大变形对称弹性理论的广义变分原理

本文以陈至达提出的变形几何非线性理论￣［１］为基础，应用Ｌａｇｒａｎｇｅ乘子法，对大变形对称弹性力学问题进行了研究，给出了相应的位能广义变分原理、余能广义变分原理，以及动力学问题的广义变分原理；同时，文中还证明了位能广义变分原理和余能广义变分原理的等价性。     

弹性理论问题中的广义变分原理研究

本文除了给出三个弹性体系的泛函以外,重点在于建立以变分式形式出现的九个似变分原理,并将弹性理论问题中的各种变分原理,按其独立未知数的种类分成五种类型。从文中可以看到建立似变分原理要比构造泛函来得方便和广泛。最后,本文从似变分原理出发,求解弹性力学问题,从例题中可看到,直接从似变分原理出发求弹性力学问题的近似解,其运算十分方便明了。     

Generalized variational principles of symmetrical elasticity problem of large deformations

ＧＥＮＥＲＡＬＩＺＥＤＶＡＲＩＡＴＩＯＮＡＬＰＲＩＮＣＩＰＬＥＳＯＦＳＹＭＭＥＴＲＩＣＡＬＥＬＡＳＴＩＣＩＴＹＰＲＯＢＬＥＭＯＦＬＡＲＧＥＤＥＦＯＲＭＡＴＩＯＮＳＺｈａｏＹｕ－ｘｉａｎｇ（赵玉祥）ＧｕＸｉａｎｇ－ｚｈｅｎ（顾祥珍）ＬｉＨｕａｎ－ｑｉｕ...     

Large deformation symmetrical elasticity problems solved by the variational method

In this paper,based on the mathematical theory of classical mechanics and Chen‘s theorem,the variational method is used in the study of large deformation symmetrical elasticity problems.The generalized variational principles of potential energy and complementary energy,based on the instantaneous configuration are obtained,and the equivalence between the two principles is proved.Besides,the generalized variational principles of dynamical problems based on the instantaneous configuration are also given.     

用变分方法求解大变形对称弹性力学问题

文中以经典力学的数学理论和陈氏定理为基础,用变分的方法求解大变形对称弹性力学问题,得出了以瞬时位形为基准的位能广义变分原理和余能广义变分原理,以及两个变分原理的等价性;此外,还给出了以瞬时位形为基准的动力学问题的广义变分原理.     

平面曲杆的广义变分原理

1. 引言本文应用Lagfange乘子法,建立了两端边界均为完全约束的地下拱形结构动力分析的广义泛函(15);对于地面拱形结构的广义泛函,只要去掉广义泛函(15)中的抗力项即可;此外,还可以很简便地推广到各种不完全约束边界的情况中。对于非保守体系的各种情况,我们考虑了非保守力,给出了非保守体系的广义变分原理。同时在弹塑性分析中也是适用的。另外还给出了地下拱形结构静力分析的广义变分泛函(22)。     

连续介质中杆件系统的振动问题

弹性连续介质中杆件系统的振动问题,是工程中经常遇到的,这是弹性动力学和结构动力学的混合求解问题。按照一般的方法进行求解,似乎有很多困难,且很复杂。本文采用Lagrange乘子法,给出了这种类型平面问题的广义泛函。并通过实例说明本文方法的应用。     

THE VIBRATION PROBLEM OF ROD SYSTEM IN THE CONTINUOUS ELASTIC MEDIUM

The vibration of rod system in the elastic continuous medium is a problem which is often met and also a composite solution problem of elastic dynamics and structural dynamics. It seems rather difficult and complex to find solutions by general method.Using Lagrangian method of multipliers, we give herethe generalized functionals concerning this kind of plane problem and show how to apply the method presented through examples.     

The vibration problem of rod system in the continuous elastic medium

The vibration of rod system in the elastic continuous medium is a problem which is often met and also a composite solution problem of elastic dynamics and structural dynamics. It seems rather difficult and complex to find solutions by general method. Using Lagrangian method of multipliers, we give here the generalized functionals concerning this kind of plane problem and show how to apply the method presented through examples.