锥壳一般弯曲,稳定和振动问题的位移型统一方程及其应用

1.前言弹性锥壳的一般弯曲、稳定和振动问题,在实际工程中经常遇到,但对其研究基本上限于轴对称问题且都是以挠度函数和应力函数为基本未知量.我们认为,对于锥壳的特征值问题、弹性地基锥壳以及锥壳组合结构,则宜采用锥壳的位移解法.本文作者之一曾对锥壳一般弯曲问题的位移解法进行了系统的研究,以广义超几何函数给出了一般解.在应用文献[1]结果的基础上,本文通过引入一个广义载荷q_n(s,θ,t),得到了以位移函数U(s,θ,t)表示的弹性锥壳一般弯曲、稳定和振动(包括弹性地基影响)问题的统一型式的控制方程.文献[2]用级数给出了锥壳横向自由振动问题的解,但应指出,由于文献[2]中     

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。     

变厚度锥壳方程及其渐近解

本文用薄壳理论导出了壁厚线性变化的锥壳在承受轴对称截荷时的复变量方程，在薄壳理论误差范围内求得了齐次方程的渐近解和工程实用载荷的非齐次解，并给出了算例。     

锥壳的轴压屈曲

依据新的精确的锥壳屈曲分支方程 ,研究承受轴向压力的刚性圆顶夹支截锥壳的稳定性。构造的屈曲模态接近分支点变形。应用 Galerkin法计算了各种截锥比壳体在全锥度的临界特征值、屈曲荷载和临界应力。结果表明 ,轴压屈曲临界应力σcr 随几何参数ν的减小和截锥比λ的增大而减小。     

板锥网壳结构的连续化分析

板锥网壳结构是一种受力性能合理，技术经济效益良好的新型空间结构形式。本文将板锥网壳结构连续化为能共同作用的特殊形式的三层薄壳，按薄壳理论建立其位移法和混合法的基本微分方程。通过对微分方程的求解，计算其整体位移及结构内力。该法具有一定的精度，可宏观地了解结构的力学性能，并可用于板锥网壳结构的初步设计。     

轴向冲击载荷作用下锥壳中弹性应力波传播的计算和实验研究

本文利用有限元分析和模型实验研究了在轴向冲击载荷作用下,锥壳中弹性应力波的传播、计算和实验结果表明,结构中存在着弹性纵波和弹性弯曲波的传播,它们传播的速度各不相同,使壳面承受不同的应力状态;讨论了纵波和弯曲波随壳面的衰减;实验指出,由于边界的影响,即使纵波的反射也会产生新的反射弯曲波沿锥面传播。     

纵筋加强的凸锥柱结合壳应力状态的有限元分析

本文应用SAP5程序对均匀外压下纵筋加强的凸锥拄结合壳的应力状态作有限元分析。计算结果与钢模试验值一致。它揭示了该结构的力学特性,证明采用纵筋加强能有效地降低凸锥柱结合壳在结合边附近的高应力。本研究为潜艇的结构设计提供了一种简易可行,且行之有效的加强方法。     

功能梯度材料扁锥壳的热弹性大变形分析

研究了功能梯度材料扁薄锥壳在横向非均匀升温场中的几何非线性大变形问题.基于von Kármán几何非线性理论推导出了以中面位移为基本未知量的功能梯度扁薄锥壳在横向非均匀热载荷作用下的轴对称大挠度控制方程.采用打靶法数值求解所得非线性常微分方程边值问题,得到了锥壳的大挠度弯曲变形数值解.给出了锥壳的变形与其形状参数、载荷和材料参数等变化的特征关系曲线,分析和讨论了温度参数和材料梯度变化参数对变形的影响.     

