半圆环截面细环壳的屈曲

本文由Sanders非线性平衡方程和Koiter小应变协调方程推导出细环壳的非线性微分方程和稳定方程。用伽辽金法求解了静水压或边界载荷作用下的半园环截面细环壳的稳定方程。对于不同的边界条件及一系列几何参数,计算得到了临界载荷及屈曲模态。     

环壳屈曲的渐近解

本文提出分析圆环壳屈曲的一种渐近解析方法,由Sanders非线性平衡方程和壳中面变形协调方程推导出静水外压下环壳的稳定方程,求出了方程的渐近解,理论计算的临界压力值与Fishlowitz的实验结果符合良好,并研究了屈曲前非线性变形对临界载荷的影响。     

考虑横向剪切变形扁球壳方程的完备解

本文导出了厚扁球壳方程的完备级数解。位移分量和内力分量都以显式的形式表示成应力函数和法向位移的函数。文中说明了应力函数多值性对位移单值条件所起的作用,以及应力函数多值性和作用于边界上的力的合力及合力矩的关系。     

锥壳固有振动的精确解

本文从锥壳的Mushtari-Donnell型位移微分方程组出发,通过引入一个位移函数U(s,θ,τ)(在极限情况下,它将退化成对于圆柱壳引入的位移函数),将基本微分方程组化成为一个可解偏微分方程。这个方程的解用级数形式给出。     

轴对称圆环壳的基本解的完全渐近展开

1.序言轴对称圆环壳的复变量方程有多种形式,经[1]修改的Tlke 方程为x″+x(iμq_1+q_2)=τ(1)式中,非齐项τ()的表达式取决于载荷沿小圆的分布形式     

环壳百年忆张维

本文介绍环壳研究百年和纪念张维先生百年诞辰.     

用复变量表示的环壳几何非线性方程及其摄动解

本文从小应变,中小转动问题的弹性薄壳一般方程出发,导出用复未知函数表示的非线性的环壳轴对称变形的基本方程,并用摄动方法分別求解了整环壳和开口环壳问题.所得到的结果与其他作者用数值方法得到的结果吻合很好。     

三维双调和方程的解

求解弹性力学的空间问题,可归结为构造各种三维双调和函数.构造二维双调和函数已有许多结果.更精采的就是平面问题的复变函数方法.用任意两个解析函数将二维双调和函数表示出来.依照二维方法,本文用复变函数求解三维双调和方程,从而给出该方程的解.     

轴对称薄圆环壳方程级数解收敛性的研究

本文研究轴对称薄圆环壳齐次方程级数解的收敛性,证明了每种环壳都有在全域上收敛的级数解。     

Approximated-asymptotic solution of the complex variable equation of toroidal shells under axial symmetric loads

The series-approach and the asymptotic-approach are usually used to solve the complex variable equation of the toroidal shells under axial symmetric loads. As is known, the convergence of the series-solution is good only for small values of . On the other hand, the convergence of the asymptotic solution is good only for large values of μ. In this paper, based on an earlier work^[1], a new approach which may be called the approximated-asymptotic solution has been developed and it is valid for both small and large values of μ. It is shown that the results of the approximated-asymptotic solution for toroidal shell with μ=0.5 coincide very well with those of the series-solution, while the results of the asymptotic solution for this value of μ are not as good, and the results of the approximated-asymptotic solution for μ=15 agree with those of the asymptotic solution. This work has been carried out under the direction of Professor Zhang Wei.     

New solutions of Novozhilov's equation of toroidal shells

New solutions are obtained for Novozhilov’s equation of toreidal shells having general slenderness ratio 0<a<1 (a=a/R). In contrast to the results by continued fractiontechnique, the exponents and expansion coefficients of our series solutions are all closed and explicit. The series satisfies shell equation identically. Convergence proof is also demonstrated.Explicit expressions for boundary effect and monodromy indices are also given. Finally, we discuss the possibility of applying the present method to solve the fundamental system of equations for elastic shells with rotational symmetry.     

