The Functional and Its Variational Principle in Coupled Thermo Elastoplasticity

Cheng He-ming; Wang Hong-gang

Volume 9 Issue 10

Turn off MathJax

Article Contents

Abstract

References

Article Navigation > Applied Mathematics and Mechanics > 1988 > 9(10): 865-870

Cheng He-ming, Wang Hong-gang. The Functional and Its Variational Principle in Coupled Thermo Elastoplasticity[J]. Applied Mathematics and Mechanics, 1988, 9(10): 865-870.

Citation:

Cheng He-ming, Wang Hong-gang. The Functional and Its Variational Principle in Coupled Thermo Elastoplasticity[J]. Applied Mathematics and Mechanics, 1988, 9(10): 865-870.

Citation:

Cheng He-ming, Wang Hong-gang. The Functional and Its Variational Principle in Coupled Thermo Elastoplasticity[J]. Applied Mathematics and Mechanics, 1988, 9(10): 865-870.

PDF( 358 KB)

The Functional and Its Variational Principle in Coupled Thermo Elastoplasticity

Kunming Institute of Technology, Kunming

Received Date: 1987-08-25
Publish Date: 1988-10-15

Abstract

Abstract

In order to solve the coupled thermoelastoplastic problems by the finite element method, it is necessary to establish suitable functional. In this paper, based on the thermoelastoplastic constitutive relation proposed by K.N. Rysinko and E.I. Blinov^[1], the functional of coupled thermoelastoplasticity is derived by means of the nonlinear functional analysis theory.

FullText(HTML)

References(5)

References

[1]	Rysinko, K.N. and E.I. Blinov, Analytical description of the thermoelastoplastic deformation of a solid, Sov. Appl. Mech., 17, 11(1981), 985-989.
[2]	杜庆华等编,《弹性力学》,科学出版社(1986).
[3]	Wang Hong-gang, The functional and variational theorem in nonlinear heat conduction, ICNM, Shanghai(1985).
[4]	程赫明、王洪纲,塑性和热弹塑性动力问题的增量泛函及其变分原理,全国第二届计算力学会议论文,上海(1986,8).
[5]	Oden, J.T. and J.N. Reddy, Variational Methods in Theoretical Mechanics, second edition, Berlin lteidelberg, New York(1983).

Relative Articles

[1]	FENG Xiao-jiu, LIANG Li-fu. Power Type Variational Principles and Work-Energy Type Quasi-Variational Principles and Their Applications[J]. Applied Mathematics and Mechanics, 2015, 36(11): 1178-1190. doi: 10.3879/j.issn.1000-0887.2015.11.006
[2]	ZHANG Hong-wu, WANG Hui. Parametric Variational Principle Based Elastic-Plastic Analysis of Heterogeneous Materials With Voronoi Finite Element Method[J]. Applied Mathematics and Mechanics, 2006, 27(8): 904-912.
[3]	LUO Xiao-hui, LI Yong-le, LUO Xin. Region-Wise Variational Principles and Generalized Variational Principles on Large Strain for Consolidation Theory[J]. Applied Mathematics and Mechanics, 2005, 26(7): 867-874.
[4]	XIAO Wan-shen, ZHOU Jian-ping, TANG Guo-jin. Periodical Interfacial Cracks in Anisotropic Elastoplastic Media[J]. Applied Mathematics and Mechanics, 2003, 24(11): 1186-1190.
[5]	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.
[6]	Ding Haojiang, Guo Fenglin, Hou Pengfei. General Solutions of Coupled Thermoelastic Problem[J]. Applied Mathematics and Mechanics, 2000, 21(6): 573-577.
[7]	Shi Zhifei, Huang Shuping, Zhang Zimao. Variational Principles of Fluid Full-Filled Elastic Solids[J]. Applied Mathematics and Mechanics, 1999, 20(3): 249-255.
[8]	Qian Rengji. A Modified Hellinger-Reissner Variational Functional Including only Two Independent Variables for Large Displacement of Thin Shallow Shell[J]. Applied Mathematics and Mechanics, 1997, 18(7): 617-624.
[9]	Ma Jinghuai. The Optimal Control Variational Principle and Finite Elements Analysis for Viscoplastic Dynamics[J]. Applied Mathematics and Mechanics, 1997, 18(1): 61-66.
[10]	Wang Zhi-guo, Tang Li-min. Hamiltonian systems in Elasticity and Their Variational Principles[J]. Applied Mathematics and Mechanics, 1995, 16(2): 117-122.
[11]	Shen Min, Sun Qi-ren. Variational Principle and Generalized Variational Principle in Hydrodynamics of a Class of Non-Newtonian Fluid[J]. Applied Mathematics and Mechanics, 1995, 16(4): 345-351.
[12]	Yin Fuxin, Sun Huanchun. A Condensed Method for Linear Complementary Equations of Elasto-Plastic Problems[J]. Applied Mathematics and Mechanics, 1995, 16(10): 861-871.
[13]	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.
[14]	Hu Ning. An Effective Boundary Method for the Analysis of Elastoplastic Problems[J]. Applied Mathematics and Mechanics, 1992, 13(8): 711-718.
[15]	Jin Fu-sheng. Variational Principles for Hydrodynamic Impact Problems[J]. Applied Mathematics and Mechanics, 1992, 13(6): 543-552.
[16]	Gao Yang, E. T. Onat. Rate Variational Extremum Principles for Finite Elastoplasticity[J]. Applied Mathematics and Mechanics, 1990, 11(7): 617-624.
[17]	S. Dost, B. Tabarrok. A Mixed Variational Formulation for Large Deformation Analysis of Plates[J]. Applied Mathematics and Mechanics, 1989, 10(7): 585-595.
[18]	Cheng Xian-sheng. The Generalized Variational Principes with their Applications in Structural Analysis[J]. Applied Mathematics and Mechanics, 1985, 6(7): 639-640.
[19]	Zheng Quan-shui. Extended Variational Principle in Non-Linear Theory of Elasticity[J]. Applied Mathematics and Mechanics, 1984, 5(2): 205-216.
[20]	Wang Hong-gang. On the Free Energy and Variational Theorem of Elastic Problem in Thermal Shock[J]. Applied Mathematics and Mechanics, 1982, 3(5): 621-627.