杂交应力元的应力子空间和柔度矩阵H对角化方法

证明了：1）杂交元假设应力模式线性无关是柔度矩阵非奇异的充分必要条件;以及2）等价假设应力模式形成相同的杂交元,在此基础上建立了假设应力模式的希尔伯特应力子空间,从而可以持方法简单地得到等价的正交归一化应力模式,实现了柔度矩阵对角化,使得杂交元形成过程中完全避免了繁杂的矩阵求逆运算,极大地提高了杂交元分析的计算效率,数值算例表明该方法是确实有效的。     

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.     

FINITE ELEMENT DISPLACEMENT PERTURBATION METHOD FOR GEOMETRIC NONLINEAR BEHAVIORS OF SHELLS OF REVOLUTION OVERALL BENDING IN A MERIDIONAL PLANE AND APPLICATION TO BELLOWS (Ⅰ)

ＩｎｔｒｏｄｕｃｔｉｏｎＢｅｌｌｏｗｓ,ａｓｈｅｌｌｏｆｗｒｉｎｋｌｅｄｍｅｒｉｄｉａｎｏｆｒｅｖｏｌｕｔｉｏｎ ,ｈａｓｂｅｉｎｇｉｎｃｒｅａｓｉｎｇｌｙｕｓｅｄｉｎｍｏｄｅｒｎｅｑｕｉｐｍｅｎｔａｓａｎｅｌａｓｔｉｃ＿ｓｅｎｓｉｔｉｖｅｅｌｅｍｅｎｔａｎｄａｆｌｅｘｉｂｌｅｊｏｉｎｔ.Ｔｈｅｆｏｒｍｅｒｉｓｕｓｕａｌｌｙｓｕｂｊｅｃｔｅｄｔｏｌａｒｇｅｄｉｓｐｌａｃｅｍｅｎｔｓａｔｉｔｓｅｎｄｓ,ａｎｄｔｈｅｌａｔｔｅｒｍａｙｐａｒｔｌｙｅｎｔｅｒｉｎｔｏｐｌａｓｔｉｃｓｔａｔｅ .Ｈｅｎｃｅ ,ｂ…     

FINITE ELEMENT DISPLACEMENT PERTURBATION METHOD FOR GEOMETRIC NONLINEAR BEHAVIORS OF SHELLS OF REVOLUTION OVERALL BEDING IN A MERIDIONAL PLANE AND APPLICATION TO BELLOW (Ⅱ)

ＩｎｔｒｏｄｕｃｔｉｏｎＴｈｅｅｑｕａｔｉｏｎｓａｎｄｔｈｅｓｏｌｕｔｉｏｎｐｒｏｃｅｄｕｒｅｓｏｆｔｈｅｆｉｎｉｔｅ＿ｅｌｅｍｅｎｔ＿ｄｉｓｐｌａｃｅｍｅｎｔ＿ｐｅｒｔｕｒｂａｔｉｏｎｍｅｔｈｏｄ (ＦＥＤＰＭ)ｆｏｒｔｈｅｇｅｏｍｅｔｒｉｃｎｏｎｌｉｎｅａｒｂｅｈａｖｉｏｒｓｏｆｓｈｅｌｌｓｏｆｒｅｖｏｌｕｔｉｏｎｓｕｂｊｅｃｔｅｄｔｏｐｕｒｅｂｅｎｄｉｎｇｍｏｍｅｎｔｓｏｒｌａｔｅｒａｌｆｏｒｃｅｓｉｎｏｎｅｏｆｔｈｅｉｒｍｅｒｉｄｉｏｎａｌｐｌａｎｅｓｗｅｒｅｐｒｅｓｅｎｔｅｄｉｎ (Ⅰ ) .…     

旋转壳在子午面内整体弯曲的几何非线性摄动有限元法及在波纹管计算中的应用(Ⅰ)

为切实有效地计算波纹管,建立了旋转壳在子午面内整体弯曲几何非线性问题的摄动有限元法。以结构环向应变的均方根为摄动小参数,将有限元节点位移列式和节点力列式直接展开。通过摄动小参数将非线性有限元的载荷分级和迭代过程有机地统一起来,即载荷的分级是有约束的,每一级载荷增量和所对应的位移增量之间的关系是已知的,每一级的计算一步到位。为叙述方便并具实用性,将旋转壳用截锥壳单元进行离散。位移分量和载荷分量沿环向按Fourier级数展开,沿子午线用多项式插值,端面弯矩和横向力化成载荷分量离散到节点上。采用Sanders中小转角非线性几何方程和各向同性广义Hooke定律。对多层材料叠合而成的旋转壳按各层薄膜应变、弯曲应变、扭转应变相等的原则进行处理,该方法能方便有效地计算单层和多层波纹管整体纯弯曲、横向弯曲的几何非线性问题。并为有限元处理非线性问题提供了一条新途径。     

