Restudy of Coupled Field Theories for Micropolar Continua(I)─Micropolar Thermoelasticity

DAI Tian-min

Volume 23 Issue 2

Turn off MathJax

Article Contents

Abstract

References

Article Navigation > Applied Mathematics and Mechanics > 2002 > 23(2): 111-118

DAI Tian-min. Restudy of Coupled Field Theories for Micropolar Continua(I)─Micropolar Thermoelasticity[J]. Applied Mathematics and Mechanics, 2002, 23(2): 111-118.

Citation:

DAI Tian-min. Restudy of Coupled Field Theories for Micropolar Continua(I)─Micropolar Thermoelasticity[J]. Applied Mathematics and Mechanics, 2002, 23(2): 111-118.

Citation:

DAI Tian-min. Restudy of Coupled Field Theories for Micropolar Continua(I)─Micropolar Thermoelasticity[J]. Applied Mathematics and Mechanics, 2002, 23(2): 111-118.

PDF( 305 KB)

Restudy of Coupled Field Theories for Micropolar Continua(I)─Micropolar Thermoelasticity

DAI Tian-min

Department of Mathematics & Center for the Application of Mathematics, Liaoning University, Shenyang 110036, P R China

Received Date: 2001-03-01
Rev Recd Date: 2001-09-11
Publish Date: 2002-02-15

Abstract

Abstract

Problems of micropolar thermoelasticity have been presented and discussed by some authors in the traditional framework of micropolar continuum field theory. In this paper the thoery of micropolar thermoelasticity is restudied. The reason why it was restricted to a linear one is analyzed.The rather general principle of virtual work and the new formulation for the virtual work of internal forces as well as the rather complete Hamilton principle in micropolar thermoelasticity are established. From this new Hamilton principle not only the equations of motion, the balance equation of entropy, the boundary conditions of stress, couple stress and heat, but also the boundary conditions of displacement, microrotation and temperature are simultaneously derived.
- micropolar continua,
- thermoelasticity,
- principle of virtual work,
- Hamilton principle

FullText(HTML)

References(5)

References

[1]	Nowacki W.Theory of Asymmetric Elasticity[M].Oxford:Pergamon Press,1986.
[2]	Eringen A C,Kafadar C B.微极场论[M].戴天民译.南京:江苏科学技术出版社,1982.
[3]	Eringen A C.Microcontinuum Field Theories[M].New York:Springer-Verlag,1998.
[4]	Stojanovic R.On the principle of virtual work in the theory of oriented media[J].ZAMM,1973,53:T79-T82.
[5]	戴天民.广义连续统场论中新的功能及功率能率原理[J].应用数学和力学,2001,22(11):1111-1118.

Relative Articles

[1]	WU Feng, ZHONG Wanxie. Internal Mechanical Shock Wave: an Explanation of the Ocean Shock Current[J]. Applied Mathematics and Mechanics, 2019, 40(8): 823-839. doi: 10.21656/1000-0887.400138
[2]	SHEN Anming, CHEN Rui, DU Qiumei. Scale Effects on Natural Frequencies and Vibration Modes of Micro Cantilever Beams Based on Generalized Elasticity[J]. Applied Mathematics and Mechanics, 2018, 39(9): 999-1008. doi: 10.21656/1000-0887.380301
[3]	YIN Chun-song, YANG Yang. Shear Deformable Bending of Carbon Nanotubes Based on a New Analytical Nonlocal Timoshenko Beam Model[J]. Applied Mathematics and Mechanics, 2015, 36(6): 600-606. doi: 10.3879/j.issn.1000-0887.2015.06.004
[4]	HU Yu-da, ZHANG Li-bao. Magneto-Elastic Vibration Equations for Axially Moving Conductive and Magnetic Beams[J]. Applied Mathematics and Mechanics, 2015, 36(1): 70-77. doi: 10.3879/j.issn.1000-0887.2015.01.006
[5]	DONG Man-sheng, GE Fei, ZHANG Shuang-yin, HONG You-shi. Dynamic Equations of Curved Submerged Floating Tunnel[J]. Applied Mathematics and Mechanics, 2007, 28(10): 1157-1165.
[6]	LIU Yan-hong, ZHANG Hui-ming. Variation Principle of Piezothermoelastic Bodies,Canonical Equation and Homogeneous Equation[J]. Applied Mathematics and Mechanics, 2007, 28(2): 176-182.
[7]	Rajneesh Kumar, Praveen Ailawalia. Deformation Due to Time Harmonic Sources in Micropolar Thermoelastic Medium Possessing Cubic Symmetry With Two Relaxation Times[J]. Applied Mathematics and Mechanics, 2006, 27(6): 690-700.
[8]	ZHANG Rong-ye. Lagrangian Mechanics on K hler Manifolds[J]. Applied Mathematics and Mechanics, 2005, 26(10): 1236-1246.
[9]	DAI Tian-min. Renewal of Basic Laws and Principles for Polar Continuum Theories(Ⅰ)-Micropolar Continua[J]. Applied Mathematics and Mechanics, 2003, 24(10): 991-997.
[10]	DAI Tian-min. Renewal of Basic Laws and Principles for Polar Continuum Theories(Ⅴ)-Polar Thermomechanical Continua[J]. Applied Mathematics and Mechanics, 2003, 24(11): 1108-1113.
[11]	DAI Tian-min. Restudy of Coupled Field Theories for Micropolar Continua (Ⅱ)──Thermopiezoelectricity and Magnetothermoelasticity[J]. Applied Mathematics and Mechanics, 2002, 23(3): 229-238.
[12]	Ma Jinghuai. The Virtual Work Principle and Linear Complementary Method for Coupling Analysis of Elasto-Plastic Damage Structure[J]. Applied Mathematics and Mechanics, 2000, 21(2): 164-170.
[13]	Lu Dongqiang, Dai Shiqiang, Zhang Baoshan. Hamiltonian Formulation of Nonlinear Water Waves in a Two-Fluid System[J]. Applied Mathematics and Mechanics, 1999, 20(4): 331-336.
[14]	Liang Lifu, Wei Yang. On the Unification of the Hamilton Principles in Non-Holonomic System and in Holonomic System[J]. Applied Mathematics and Mechanics, 1996, 17(5): 439-444.
[15]	Zhu Chang-ming, Jin Yong-jie. A Finite Element——Mathematical Programming Method for Elastoplastic Problems Based on the Principle of Virtual Work[J]. Applied Mathematics and Mechanics, 1993, 14(7): 601-608.
[16]	Zheng Quan-shui. Extended Variational Principle in Non-Linear Theory of Elasticity[J]. Applied Mathematics and Mechanics, 1984, 5(2): 205-216.
[17]	Chen Ying-tian. The Derivation of J-lntegral Conservation Law from the Principle of Virtual Work[J]. Applied Mathematics and Mechanics, 1983, 4(3): 411-413.
[19]	Tai Tien-min. On a Theory of Micropolar Protoelastic Material Bodies and Constitutive Equations for Nonlocal Micropolar Elastic Continua[J]. Applied Mathematics and Mechanics, 1981, 2(2): 167-172.
[20]	Tai Tien-min. Various Reciprocal Theorems and Variational Principles in the Theories of Nonlocal Micropolar Linear Elastic Mediums[J]. Applied Mathematics and Mechanics, 1980, 1(1): 89-106.