A novel solution of toroidal shells under axisymmetric loading

μ＝ｒ０／Ｒ０,κ＝１２（１－ν２）μｒ０／ｈ,λ２＝ｉκ,ν—Ｐｏｉｓｏｎ’ｓｒａｔｉｏ,θ—ｔａｎｇｅｎｔｉａｌａｎｇｌｅｏｆｓｈｅｌ,ｒ０—ｒａｄｉｕｓｏｆｔｈｅｍｅｒｉｄｉａｎｃｉｒｃｌｅ,ｈ—ｗａｌｔｈｉｃｋｎｅｓｏｆｓｈｅｌｓ,ｃｏｎｓｔ...     

Exact solution of the Boltzmann equation

We build up immediate connection between the nonlinear Boltzmann transport equation and the linear AKNS equation, and classify the Boltzmann equation as the Dirac equation by a new method for solving the Boltzmann equation out of keeping with the Chapman, Enskog and Grad’s way in this paper. Without the effect of other external fields, the exact solution of the Boltzmann equation can be obtained by the inverse scattering method.     

Exact solution for laminated continuous open cylindrical shells

I.Introducti0nNowadays,thecurrenttheoriesofplatesandshe1ls,suchasthetheoriesofReissner's,KirchhoffLove'sandAmbartsumyan'setc,areestablishedons0mehypotheses.Forexample-assumethatthemechanicalquantitiesarethepolynomialsofacertaincoordinatevariable.Itisshown…     

The capacity of slender toroidal sets in ℝN

Communicated by H. Weinberger     

Complex equations of flexible circular ring shells overall-bending in a meridian plane and general solution for the slender ring shells

ＩｎｔｒｏｄｕｃｔｉｏｎＥｑｕａｔｉｏｎｓｆｏｒｃｉｒｃｕｌａｒｒｉｎｇｓｈｅｌｌｓａｒｅｄｉｆｆｉｃｕｌｔｔｏｓｏｌｖｅ．Ｔｈｅｒｅｓｅａｒｃｈｏｆｔｈｉｓｐｒｏｂｌｅｍｓｔａｒｔｅｄａｔｔｈｅｂｅｇｉｎｎｉｎｇｏｆｔｈｉｓｃｅｎｔｕｒｙ．Ｉｎｔｈｅｌａｔｅ１９７０ｓａｎｄｅａｒｌｙ１９８０ｓ,Ｗ．Ｚ．Ｃｈｉｅｎ（１９７９,１９８０,１９８１）［１～３］ｒｅｂｕｉｌｔｔｈｅｃｏｍｐｌｅｘｅｑｕａｔｉｏｎｓｏｆａｘｉｓ＿ｓｙｍｍｅｔｒｉｃａｌｌｙｌｏａｄｅｄｒｉｎｇｓｈｅｌｌｓｐｒｅｓｅｎｔｅｄ…     

GENERAL SOLUTION OF THE OVERALL BENDING OF FLEXIBLE CIRCULAR RING SHELLS WITH MODERATELY SLENDER RATIO AND APPLICATIONS TO THE BELLOWS (Ⅰ)-GOVERNING EQUATION AND GENERAL SOLUTION

The overall bending of circular ring shells subjected to bending moments and lateral forces is discussed. The derivation of the equations was based upon the theory of flexible shells generalized by E.L. Axelrad and the assumption of the moderately slender ratio less than 1/3 (i.e., ratio between curvature radius of the meridian and distance from the meridional curvature center to the axis of revolution). The present general solution is an analytical one convergent in the whole domain of the shell and with the necessary integral constants for the boundary value problems. It can be used to calculate the stresses and displacements of the related bellows. The whole work is arranged into four parts: (Ⅰ) Governing equation and general solution; (Ⅱ) Calculation for Omega-shaped bellows; (Ⅲ) Calculation for C-shaped bellows; (Ⅳ) Calculation for U-shaped bellows. This paper is the first part.