旋转壳在子午面内整体弯曲的几何非线性摄动有限元法及在波纹管计算中的应用(Ⅱ)

利用(Ⅰ)提出的旋转壳在子午面内整体弯曲的几何非线性摄动有限元法分析了波纹管在纯弯矩、横向力作用下的刚度和应力分布。首先,将其中的一阶摄动解(线性解)和作者曾经提出的中细环壳一般解、初参数积分解进行了比较,以及与他人的实验、有限元分析进行了比较,表明本法具有良好的精度和可靠性,且如(Ⅰ)所指出的那样,波纹管子午线曲率的突变不妨碍一般直线单元的应用。然后,讨论了波纹管的非线性特征,结果显示,波纹管的非线性效应主要来自其环板,而且环板愈宽非线性效应愈大,例如,C型波纹管相当于环板宽度为零的U型波纹管,因而其非线性效应几乎可以忽略不计。此外,在纯弯矩作用下,依线性解波纹管各个波的应力分布是相同的,而依非线解各个波的应力分布是不相同的,但对于常见的波纹管,在工程精度内线性解是有效的。     

GENERAL SOLUTION OF THE OVERALL BENDING OF FLEXIBLE CIRCULAR RING SHELLS WITH MODERATELY SLENDER RATIO AND APPLICATIONS TO THE BELLOWS (Ⅲ)-CALCULATION FOR C-SHAPED BELLOWS

ＩｎｔｒｏｄｕｃｔｉｏｎＣ＿ｓｈａｐｅｄｂｅｌｌｏｗｓｏｒｒｅｆｅｒｒｅｄｔｏａｓｓｅｍｉ＿ｃｉｒｃｌｅｂｅｌｌｏｗｓａｒｅｗｉｔｈｃｏｍｐｌｅｘｃｏｎｆｉｇｕｒａｔｉｏｎ(Ｆｉｇ .1) .Ａｔｔｈｅｃｏｎｃａｖｅａｎｄｃｏｎｖｅｘｊｏｉｎｔｓｏｆｔｈｅｓｈｅｌｌ,ｆｏｒｅｘａｍｐｌｅａｔｐｏｉｎｔＣ ,ｔｈｅｌａｔｉｔｕｄｅａｎｇｌｅψｉｎｃｒｅａｓｅｓｂｙ 180°ａｂｒｕｐｔｌｙ .Ｓｏｉｔｉｓｔｈｅｋｅｙｔｏｃａｌｃｕｌａｔｉｏｎｆｏｒｂｅｌｌｏｗｓｔｈａｔｍａｋｉｎｇｕｐｓｏｌｕｔｉｏｎｓｅｘａｃｔ…     

Large deflection of circular plate under compound load

By means of the perturbation method, this paper presents an approximate solution for large deflection of clamped circular plate under uniform pressure together with a concentrated load at the center. The special case of vanishing central deflection is also discussed. In this paper, a load distribution function is introduced so as to make the compound loads depend on a single load parameter, and average angular deflection is used as the single displacement perturbation parameter.     

Calculation of stresses and deformations of bellows by initial parameter method of numerical integration

By reducing the boundary value problem in stress analysis of bellows into initial value problem, this paper presents a numerical solution of stress distribution in semi-circular arc type bellows based upon the toroidal shell equation of V. V. Novozelov^[8]. Throughout the computation, S. Gill’s method^[1O] of extrapolation is used. The stresses and deformations of bellows under axial load and internal pressure are c-alculated, the results of which agree completely with those derived from the general solution of Prof. Chien Wei-zang^[1-4]. The extrapolation formula presented in this paper greatly promotes the accuracy of discrete calculation.The computer program in BASIC language of Wang 2200 VS computer is included in the appendix.     

复合材料对称层合板单向拉伸与面内剪切下的三维应力分析

本文给出了单向拉伸与面向剪切载荷下复合材料对称层合板中心区域的应力和应变沿板厚的数值计算分布规律。计算结果表明，在斜交对称辅层的层合板中心区域层间界面附近存在着层间边界层效应。层间界面处纤维走向的突变导致局部的三维应力状态和很强的应力集中。