薄板弯曲理论中一个新的广义变分原理及其交替max,min性质

本文在薄板弯曲的经典理论中提出一个以挠度、横向剪应变、曲率、弯矩、横向剪力、边界上的未知反力为自变函数的新的变分原理,在对自变函数预加不严厉的约束后,新泛函具有一连串交替max,min的性质。     

各向同性平面弹性力学求解新体系正交关系的研究

在平面弹性力学求解新体系中，将文献[2]对偶向量进行重新排序后，提出了一种新的对偶微分矩阵L，对于各向同性平面问题发现了一种新的正交关系。文中证明了这种正交关系的成立，并研究了各向同性平面问题的功互等定理与正交关系的联系。对于各向同性平面问题，新的正交关系包含文献[2]的正交关系。     

平面扇形域问题的新正交关系和变分原理

通过构造新的对偶向量, 用空间的环向坐标数学上比拟Hamilton体系的时间变量,在平面弹性扇形域问题中导出了一个斜对角Hamilton算子. 该算子具有主对角元为零,斜对角元是非零对称算子的结构特性. 得到两个独立的、对称的子正交关系.恰当选择对偶向量后, 直角坐标系下各向同性平面弹性问题的新正交关系被推广到极坐标情形. 根据控制微分方程的弱(积分)形式及相应的边界条件,建立了对应边值问题的变分原理, 并提出了相应的泛函表达式.      

弹性力学的一种正交关系

在弹性力学求解新体系中，将对偶向量进行重新排序后，提出了一种新的对偶微分矩阵，对于有一个方向正交的各向异性材料的三维弹性力学问题发现了一种新的正交关系．将材料的正交方向取为z轴，证明了这种正交关系的成立．对于z方向材料正交的各向异性弹性力学问题，新的正交关系包含弹性力学求解新体系提出的正交关系。     

薄板弯曲理论中一个新的广义变分原理及其交替max,min性质

本文在薄板弯曲的经典理论中提出一个以挠度、横向剪应变、曲率、弯矩、横向剪力、边界上的未知反力为自变函数的新的变分原理,在对自变函数预加不严厉的约束后,新泛函具有一连串交替max,min的性质。     

各向同性弹性力学求解新体系正交关系的研究

在弹性力学求解新体系中,将文献[3]对偶向量进行重新排序后,提出了一种新的对偶微分矩阵L,对于各向同性3维弹性力学问题发现了一种新的正交关系.文中证明了这种正交关系的成立.对于各向同性问题,新的正交关系包含文献[3]的正交关系.     

线弹性力学广义变分原理的构造函数理论

本文从构造函数理论来讨论广义变分原理,得到了构造函数与广义变分原理之间的对应关系,以及单值构造函数的一般解.     

软铁磁薄板磁弹性耦合作用的变分原理

研究磁弹性耦合问题的关键是正确计算作用在铁磁弹性体上的磁力，该文以磁场系统的磁能与磁介质弹性板应变能之和作为软铁磁薄板位于外加磁场合作用系统的能量泛函，以磁标势函数和位移函数的变分为独立变量，给出软铁磁薄板在任意外磁场中磁弹性耦俣作用变分原理，由此不仅导出磁和结构变形的联立控制方程，而且获得作用在薄板上的磁力表达式，进而可以对两类不同性质的铁磁板耦合作用的实验现象进行理论模拟     

等价变分原理泛函之间的联系

本文证明了等价变分原理的泛函,实质上都只相差某种加权残差项,这也就表明了,在已知的泛函后附加加权残差项,是建立等价变分原理最简便的方法.     

欧拉和力学的变分原理

<正> 欧拉(Leonhard Euler 1707—1783)在经典力学发展中的历史功绩,在于将数学分析方法应用于力学问题。因此,欧拉理应被认为是分析力学的奠基人之一。分析力学这门科学是以少数假定为基础,山这些假定出发,导出物体的平衡和运动的全部规律。目前,力学的变分原理是分析力学的基础,也就是数学上用变分关系的形式表示的基本的、原始的规则,     

Mixed variational principle in elasticity theory and canonical systems of equations

The paper proposes a modification of the mixed variational principle from which stationarity conditions are derived in the form of a mixed system of equations resolved for the first derivatives of the displacement and stress components acting in a plane perpendicular to one of the coordinate axes. The variational principle allows decreasing the dimension of the problem of elasticity thus reducing the system of equations to a canonical form. The modified mixed principle helps immediately obtain a canonical system of equations for various applied theories. This possibility is demonstrated with the example of the Timoshenko theory of plates __________ Translated from Prikladnaya Mekhanika, Vol. 43, No. 5, pp. 55–62, May 2007.     

A variational principle of perturbed motion on viscoelastic thin plates with applications

In this paper, in the light of the Boltzmann superposition principle in linear viscoelasticity, a mathematical model of perturbed motion on viscoelastic thin plates is established. The corresponding variational principle is obtained in a convolution bilinear form. For application the problems of free vibration, forced vibration and stability of a viscoelastic simply-supported rectangular thin plate are considered. The results show that numerical solutions agree well with analytical solutions. The project was supported by the National Natural Science Foundation of China (No. 19772027) and the Shanghai Municipal Development Foundation of Science and Technology (No. 98JC14032).     

特征函数展开解法的研究

以常微分方程的理论为基础,利用新的对偶变量、对偶微分矩阵和正交关系,以单连续坐标弹性体系为例,建立了与弹性力学求解新体系平行的特征函数展开解法.并将正交关系应用于可对角化边界条件的处理,实现了求解待定系数方程组的解耦,求得问题的显式封闭解.     

Formulation of a semi-analytical approach based on Gurtin variational principle for dynamic response of general thin plates

4 semi-analytical approach for the dynamic response of general thin plates which employes finite element discretization in space domain and a series of representation in time domain is developed on the basis of Gurtin variational principles. The formulation of time series is also investigated so that the dynamic response of plates with arbitrary shape and boundary constraints can be achieved with adequate accuracy.Project supported by the National Natural Science Foundation of China     

On the connections between the functionals of equivalent variational principles

It is proved in this paper that the functionals of equivalent variational principles are different essentially only in terms of weighted residues. Consequently, the simplest method for constructing equivalent variational principles is to add weighted residues to known functionals as first used by Courant [4].     

THE MATHEMATICAL MODELS AND GENERALIZED VARIATIONAL PRINCIPLES OF NONLINEAR ANALYSIS FOR PERFORATED THIN PLATES

ＴＨＥＭＡＴＨＥＭＡＴＩＣＡＬＭＯＤＥＬＳＡＮＤＧＥＮＥＲＡＬＩＺＥＤＶＡＲＩＡＴＩＯＮＡＬＰＲＩＮＣＩＰＬＥＳＯＦＮＯＮＬＩＮＥＡＲＡＮＡＬＹＳＩＳＦＯＲＰＥＲＦＯＲＡＴＥＤＴＨＩＮＰＬＡＴＥＳＣｈｅｎｇＣｈａｎｇｉｕｎ（程昌钧）；ＹａｎｇＸｉａｏ...     

Subspace variational principle of rods and shells

This paper builds the general forms of subspace variational principles of rods andshells which are taken as the controlled equations of the constitutive theories developedfrom the three-dimensional (non-polar) continuum mechanics. And the constitutiveequations of rods and shells using the principles are satisfactory.