaiUniversityShanghai200444China

Based on the porous media theory and by taking into account the efects of the pore fuid viscidity, energy exchanges due to the additional thermal conduction and convection between solid and fuid phases, a mathematical model for the dynamic-thermo-hydro-mechanical coupling of a non-local thermal equilibrium fuid-saturated porous medium, in which the two constituents are assumed to be incompressible and immiscible, is established under the assumption of small de- formation of the solid phase, small velocity of the fuid phase and small temperature changes of the two constituents. The mathematical model of a local thermal equilibrium fuid-saturated porous medium can be obtained directly from the above one. Several Gurtin-type variational principles, especially Hu-Washizu type variational principles, for the initial boundary value problems of dy- namic and quasi-static responses are presented. It should be pointed out that these variational principles can be degenerated easily into the case of isothermal incompressible fuid-saturated elastic porous media, which have been discussed previously.

关键词： non-local thermal equilibrium thermal-mechanical coupling mathematical model variational principle porous media theory

SINGULARITIES OF SPHERICAL FOUR-BAR MOTION

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Applied Mathematics(A Journal of Chinese Universities) 1998年第1期13卷 95-102页

作者： HUAXUANJI ZHANGHUAI DepartmentofMathematics FudanUniversityShanghai200433. instituteofappliedmathematicsandmechanics Shanghai200072.

The link curve of a spherical four bar mechanism can be separated into two branches. The condition that the double points of the curve must satisfy is given. The double points may be the double points of either branc... 详细信息

关键词： Spherical four bar mechanism link curve double point singularity.

ASYMPTOTIC DYNAMIC SOLUTION TO THE MODE Ⅰ PROPAGATING CRACK-TIP FIELD IN ELASTIC-VISCOPLASTIC MATERIAL

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Applied Mathematics and Mechanics(English Edition) 2003年第2期24卷 208-215页

作者：李范春 instituteofappliedmathematicsandmechanics

A new elastic_viscoplastic mode was proposed to analyze the stress and strain fields surrounding the tip of a propagating mode Ⅰ cracks. A proper displacement pattern was suggested and asymptotic equations were derived, and numerical solutions were illustrated. The analysis and calculation show that the crack_tip field is of logarithmic singularity for smaller viscosity, however no solution exists for large viscosity. By a careful analysis and comparison, it is found that the present results retain all merits of those given by Gao Yu_chen, while removing existing problems.

关键词： crack_tip field dynamic propagating viscoplastic

Fractal　localized　structures　related　to　Jacobian　elliptic　functions　in　the　higher-order　Broer-Kaup　system

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Chinese Physics B 2004年第9期13卷 1382-1385页

作者：马正义朱加民郑春龙 DepartmentofPhysicsandMathematics LishuiUniversityLishui323000China instituteofappliedmathematicsandmechanics ShanghaiUniversityShanghai200072China

This work reveals a novel phenomenon—that the localized coherent structures of a (2+1)-dimensional physical model possesses fractal behaviours. To clarify the interesting phenomenon, we take the (2+1)-dimensional higher-order Broer–Kaup system as a concrete example. Starting from a B?cklund transformation, we obtain a linear equation and then a general solution of the system is derived. From this some special localized excitations with fractal behaviours are obtained by introducing some types of lower-dimensional fractal patterns that related to Jacobian elliptic functions.

关键词： higher-order Broer-Kaup system Backlund transformation variable separation approach Jacobian elliptic function fractal

The Schro^edinger equation for a Kirchhoff elastic rod with noncircular cross section

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Chinese Physics B 2004年第6期13卷 794-797页

作者：薛纭刘延柱陈立群 instituteofappliedmathematicsandmechanics ShanghaiUniversityShanghai200072China DepartmentofEngineeringMechanics ShanghaiJiaotongUniversityShanghai200030China

Growth of a Void in a Rubber Rectangular Plate under Uniaxial Extension

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Journal of Shanghai University(English Edition) 2001年第3期5卷 177-182页

作者： RENJiu－sheng SHANGXin－chun instituteofappliedmathematicsandmechanics andDepartmentofMechanicsShanghaiUniversityShanghai200072China DepartmentofMathematicsandMechanics UniversityofScienceandTechnologyBe

The finite deformation and stress analyses for a rectangular plate with a center void and made of rubber with the Yeoh elastic strain energy function under uniaxial extension were studied in this paper. An approximation solution was obtained from the minimum potential energy principle. The numerical results for the growth of the cavitation and stresses along the edge of the cavitation were discussed. In addition, the stress concentration phenomenon was considered.

关键词： rubber rectangular plate finite deformation Yeoh strain energy function potential energy principle growth of void

Cavitation for Incompressible Anisotropic Hyper-Elastic Materials

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Journal of Shanghai University(English Edition) 2002年第3期6卷 185-190页

作者：任九生程昌钧 instituteofappliedmathematicsandmechanics DepartmentofMechanicsShanghaiUniversityShanghai200072China instituteofappliedmathematicsandmechanics DepartmentofMechanicsShanghaiUniver

The cavitation problem in a solid sphere composed of an incompressible anisotropic hyper elastic material under a uniform radial tensile dead load was examined. A new analytical solution was obtained. The stress contributions were given and the jumping and concentration of stresses were discussed. The stability of solutions and the effect of the degree of anisotropy of the material were analyzed.

关键词： anisotropic incompressible hyper elastic material cavitated bifurcation jumping and concentration of stress energy comparison.