General solutions of axial symmetrical ring shells

This paper gives the general solutions of axial symmetrical ring shells for all values of slenderness ratio. This solution is newly brought out, and can be used to solve various practical problems, including corrugated tubes, thermal expansion joints, Borden tubes, etc.     

Method of high-order lagrange multiplier and generalized variational principles of elasticity with more general forms of functionals

It is known[1]that the minimum principles of potential energy andcomplementary energy are the conditional variation principles underrespective conditions of constraints.By means of the method of La-grange multipliers,we are able to reduce the functionals of condi-tional variation principles to new functionals of non-conditionalvariation principles.This method can be described as follows:Mul-tiply undetermined Lagrange multipliers by various constraints,andadd these products to the original functionals.Considering these un-determined Lagrange multipliers and the original variables in thesenew functionals as independent variables of variation,we can see thatthe stationary conditions of these functionals give these undeter-mined Lagrange multipliers in terms of original variables.The sub-stitutions of these results for Lagrange multipliers into the abovefunctionals lead to the functionals of these non-conditional varia-tion principles.However,in certain cases,some of the undetermined Lagrangemultipliers ma     

圆薄膜中心部份受均布载荷产生的对称变形

本文给出了圆薄膜中心部份受均布载荷产生的对称弯曲变形的解,它的极限给出圆薄膜在中心集中载荷下的解.它们是Hencky圆薄膜解以后,第三种有关的圆薄膜解.     

对于“轴对称弹性体的有限元分析”一文的讨论

关于线性三角形单元精确刚度矩阵的计算,确实存在有不收敛的项,但是与这些项相对应的行列,最终都是要处理掉的.因为这些项只发生于节点在对称轴上的时候,而此时总有u_i=0,因此只需在程序编制上预先作一次判断就行.我曾作过大量的精确矩阵的计算,结果表明是良好的.Zienkiewicz的错误结论,主要在于Ⅰ₁的错误公式,从而引起计算结果偏离实际.     

一般旋转壳在轴对称变形下的复变量方程

本文在Love-Kirchhoff的假定下,求得了一般旋转壳在轴对称变形下的复变量方程.当旋转壳是圆截面环壳时,这些方程简化为F.T?lke(1938)[3],R.A.Clark(1950)和B.B.Новожилов(1951)[3]的方程.当平均半径R比环截面半径a大得很多时,求得了细环壳的复变量方程,当这个细环壳的截面是圆形时,简化作为作者(1979)[6]的圆截面的细环壳复变量方程,我们列出了椭圆截面的细环壳复变量方程.当椭圆截面近似于圆截面时,该方程在形式上和圆细环壳方程基本相同.     

弹性圆板在一侧受均载而四周固定的条件下不用Kirchhoff-Love假设的一级近似理论(Ⅰ)

根据一般形状的三维弹性板不用Kirchhoff-Love假设的近似理论[1],[2],作者导出了三维弹性圆板的广义变分泛函,从而得到了圆板四周固定和一侧受均布载荷下的一级近似理论的微分方程和有关边界条件,其解析解答留待另文处理.     

TORSIONAL RIGIDITY OF SHELLS OF REVOLUTION

In this paper,the general equations of equilibrium for axisymmetrical deformationincluding the torsional deformation of revolutional shells are derived.It is shown that theshearing stress distribution due to torsion is independent of other stress componentsincluding those of membrane stress and bending stress.In this paper,the torsional deformation is considered to be represented by membraneaction only,and also by the combined action of bending membrane deformation.It is shownthat the main contribution of torsional rigidity is that related to membrane action.     

VARIATIONAL PRINCIPLES AND GENERALIZED VARIATIONAL PRINCIPLES FOR NONLINEAR ELASTICITY WITH FINITE DISPLACEMENT

In a previous paper (1979), the minimum potential energy principle and stationary complementary energy principle for nonlinear elasticity with finite displacement, together with various complete and incomplete generalized principles were studied However, the statements and proofs of these principles were not so clearly stated about their constraint conditions and their Euler equations. In somecases, the Euler equations have been mistaken as constraint conditions. For example, the stress displacement relation should be considered as Euler equation in complementary energy principle but have been mistaken as constraint conditions in variation. That is to say, in the above mentioned paper, the number of constraint conditions exceeds the necessary requirement. Furthermore, in all these variational principles, the stress-strain relation never participate in the variation process as constraints, i.e., they may act as a constraint in the sense that, after the set of Euler equations is solved, the stress-strain     

COMPARISON OF THE CALCULATIONS OF THREE-CONVOLUTION CIRCULAR ARC CORRUGATED DIAPHRAGMS BY TOROIDAL SHELL THEORY AND BY ORTHOGONAL ANISOTROPY PLATE THEORY

The calculation of elastic deformations of corrugated diaphragms was given by orthogonal anisotropy plate theory, and its result agrees with the experimental results. But it has never been discussed seriously how the number and form of convolutions affect the elastic deformations and stress distributions of anisotropyplate. As a result, adaptable limits of orthogonal anisotropy plate theory cannot be indicated when it is used to calculate diaphragms. It is said that the theory is fairly good for calculating elastic deformations of the diaphragms which have more convolutions. It is also said that the error in calculating stresses is rather large. This paper, by using the toroidal shell theory, presents the calculation of deformationsand stresses of three-convolution circular are corrugated diaphragms both symmetrical and unsymmetrical, compares its result with that of the orthogonal anisotropy plate theory and gives definite adaptable limits of the latter theory.