耦合热弹塑性问题的泛函及其变分原理*
The Functional and Its Variational Principle in Coupled Thermo Elastoplasticity
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摘要: 为用有限元法求解耦合热弹塑性问题,建立适当的泛函是有必要的.本文试图在K.N.Rysinko和E.I.Blinov提出的热弹塑性本构方程和热传导方程[1]的基础上,用泛函分析理论导出耦合热弹塑性问题的泛函.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.
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[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). -
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