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泛函变量
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  “泛函变量”译为未确定词的双语例句
    The first one is to expand the nonlinear systems according to multi_arbitrary functions, the second one is to expand the variable separation ansatz. The third one is the MLVSA based on the Darboux transformation (DT_MLVSA) and the last one is the derivative_dependent functional variable separation method.
    实现GMLVSA主要有四种途径,一是先把场量按照多个任意函数(通常考虑两个函数的情形)展开得到关于多个函数的多线性方程,另一种途径是推广变量分离的假设,第三类是基于Darboux变换的多线性变量分离方法(DT_MLVSA),第四类是导数相关泛函变量分离法.
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The functional arguments call for thresholds so that jurisdictions are large enough, and accessibility to assure that they are small enough.
      
These results involve, as a particular case, a system of integro-differential evolution equations with functional arguments.
      
A collocation method for boundary value problems of differential equations with functional arguments
      
Entropy-like (Lyapunov functional) arguments are developed here to demonstrate the asymptotic trend to self-similarity or traveling-waves in a broad class of nonlinear diffusion problems.
      
Higher order functions are functions with functional arguments and/or functional results.
      
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The purpose of this paper is to present my personal point of view about the con-traversy existed in the problem of equivalent theorem mentioned by Mr. Hu Hai-Chang[1,2].My point of view is as following:(1) By means of the method of undetermined Lagrange multiplier, it can be proved that the three kinds of variational functions in Hu-Washizu principle are not independent to. each other, and the stress-strain relationships are the constraint conditions in the process of variation. There have three kinds of variational...

The purpose of this paper is to present my personal point of view about the con-traversy existed in the problem of equivalent theorem mentioned by Mr. Hu Hai-Chang[1,2].My point of view is as following:(1) By means of the method of undetermined Lagrange multiplier, it can be proved that the three kinds of variational functions in Hu-Washizu principle are not independent to. each other, and the stress-strain relationships are the constraint conditions in the process of variation. There have three kinds of variational functions in the principle, but only two of which are independent.(2) By means of the method of high-order Legrange multiplier, we find a family of infinite numbers of functionals, with three kinds of variational functions, all of which are more general than that of Hu-Washizu principle. All these principles treat the same physical problem in elasticity, possess same three kinds of variational functions, and free from any constraint. Therefore, these functionals must be equivalent to each other. This is an uniqueness theorem in variational method, from which the stress-strain relation is derived. That is to say, in these infinite variaty of functionals, the stress-strain relation must be satisfied between stresses and strains. Similarly, we find that in Hu-Washizu principle, the stress-strain relation must be also satisfied between stresses and strains. Hence, in Hu-Washizu principle, three kinds of variational functions are not independent. Hu-Washizu principle is not a non-conditional variational principle, and in fact, the stress-strain relation is actually the existing condition of variation.(3) Under the variaticnal constraint of stress-strain relation, it is shown that Hellinger-Reissner principle and Hu-Washizu principle are but equivalent principles in elasticity. The conclusion of this paper is as following. Equivalent theorem is correct, and is not misinterpretation. The works done by various authors including Guo, Zhong-heng[10], Dai, Tian-min[11], Chen, Zhi-da[12], Liu, Dian-kui and Chang, Qi-jie[13], Wu, Rui-duo and Xi, Xiao-feng[14] on equivalent theorems of various variational problems are all correct, no any misinterpretation, and cannot labelled as "one has gone astrey from right path". The reason for the mis-understanding appears to be the 'try and error' method used by Mr. Hu in his work, with which it is impossible to justify the independence of three kinds of variational functions, and the non-existance of variational constraint in Hu-Wzshizu principle.

