钱氏定理在有限变形极矩弹性力学广义变分原理的应用
Application of Chien’s Theorem to the Establishing of General Variational Principle in Polar Elasticity of Finite Deformation
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摘要: 应用Lagrange乘子法和钱伟长证明的两类广义变分原理的等价定理,在本文中导出有限变形极矩弹性力学的广义变分原理.文中采用了在拖带坐标系描述法建立的有限变形应变张量(称为Biot有限变形应变定义的准确形式)和应变速率定义与拖带系应力张量构成完整的数学描述.Abstract: Variational principles of minimum potential energy and complementary energy of linear polar elasticity has been formulated by No,packi[3].As it has been proved by Chien Wei-zang, that the tveo generalized variational principles are equivalent in functionals; we now apply this important statement Chien's theorem, and Lagrange's method of multiphers to the establishing of generalized variational principle in polar elasticity for finite deformation. The fundamental equations of mechanics of finite deformation used are of which has been established in the author's paper[7],[4].
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[1] Nemat-Nasser, S,,General variation principles in nonlinear and linear elasticity with applications, Mechanics Today, 1,(1972), 214-258. [2] 钱伟长,弹性理论中广义变分原理的研究及其在有限元计算中的应用,清华大学科学报告,TH 78011, 1978年. [3] Nowacki, W.,Theory of micropolar elasticity, CISM, Udine,(1972), §3.2. [4] 陈至达,连续介质有限变形力学几何场论(弹性有限变形能鼠原理),清华大学学报,19卷,第4期,1979年. [5] Biot, M.A.,Variational irreversible thermodynamics of physical-chemical solids with finite deformation, Int.T.Solids Structures, 14, 4 (1978).881-903 [6] Fraeijs de veubeke, B, M.,A new variational principle for finite elastic displacemeats, Int.J.ENG.Sci, 10. 9 (1972) 754-764 [7] 陈至达连续介质有限变形力学几何场论(几何理论),力学学报,2期,107-117页,1979年. -
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