弹性力学中混合变量的能量原理

建立了弹性力学中混合变量的虚功原理和虚余功原理,混合变量的最小势能原理和最小余能原理,混合变量最小势能的广义原理和最小余能的广义原理。同时,应用混合变量的最小势能原理于计算一复杂边界条件矩形板的弯曲。     

有限位移弹性理论混合变量的变分原理

建立了有限位移弹性理论混合变量的最小势能原理、驻值余能原理、广义势能原理、广义余能原理、虚功原理和虚余功原理。     

用势能最小原理解决费马一斯坦勒尔问题

势能最小原理为解决费马问题提供了力学依据，本文用不同的数学方法进行了证明。同时，用势能最小原理和数学方法相结合，可以更简便地解决费马一斯坦勒尔问题。     

用势能最小原理解决费马-斯坦勒尔问题

势能最小原理为解决费马问题提供了力学依据,本文用不同的数学方法进行了证明。同时,用势能最小原理和数学方法相结合,可以更简便地解决费马—斯坦勒尔问题。     

数学问题中的物理方法简介

本举例介绍了用物理学中的重心原理，力的平衡原理，光路最短原理，势能最小原理等简捷地求解一些数学疑难问题的方法。     

输油管的优化铺设模型

研究了在不同情况下铺设输油管道的费用问题。在非共用与共用管道耗费相同时,把三角形两边之和大于第三边的原理与函数方程相结合,用函数最小值的思想分类讨论求出线路最短时的最小费用;在非共用与共用管道耗费不同时,利用费马点与势能最小原理找出最合理的车站位置和最节约的耗费。     

最小势能原理及其应用

当一个力学体系处于稳定平衡时,势能为极小值,这称为最小势能原理．最小势能原理是物理学中一个很重要的原理,在材料力学和弹性力学中有广泛的应用．在中学阶段,通过合理的构建物理模型,寻找系统的能量关系和平衡态的特点,再利用最小势能原理,我们可以解决物理中的一些疑难问题,甚至可以解决一些数学难题．     

《有限单元法基础》的授课思路

王焕定、焦兆平编著的《有限单元法基础》这本教材,以能量法为纽带,通过能量法求解杆件结构、平面问题、空间问题。通过建立单元的位移模式,得到单元的应变与应力;通过求单元的应变能与外力势能,从而得到单元的总势能;用最小势能原理求单元刚度矩阵与等效节点载荷。最后由单元刚度矩阵组集总纲,引入边界条件,解线性方程组,求出节点位移。再将求出的节点力代入相应单元,求得单元应力与应变。     

应用结点电压法分析电路探讨

在进行电路分析时，对仅含电压源支路的电路，结点电压法通常采用混合变量，即多引入一个电流变量，同时也增加一个方程，因此求解过程相对复杂。对有一条仅含电压源支路的电路，不必采用混合变量即可解决问题。     

关于压缩映象原理的一个应用

本文研究一个数学分析问题,通过对常微分方程变量分离法及压缩映象原理的运用对比,在一定条件下证明了该问题解的存在性及唯一性结果。     

Growth of a Void in a Rubber Rectangular Plate under uniaxial Extension

The finite deformation and stress analyses for a rectangular plate with a center void and center void and made of rubber with the Yeoh elastic strain energy function under uniaxial extension were studied in this paper.An approximation solution was botained from the minimum potential energy principle.The num,erical results for the growth of the cavitation and stresses along the edge of the cavitation were discussed.In addition,the stress concentration phenomenon was considered.     

Equivalent Theorem of Hellinger-Reissner and Hu-Washizu Variational Principles

lintroductionIn1954,byso-calledtry-and-el.l.ormethodHull]deducedtheHu-Washizupl'inciple,whichplaysan.importantroleinthehistoryofvariation.In1964,ChienlZIsystematicallydiscussedtheLagrangemultipliermethod.Withthemethod,hesuccessfullydeducedHu-Washizuprinci…     

Equivalent theorem of Hellinger-Reissner and Hu-Washizu variational principles

The paper has proved that Hellinger-Reissner and Hu-Washizu variational principles are but equivalent principles in elasticity by following three ways: 1) Lagrange multiplier method. The paper points out that only a new independent variable can be introduced when one constraint equation has been eliminated by one Lagrange multiplier, which must be expressed as a function of the original variable(s) and/or the new introduced variable after identification. In using Lagrange multiplier method to deduce Hu-Washizu principle from the minimum potential energy principle, which has only one kind of independent variable namely displacement, by eliminating the constraint equations of stress-displacement relations, one can only obtain a principle with two kinds of variables namely displacement and stress; 2) involutory transformation, with such method Hu-Washizu variational principle can be deduce directly from the Hellinger-Reissner variational principle under the same variational constraints of stress-strain relation, and vice verse; 3)semi-inverse method, by which both of the above variational principles can be deduced from the minimum potential energy principle with the same variational constraints. So the three kinds of variational functions in Hu-Washizu variational principle are not independent to each other, the stress-strain relationships are still its constraint conditions.     

损伤粘弹性梁-柱的广义变分原理

从损伤的粘弹性材料的卷积型本构关系出发,建立了在小变形下损伤粘弹性梁-柱的控制方程,提出了以卷积形式表示的损伤粘弹性梁-柱弯曲问题的泛函,并给出了损伤粘弹性梁-柱的广义变分原理.应用这个广义变分原理,可分别给出梁-柱位移和损伤满足的基本方程,以及相应的初始条件和边界条件.     

多孔超弹性矩形板中微孔的增长

The analyses of finite deformation and stress for a hyperelastic rectangular plate with some voids under an uniaxial extension were conducted. The governing differential equations were given from the incompressibility condition of the material. The solution was approximately obtained from the minimum potential energy principle. The growth of voids was discussed. One can see that an initial central circular-cylinder void becomes an elliptic-cylinder void, but an initial non-centeral circular-cylinder void becomes an elliptic-like cylinder void and the center of void has a shift. The stress distributions along the edges of voids were given and the phenomenon of stress concentration was observed. The influences of the distribution manner and size of voids, as well as the distance between them on the growth of voids were analyzed.     

关于质点系功能原理和机械能守恒定律相关问题的讨论

阐述了引入外势能质点系的"功能原理"和机械能守恒定律在一般情况下不成立,而且有悖常识,没有存在的必要;并进一步指出质点系的"功能原理"应改为质点系的机械能定理,质点系的机械能守恒定律是力学中的能量转化与守恒定律,是力学中一条独立定律,而不是"功能原理"的推论.