RENEWAL OF BASIC LAWS AND PRINCIPLES FOR POLAR CONTINUUM THEORIES (Ⅳ)——SURFACE COUSERVATION LAWS

Applied Mathematics and Mechanics (English Edition) ›› 2003, Vol. 24 ›› Issue (11): 1245-1252.

• 论文 • 下一篇

RENEWAL OF BASIC LAWS AND PRINCIPLES FOR POLAR CONTINUUM THEORIES (Ⅳ)——SURFACE COUSERVATION LAWS

戴天民

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

收稿日期:2002-07-03 修回日期:2003-06-06 出版日期:2003-11-18 发布日期:2003-11-18
基金资助:
the National Natural Science Foundation of China (10072024);the Research Foundation of Liaoning Education Committee (990111001)

RENEWAL OF BASIC LAWS AND PRINCIPLES FOR POLAR CONTINUUM THEORIES (Ⅳ)——SURFACE COUSERVATION LAWS

DAI Tian-min

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

Received:2002-07-03 Revised:2003-06-06 Online:2003-11-18 Published:2003-11-18
Supported by:
the National Natural Science Foundation of China (10072024);the Research Foundation of Liaoning Education Committee (990111001)

摘要/Abstract

摘要： The purpose is to reestablish rather complete surface conservation laws for micropolar thermomechanical continua from the translation and the rotation invariances of the general balance law. The generalized energy-momentum and energy-moment of momentum tensors are presented. The concrete forms of surface conservation laws for micropolar thermomechanical continua are derived. The existing related results are naturally derived as special cases from the results proposed in this paper. The incomplete degrees of the existing surface conservation laws are clearly seen from the process of the deduction. The surface conservation laws for nonlocal micropolar thermomechanical continua may be easily obtained via localization.

Abstract: The purpose is to reestablish rather complete surface conservation laws for micropolar thermomechanical continua from the translation and the rotation invariances of the general balance law. The generalized energy-momentum and energy-moment of momentum tensors are presented. The concrete forms of surface conservation laws for micropolar thermomechanical continua are derived. The existing related results are naturally derived as special cases from the results proposed in this paper. The incomplete degrees of the existing surface conservation laws are clearly seen from the process of the deduction. The surface conservation laws for nonlocal micropolar thermomechanical continua may be easily obtained via localization.

中图分类号:

戴天民. RENEWAL OF BASIC LAWS AND PRINCIPLES FOR POLAR CONTINUUM THEORIES (Ⅳ)——SURFACE COUSERVATION LAWS[J]. Applied Mathematics and Mechanics (English Edition), 2003, 24(11): 1245-1252.

DAI Tian-min . RENEWAL OF BASIC LAWS AND PRINCIPLES FOR POLAR CONTINUUM THEORIES (Ⅳ)——SURFACE COUSERVATION LAWS[J]. Applied Mathematics and Mechanics (English Edition), 2003, 24(11): 1245-1252.

参考文献

[1] DAI Tian-min. Renewal of basic laws and principles for polar continuum theories (Ⅰ)-Micro-morphic continuum [J]. Applied Mathematics and Mechanics (English Edition), 2003, 24 (10):1119-1125.
[2] DAI Tian-min. Renewal of basic laws and principles for polar continuum theories (Ⅱ)-Micro-morphic continuum theory and couple stress theory[J]. Applied Mathematics and Mechanics (En-glish Edition),2003,24(10):1126-1133.
[3] DAI Tian-min. Renewal of basic laws and principles for polar continuum theories (Ⅲ)-Noether' stheory[J]. Applied Mathematics and Mechanics (English Edition),2003,24(10):1134-1140.
[4] Gross D. Beitrag zu den Dynamischen Problemen der Bruchmechanik [M]. Habilitationsschrift derUniversitaet Stuttgart: Verlay der Universiteat Stuttgrat,1974.
[5] Jaric J. Conservation laws of the J-integral type in micropolar elastostatics[J]. Int J Engng Sci,1978,16:967-984.
[6] DAI Tian-min. Conservation laws and jump conditions in linear micropolar elastodynamics[J]. Ac-ta Mechanica Sinica, 1981,13(5): 271-279.(in Chinese)
[7] Fletzer D C. Conservation laws in linear elastodynamics[J]. Arch Rat Mech Anal, 1976,60:329-353.
[8] JIN Fu-sheng. The theorem of conservation of non-conservative field and the conservation laws fora certain class of continuum mechanics[J]. Acta Mechanica Sinica, 1983,15(3): 184-189. (inChinese)
[9] DAI Tian-min. Some path independent integrals for micropolar media[J]. Int J Solids Struct,1986,22(7):729-735.
[10] Vukobrat M. Conservation laws in micropolar elastodynamics and path-independent integrals[ J].Int J Engng Sci, 1989,27(9):1093-1106.
[11] Jaric J. The energy release rate and the J-integral in nonlocal micropolar field theory[ J]. Int J Engng Sci,1990,28 (12):1303-1313.
[12] DAI Tian-min. Generalized surface conservation laws for nonlocal polar thermomechanical continua[A]. In:CHIEN Wei-zang Ed. Proceedings of the 3 rd International Conference on Nonlinear Me-chanics[C]. Shanghai: Shanghai University Press, 1998,181-184.
[13] Buggisch H,Gross D,Krueger K H. Einige Erhaltungssaetze der Kontinuumsmechanik vom J-Integral Typ[J]. Ing Archiv, 1981,50:103-111.
[14] Lubarda V A, Markenscoff X. Conservation laws in couple stress elasticity[J]. J Mech Phys Solids,2000,48:553-564.
[15] Knowles J K, Sternberg E. On a class of conservation laws in linearized and finite elastostatics[J].Arch Rat Mech Anal, 1972,44:187-211.
[16] Dluzewski P H. Finite deformations of polar elastic media[J]. Int J Solids Struct, 1993,30(16):2277-2285.
[17] DAI Tian-min. Three systems of balance equations and jump conditions for nonlocal polar themo-mechanical continua[J]. Science in China Ser A, 1997,41(2):211-215. (in Chinese)
[18] Kraemer D. On the applicability of the I-integral in fracture mechanics[J]. Arch Appl Mech, 1993, 63:551-555．