本文就胡海昌先生提出的等价定理的论争,申述个人的观点和论证,与胡海昌先生商榷。 本文主要论证了下列三点: (1)通过待定的拉格朗日乘子法证明了胡海昌-鹫津久一郎原理(下文简称胡鹫原理)的三类变量之间并不独立,应力应变关系仍然是应力和应变之间应该首先满足的变分约束条件。这个变分原理只是在形式上有应力、应变、位移三类变量,在实际上,这些变量中只有两类是独立的。(2)通过高阶拉格朗日乘子法,我们求得了比胡海昌鹫津久一郎原理的泛函更一般形式的具有三类变量的变分泛函,而且证明有无穷个这样的变分泛函。利用唯一性定理,我们证明了这些泛函的变量中必须满足应力应变关系这个条件。同样也证明了胡鹫原理并不是三类变量都独立的和没有任何约束条件的完全的变分原理,而是一个以应力应变关系为变分约束条件的变分原理。(3)在应力应变关系的变分约束条件下,我们证明了Hellinger-Reissner原理和胡鹫原理的等价定理。 本文的结论是:等价定理是正确的,并非象胡海昌先生所指的那样是“误解”。郭仲衡、戴天民、陈至达、刘殿魁、张其洁、邬瑞铎、奚肖风等通过各自的努力,在各种变分问题上论证了等价定理,都是正确的,没有什么“误解”,更没有“误入迷途...

本文就胡海昌先生提出的等价定理的论争,申述个人的观点和论证,与胡海昌先生商榷。 本文主要论证了下列三点: (1)通过待定的拉格朗日乘子法证明了胡海昌-鹫津久一郎原理(下文简称胡鹫原理)的三类变量之间并不独立,应力应变关系仍然是应力和应变之间应该首先满足的变分约束条件。这个变分原理只是在形式上有应力、应变、位移三类变量,在实际上,这些变量中只有两类是独立的。(2)通过高阶拉格朗日乘子法,我们求得了比胡海昌鹫津久一郎原理的泛函更一般形式的具有三类变量的变分泛函,而且证明有无穷个这样的变分泛函。利用唯一性定理,我们证明了这些泛函的变量中必须满足应力应变关系这个条件。同样也证明了胡鹫原理并不是三类变量都独立的和没有任何约束条件的完全的变分原理,而是一个以应力应变关系为变分约束条件的变分原理。(3)在应力应变关系的变分约束条件下,我们证明了Hellinger-Reissner原理和胡鹫原理的等价定理。 本文的结论是:等价定理是正确的,并非象胡海昌先生所指的那样是“误解”。郭仲衡、戴天民、陈至达、刘殿魁、张其洁、邬瑞铎、奚肖风等通过各自的努力,在各种变分问题上论证了等价定理,都是正确的,没有什么“误解”,更没有“误入迷途”。胡海昌先生认为大家都有“误解”的原因,似乎在于

The functional transformations of variational principles in elasticity are classified as three patterns: J relaxation pattern, I augmented pattern and I equivalent pattern.

弹性力学变分原理的泛函变换可分为三种格式:Ⅰ、放松格式,Ⅱ、增广格式,Ⅲ、等价格式。 根据格式Ⅲ,提出含多个任意参数的广义变分原理及其泛函表示式,其中包括:以位移u为一类泛函变量的多参数广义变分原理;以位移u和应力σ为二类泛函变量的多参数广义变分原理;以位移u和应变ε为二类泛函变量的多参数广义变分原理;以位移u应变ε和应力σ为三类泛函变量的多参数广义变分原理。由这些原理可得出等价泛函一系列新形式,此外,通过参数的合理选择,可构造出一系列有限元模型。 本文还讨论了拉氏乘子法“失效”问题,指出“失效”现象产生的原因,提出乘子法“恢复有效”的作法——换元乘子法。

Using Kantorovich Method, the tube structures with Complicated plane shape are analyzed in this paper. According to the spare thin—walled structure theory, the displacement trial functions are given by taking the "shear lag effect" into account. Then, the Euler's differential equations as well as natural boundary. condition are established with the help of variational method. The homogeneous solution of the differential equation system is solved by using matrix notations. An example is given at last. This method...

Using Kantorovich Method, the tube structures with Complicated plane shape are analyzed in this paper. According to the spare thin—walled structure theory, the displacement trial functions are given by taking the "shear lag effect" into account. Then, the Euler's differential equations as well as natural boundary. condition are established with the help of variational method. The homogeneous solution of the differential equation system is solved by using matrix notations. An example is given at last. This method can be used in primary design.

本文将康托诺维奇法应用于由复杂基底平面构成的简体结构的分析。根据空间薄壁结构理论并考虑简体结构的剪力滞后效应建立了简体结构的位移试函数表达式。然后根据泛函变分原理得到了泛函变量的欧拉方程组以及自然边界条件,运用微分方程的矩阵解法求得了欧拉方程组的齐次解。算例表明。该方法能适用于工程的初步设计且应用灵活、方便。

 
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