非线性弹性理论的混合能量形式广义变分原理
The Generalized Variational Principles about Blending Energy Form of Non-Linear Elasticity
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摘要: 本文首先对弹性材料的应变能函数∑(Eij)和余应能函数∑C(Sij)的部分“对应”变量作Legendre变换,引进“对应”的混合余应变能函数∑klC和混合应变能函数∑kl。进而,给出非线性弹性理论的各种“对应”的混合能量形式广义变分原理。线性弹性理论也有相应结果,它是本文结果的特殊情况。Abstract: First of all, this paper gives Legendre transformation for the so-called partial corresponding variables of strain energy function Σ(Eij) and complementary strain energy function ∑C(Sij) of the elastic materiel, and introduces the corresponding blending complementary strain energy function ∑klC and blending strain energy function Σkl. Moreover, a series of generalized variational principles of the corresponding blending energy form of non-linear elasticity is given. As a special case, there exist corresponding results[1] in linear elasticity.
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[1] 胡海昌,《弹性力学的变分原理及其应用》,科学出版社(1980), 407-414. [2] Fung, Y, C,,Foundations of Solid Mechanics, Prentice-Hall (1965),351,463-470. [3] 戴天民,论非线性弹性理论的各种变分原理,应用数学和力学,3, 5 (1982), 585-585. [4] 郭仲衡,非线性弹性理论变分原理的统一理论应用数学和力学.1,1 (1980), 5-23. [5] 郭仲衡,《非线性弹性理论》,科学出版社(1980), 186-202. [6] 钱伟长,《变分法及有限元》上册,科学出版社(1980). [7] Гантмахер Ф.Р.,Лекчuu no Аналumuческоu Механuке,Физматгиз,Москва(1960) [8] Courant,R.and D.Hilbert,Method of Mathematical Physics,Vol.2,John Wiley and Sons,New York,London(1962),32-39. -
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