RENEWAL OF BASIC LAWS AND PRINCIPLES FOR POLAR CONTINUUM THEORIES (Ⅳ)——SURFACE COUSERVATION LAWS

RENEWAL OF BASIC LAWS AND PRINCIPLES FOR POLAR CONTINUUM THEORIES (Ⅳ)——SURFACE COUSERVATION LAWS

PDF

可视化

摘要/Abstract

引用本文

使用本文

参考文献

相关文章 15

编辑推荐

Metrics

本文评价

[1]	Bohua SUN. Incompatible deformation field and Riemann curvature tensor[J]. Applied Mathematics and Mechanics (English Edition), 2017, 38(3): 311-332.
[2]	Heng XIAO. Quantum enigma hidden in continuum mechanics[J]. Applied Mathematics and Mechanics (English Edition), 2017, 38(1): 39-56.
[3]	Xiaodong LI, Baohong BAI, Yingbo XU, Min JIANG. Research status and trend of wind turbine aerodynamic noise[J]. Applied Mathematics and Mechanics (English Edition), 2016, 37(S1): 43-50.
[4]	Haoyuan GUO, Liyuan ZHANG, YajunYIN, Yongxin GAO. Relations between cubic equation, stress tensor decomposition, and von Mises yield criterion[J]. Applied Mathematics and Mechanics (English Edition), 2015, 36(10): 1359-1370.
[5]	Lidan YU, Tianfu JIN, Zhengnan YIN, Heng XIAO. Multi-axial strain-stiffening elastic potentials with energy bounds: explicit approach based on uniaxial data[J]. Applied Mathematics and Mechanics (English Edition), 2015, 36(7): 883-894.
[6]	B. AMIRIAN;R. HOSSEINI-ARA;H. MOOSAVI. Surface and thermal effects on vibration of embedded alumina nanobeams based on novel Timoshenko beam model[J]. Applied Mathematics and Mechanics (English Edition), 2014, 35(7): 875-886.
[7]	朱永安, 王璠, 刘人怀. Thermal buckling of axisymmetrically laminated cylindrically orthotropic shallow spherical shells including transverse shear[J]. Applied Mathematics and Mechanics (English Edition), 2008, 29(3): 291-300 .
[8]	王志乔;兑关锁. Basis-free expressions for derivatives of a subclass of nonsymmetric isotropic tensor functions[J]. Applied Mathematics and Mechanics (English Edition), 2007, 28(9): 1249-1257 .
[9]	戴天民. Renewal of basic laws and principles for polar continuum theories (XI)---consistency problems[J]. Applied Mathematics and Mechanics (English Edition), 2007, 28(2): 163-172 .
[10]	戴天民. RENEWAL OF BASIC LAWS AND PRINCIPLES FOR POLAR CONTINUUM THEORIES (Ⅹ) —MASTER BALANCE LAW[J]. Applied Mathematics and Mechanics (English Edition), 2006, 27(2): 167-174 .
[11]	戴天民. RENEWAL OF BASIC LAWS AND PRINCIPLES FOR POLAR CONTINUUM THEORIES (Ⅸ)— THERMOMECHANICS[J]. Applied Mathematics and Mechanics (English Edition), 2005, 26(6): 709-715 .
[12]	. MOVING INCLINED LOAD AT BOUNDARY SURFACE[J]. Applied Mathematics and Mechanics (English Edition), 2005, 26(4): 476-485 .
[13]	戴天民. RENEWAL OF BASIC LAWS AND PRINCIPLES FOR POLAR CONTINUUM THEORIES (Ⅷ)—PRINCIPLE OF TOTAL WORK AND ENERGY[J]. Applied Mathematics and Mechanics (English Edition), 2005, 26(3): 313-318 .
[14]	梁建术;陈予恕;梁以德. ROBUST CONTROL OF PERIODIC BIFURCATION SOLUTIONS[J]. Applied Mathematics and Mechanics (English Edition), 2004, 25(3): 263-271.
[15]	戴天民. RENEWAL OF BASIC LAWS AND PRINCIPLES FOR POLAR CONTINUUM THEORIES (Ⅵ)—CONSERVATION LAWS OF MASS AND INERTIA[J]. Applied Mathematics and Mechanics (English Edition), 2003, 24(12): 1369-1374.