关于弹性扁壳边界补充条件问题

文献[1]曾提出了确定四边简支矩形底扁壳边界应力函数的计算公式,此公式实为文献[2]所称的四边简支情形的补充条件。文献[2]在提出扁壳的广义变分原理的同时,利用此原理解决了许多扁壳边界问题,导出了比较广泛的扁壳边界补充条件,其结果我们曾在实际工作中有效地应用过。现在本文提出一个求扁壳边界补充条件的结构力学方法,此法简明、直观,而且适用于各种边界情形。     

关于40个自由度八结点壳体单元的一些计算试验

1.引言由等参数单元发展而来的40个自由度八结点的壳体单元不仅可应用来计算厚壳,而且可用来计算薄壳.文[6]对单元通过任一点的中面法线的计算,给出一个与文[1—4]所采用的不同的合理的方案,文[6,7]进行过实例计算.我们对国内及国外这两种方案,都编制了程序,进行比较性计算.应力计算使用了一个线性外推公式,可     

环向加筋园柱壳在静水压力作用下的总体塑性屈曲

一、前言环向加筋园柱壳是潜艇的主要承载部件,因此,研究它在静水压力作用下的总体塑性屈曲问题,具有很大的实用意义。在[1],[2],[5],[6][8]中都曾研究过此问题,在[7]中将以往的工作加以总结。并建议了与[6]中相似的近似计算公式。由于以往的工作都停留在公式推导,最后只是计算几个例子,不可能看出环向加筋园柱壳的各个几何参数对总体屈曲压力的影响,也难以评价[6][7]中的近似公式的误差程度。本文以典型的材料拉伸曲      

正交异性圆柱壳受局部外压的临界力

以往计算正交异性圆柱壳的临界力,多从微分方程组出发,编写较长的计算程序,化费很多机时才能得到结果。本文应用Cheng提出的准确四阶控制方程,把问题归化为解无限行列式的特征值。对于全部受外压,周向波数较多的壳导出了一个临界力公式。1.部分长度承受均布外压壳的临界力(图1) 文献[2]建立了正交异性圆柱壳准确的控制方程(本文使用的符号与[2]相同)     

正交各向异性柱壳的非线性参数共振问题——多频共振问题研究的应用

弹性结构动力稳定性问题,近年来一直受到各国的重视[1—13]。除研究线性与非线性弹性结构中的参数主共振外,在文献[2,3,4,7,8,13]中,还讨论了参数组合共振问题,在梁、杆、板方面组合共振已有较多的研究,在壳的组合共振问题方面文献较少。本文使用文献[18,19]中的多个快转相位方法和多频共振性质,论证了正交各向异性柱壳中参数主共振与组合共振的存在性和稳定性。     

旋转壳对称载荷有限元应力分析的系数配置法

本文用有限元系数配置法分析轴对称旋转壳,计算时不需坐标转换,对各种类型的壳体元素统一采用同一组基本公式协调求解。算法简单,精度高,可用于圆柱壳,圆锥壳,平法兰等工程上常用的旋转壳结构。由于在协调求解中可插入解析公式,便于处理螺栓连接,结合裙等不连续结构。本法是在文献[1]基础上改进而成。     

圆柱壳在静水压力作用下弹性屈曲的简化计算公式

圆柱壳在静水压力作用下发生弹性屈曲时,它的临界压力的计算公式最早是米赛斯(Von Mises)提出的。文献[2]曾将此公式进行了简化,建议了简化计算公式。文献[3]将二者进行了比较,表明在壳体较短或较厚时,文献[2]的公式与米赛斯公式结果有较大的误差。为了缩小简化计算公式的误差,本文建议了一个新的简化计算公式,通      

环向加肋旋转壳自由振动的样条函数解法

本文成功地应用样条函数对环向加肋旋转壳自由振动问题进行了分析。导出了截面惯性主轴为任意方向的环梁空间变形与位移谐调关系公式。这一公式较之文献[1]所给公式更具一般性,从而使得对环向加肋一般形状旋转壳的有限元分析有可能实现。本文方法同采用埃尔米特插值的通常有限元法相比较,具有多项式次数低,自由度少而连续性强、计算速度快、内存小等优点。数字算例表明,计算结果是令人满意的。     

薄扁壳非线性的变形协调方程

本文应用Koiter[1]、John[2]和Pietraszkiewicz[3]的理论,推导了薄扁壳非线性的变形协调方程。     

超声速流中有限长柱壳蒙皮颤振的精确线性理论

本文讨论了有限长柱壳超声速颤振的线性问题的数学基础,包括问题的提法以及气动力和颤振振型的精确求法;所采用的方法是作者在前文[11]中提出的方法的推广. 考虑到壳面气动力的非定域性以及壳体的精确力短理论,根据严格的线性理论,将柱壳蒙皮颤振问题化成了讨论一个新型的八阶非自共轭微分积分方程以及相应的八个边界条件所构成的复固有值问题:     

Instability of solution for a class of the third order nonlinear differential equation

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A SUPPLEMENTARY STUDY OF ANISOTROPIC PLASTIC FIELDS AT A RAPIDLY PROPAGATING PLANE－STRESS CRACK－TIP（I）

ＡＳＵＰＰＬＥＭＥＮＴＡＲＹＳＴＵＤＹＯＦＡＮＩＳＯＴＲＯＰＩＣＰＬＡＳＴＩＣＦＩＥＬＤＳＡＴＡＲＡＰＩＤＬＹＰＲＯＰＡＧＡＴＩＮＧＰＬＡＮＥ－ＳＴＲＥＳＳＣＲＡＣＫ－ＴＩＰ（Ｉ）ＬｉｎＢａｉｓｏｎｇ（林拜松）（ＲｅｃｅｉｖｅｄＪｕｌｙ１５．１９９４...     