旋转壳的数值传递函数方法

应用数值传递函数方法建立了一种用于分析旋转壳静力、动力响应的截锥壳单元。在本方法中,单元的位移在环向展开为Fourier级数的形式,应用薄壳理论可以得到解耦的微分方程。通过Laplace变换可以将方程转化为频域内的常微分方程,将其表示为状态空间形式后,可以应用数值传递函数方法求解。对复杂的系统可以应用与有限元类似的方法,划分多个单元组合求解。文中给出了几种旋转壳的动力、静力问题的数值算例,并与其它方法进行了比较,表明本文方法具有精度高、计算方便等特点。     

The displacement solution of conical shell and its application

In this paper,the displacement solution method of the conical shell is presented.Fromthe differential equations in displacement form of conical shell and by introducing adisplacement function,U(s,θ),the differential equations are changed into an eight-ordersoluble partial differential equation about the displacement function U(s,θ)in which thecoefficients are variable.At the same time,the expressions of the displacement and internalforce components of the shell are also given by the displacement function.As special casesof this paper,the displacement function introduced by V.Z.Vlasov in circular cylindricalshell,the basic equation of the cylindrical shell and that of the circular plate are directlyderived.Under the arbitrary loads and boundary conditions,the general bending problem of theconical shell is reduced to finding the displacement function U(s,θ),and the generalsolution of the governing equation is obtained in generalized hypergeometric function,Forthe axisymmetric bending deformation of the     

在均布外压作用下复合材料三角形网格加筋圆锥壳体总体稳定性分析

本文在文献[1]的基础上加以推广,分析了在均布外压作用下复合材料三角形网格加筋圆锥壳体总体稳定性,考虑了蒙皮的正交拉弯耦合效应和加筋筋条的偏心效应.基于外压实验观察结果,通过选择恰当的位移分量表达式,本文利用Galerkin法获得了临界外压的近似表达式,并对某一C/E复合材料三角形内网格加筋圆锥壳体的临界外压值进行了理论计算,所得结果与实验值相当吻合.文中所得结果可供工程应用参考.     

A Donnell type theory for finite deflection of stiffened thin conical shells composed of composite materials

A Donnell type theory is developed for finite deflection of closely stiffened truncatedlaminated composite conical shells under arbitrary loads by using the variational calculusand smeared-stiffener theory.The most general bending-stretching coupling and the effectof eccentricity of stiffeners are considered.The equilibrium equations,boundary conditionsand the equation of compatibility are derived.The new equations.of the mixed-type ofstiffened laminated composite conical shells are obtained in terms of the transversedeflection and stress function.The simplified equations are also given for some commonlyencountered cases.     

一类偏微分方程组的一般解及其在壳体理论中的应用

本文给出了构造一类偏微分方程组一般解的方法,用这种方法构造的一般解是完备的。最后,利用这个方法构造了壳体中的柱壳平衡方程和锥壳运动方程的一般解。     

Effect of local loads on the stress-strain state of nonthin orthotropic conical shells

The paper analyzes the stress-strain state of nonthin orthotropic conical shells under local loads. The distribution of deflections and stresses in conical shells under local loads of some types is given as an example Translated from Prikladnaya Mekhanika, Vol. 44, No. 8, pp. 103–113, August 2008.     

On a Discrete Fourier Series Solution to Static Problem for Conical Shells of Circumferentially Varying Thickness

An approach is developed to solve the two-dimensional boundary-value problems of the stress-strain state of conical shells with circumferentially varying thickness. The approach employs discrete Fourier series to separate variables and make the problem one-dimensional. The one-dimensional boundary-value problem is solved by the stable discrete-orthogonalization method. The results obtained are presented as plots and tables __________ Translated from Prikladnaya Mekhanika, Vol. 41, No. 9, pp. 26–37, September 2005.     

Displacement type unified equation for bending, buckling and vibration of conical shells and its applications

By using Donnell's simplication and starting from the displacement type equations of conical shells, and introducing a displacement functionU(s,,) (In the limit case, it will be reduced to cylindrical shell displacement function introduced by V. S. Vlasov) and a generalized loadq,(s,,),the equations of conical shells are changed into an eighth—order solvable partial differential equation about the displacement functionU(s,,). As a special case, the general bending problem of conical shells on Winkler foundation has been studied. Detailed numerical results and boundary coefficients for edge unit loads are obtained.The project supported by the National Natural Science Foundation of China.     

Stability of laminated composite circular conical shells under external pressure

In this paper,based on the mixed-type theory developed by the same authors.atheoretical analysis is presented for the stability of laminated composite circular conicalshells under external pressure.The formulas for critical external pressure are obtained byusing the potential energy variation principle.Very good agreement is shown between thetheoretical prediction of critical external pressure and the experimental data.Finally,theinfluence of some parameters on critical external pressure is discussed numerically.Themixed-type theory developed by the same authors and the results obtained in this paperare very useful in aerospace engineering design.