On completeness for a 3-D linear theory of composite laminate

ＯＮＣＯＭＰＬＥＴＥＮＥＳＳＦＯＲＡ３－ＤＬＩＮＥＡＲＴＨＥＯＲＹＯＦＣＯＭＰＯＳＩＴＥＬＡＭＩＮＡＴＥＪｉａｎｇＹｏｕ－ｌｉａｎｇ（蒋友谅）（ＤｅｐａｒｔｍｅｎｔｏｆＡｐｐｌｉｅｄＭｅｃｈａｎｉｅｓ．ＰｅｋｉｎｇＩｎｓｔｉｔｕｔｅｏｆＴｅｃｈｎｏｌ...     

Vibration analysis of elliptical column partially submerged in water

In this paper, a general analytical method based on Ref. [1] is presented to study the bending vibration of an elliptical column partially submerged in water. Besides, it is pointed out that there is a limitation to the method mentioned in Ref. [2]. As a special example, the natural frequencies of circular column submerged in water considering compressibility are calculated, and the extent of compressible effect is given. Projects Supported by the Science Fund of the Chinese Academy of Sciences.     

Supplementary study on anisotropic plastic stress fields at a stationary plane-stress crack-tip

The results in Ref.[1]are not suitable for the cases of a≥2 .For this reason,we use the method in Ref.[1]to derive the general expressions of the anisotropic plastic stress fields at a stationary plane-stress crack-tip for both of the cases of a=2 and a>2 .As an example,we give the analytical expressions of the anisotropic plastic stress fields at the stationary tips of modeⅠand modeⅡplane-stress cracks for the case of a=2.     

CHAPLYGIN EQUATION IN THREE-DIMENSIONAL NON-CONSTANT ISENTROPIC FLOW-THE THEORY OF FUNCTIONS OF A COMPLEX VARIABLE UNDER DIRAC-PAULI REPRESENTATION AND ITS APPLICATION IN FLUID DYNAMICS(Ⅲ)

This work is the continuation of the discussion of Ref. [1]. In this paper we resolve the equations of isentropic gas dynamics into two problems: the three-dimensional non-constant irrotational flow (thus the isentropic flow, too), and the three-dimensional non-constant indivergent flow (i. c. the in compressible isentropic flow). We apply the theory of functions of a complex variable under Dirac-Pauli representation and the Legendre transformation, transform these equations of two problems from physical space into velocity space, and obtain two general Chaplygin equations in this paper. The general Chaplygin equation is a linear difference equation, and its general solution can be expressed at most by the hypergeometric functions. Thus we can obtain the general solution of general problems for the three-dimensional non-constant isentropic flow of gas dynamics.     

Generalized variational principles for linear elastic materials with voids

In this paper, the idea of variational principles of linear elastic theory is used to establish generalized variational principles for linear elastic materials with voids. The fundamental equations of linear elastic materials with voids used have already been established in Ref. [5].     

A polynomial method for solving the problems for lateral instability of cantilever plates

The present article researches the problems of the lateral instability of cantilever rectangular plates under a concentrated force or a uniformly distributed load respectively.We select the polynomial(2.1)instead of the cosecant function in Ref.[1]as the flexural functions.The minimum critical load obtained here is more exact than the results obtained in Ref.[1]     

AGAIN DISCUSSING ABOUT SINGULAR PERTURBATION OF GENERAL BOUNDARY VALUE PROBLEM FOR HIGHER ORDER ELLIPTIC EQUATION CONTAINING TWO-PARAMETER

In this paper using the method of "The Two-Variable Expansion Procedure" we again discuss the construction of asymptotic expression of solution of general boundary value problem for higher order ellitptic equation containing two-parameter whose boundary condition is more general than [1]. We give asymptotic expression of solution as well as the estimation corresponding to the remainder term.     

THE APPLICATION OF MULTI－SCALE PERTURBATION METHOD TO THE STABILITY ANALYSIS OF PLANE COUETTE FLOW

ＴＨＥＡＰＰＬＩＣＡＴＩＯＮＯＦＭＵＬＴＩ－ＳＣＡＬＥＰＥＲＴＵＲＢＡＴＩＯＮＭＥＴＨＯＤＴＯＴＨＥＳＴＡＢＩＬＩＴＹＡＮＡＬＹＳＩＳＯＦＰＬＡＮＥＣＯＵＥＴＴＥＦＬＯＷＺｈｏｕＺｈｅ－ｗｅｉ（周哲玮）（ＳｈａｎｇｈａｉＵｎｉｖｅｒｓｉｌｙ;Ｓｈａｇ...