Green函数法在轴对称板壳理论中的应用

本文从轴对称板壳理论的基本方程出发,通过建立Green函数,导出了轴对称线载荷下解的一般表述式,由此可以求出任意轴对称载荷下的解,然后本文分别讨论了圆板和扁球壳受线载问题的解,文中的结果适用于各种边界条件。     

扁球壳在对称线布荷载作用下的稳定性问题

本文用三次B样条函数和逐步迭代方法求解扁球壳在对称线布荷载作用下的非线性稳定性问题,并引入截断单项式x_+~m克服了由于剪力突变所引起的求解困难。对于α=0.8831周边简支圆底扁球壳的计算结果表明:当K<25时所求得的临界荷载与前人结果一致,当K>25直到400本文所用方法仍然给出收敛良好的解答。文中还讨论了荷载作用半径趋于零时的极限情况,并与其他作者在集中荷载作用下的计算结果和实验结果进行了比较。     

浅悬链线壳的轴对称问题

本文得到了中心无孔口和有孔口的浅悬链线壳的一般解答,并给出了有关算例.     

极坐标有限条法解扁球壳问题

本文用有限条法解扁球壳问题,对于轴对称问题与位移和内力沿环向按cosnθ或sinnθ分布的非轴对称问题,分别推导了三类壳元(圆底壳元,圆孔外无限壳元,圆环底壳元)刚度矩阵的精确解。对于沿环向按cosnθ或sinnθ分布的环形面荷载和环形线荷载推导了单元等价节线荷载的表达式。编制了相应的计算程序,计算了典型例题。结果表明,此法具有计算工作量少而计算精度高的优点。     

扁球壳轴对称屈曲问题的样条函数解法

本文用三次B样条函数和迭代法求解圆底扁球壳在逐次加载时挠度增量和内力增量所满足的变系数非线性微分方程,从而得出均布荷载作用下周边固定圆底扁球壳轴对称弯曲问题的解答。文中计算了λ≤46的各种λ值的极值屈曲荷载,所得结果在λ≤20时与Budiansky等所得结果一致。     

扁球壳轴对称非线性弯曲和稳定的权余解

本文从扁球壳的积分方程组出发,通过新定义的残差表达式,用权余法详细地研究了扁球壳轴对称非线性弯曲和稳定问题.通过数值计算可以看出,本方法应用方便,精确可靠.     

刃型位错和圆弧形刚性线夹杂的干涉效应

位错和夹杂的干涉效应对于理解材料的强化和韧化机理具有十分重要的意义。文中研究了晶体材料中刃型位错和多条共圆弧刚性线夹杂的干涉作用。利用Riemann—Schwarz反照原理和复势函数的奇性主部分析技术，得到了问题的一般解答；对于只含一条刚性线夹杂的情况，给出了复势函数的封闭形式解。由Peach-Koehler公式求出了作用在刃型位错上的位错力，并讨论了圆弧形刚性线夹杂对位错力的影响规律，发现弧形刚性线对刃型位错有很强的排斥作用。本文解答不但可作为格林函数获得任意分布位错的相应解答，而且可以用于研究刚性线夹杂和任意形状裂纹的干涉效应问题。     

轴对称弹性圆锥扁壳非线性自由振动直接摄动解法

本文采用弹性圆锥扁壳中心无量纲振幅和壳体母线的倾角为参数，将挠度、应力函数的导数以及自由振动频率展开为双参量的幂级数形式，用直接摄动法获得各级递推线性偏微分方程，应用变分法求得各级递推方程的近似解答，从而给出弹性圆锥扁壳非线性自由振动频率的基本公式。     

轴对称弹性圆锥扁壳非线性自由振动直接摄动解法

本文采用弹性圆锥扁壳中心无量纲振幅和壳体母线的倾角为参数，将挠度、应力函数的导数以及自由振动频率展开为双参量的幂级数形式．用直接摄动法获得各级递推线性偏微分方程．应用变分法求得各级递推方程的近似解答．从而给出弹性圆锥扁壳非线性自由振动频率的基本公式。     

开孔固支和固定铰支轴对称球扁壳在双剪应力屈服准则下的极限荷载

导出轴对称球面扁壳在双剪应力屈服准则下的屈服条件，并求出开孔固支和固定铰支下轴对称球扁壳的极限载荷。     

The singular perturbation for the buckling of a truncated shallow spherical shell with the large geometrical parameter

A problem of practical interest for nonlinear axisymmetrical stability of a truncated shallow spherical shell of the large geometrical parameter with an articulated external edge and a nondeformable rigid body at the center under compound loads is investigated in this paper. By using modified method of multiple scales, the uniformly valid asymptotic solutions of this boundary value problem are obtained when the geometrical parameter k is large. Project supported by the National Natural Science Foundation of China     

考虑横向剪切变形的扁球壳在集中力作用下的分析

采用适于夹层壳的直线假设扁壳理论，应用三角级数法，导出了扁球壳齐次方程的解析解。进而分析了在顶点作用法向集中力和在偏心集中力作用下的解。计算了在偏心集中力作用下带孔球壳的位移和应力，并将结果与经典理论的结果进行了比较分析，结果表明，在集中力作用处和孔边处两种理论结果明显不同。     

Deformation and reverse snapping of a circular shallow shell under uniform edge tension

In this paper we study the deformation and stability of a shallow shell under uniform edge tension, both theoretically and experimentally. Von Karman’s plate model is adopted to formulate the equations of motion. For a shell with axisymmetrical initial shape, the equilibrium positions can be classified into axisymmetrical and unsymmetrical solutions. While there may exist both stable and unstable axisymmetrical solutions, all the unsymmetrical solutions are unstable. Since the unsymmetrical solutions will not affect the stability of the axisymmetrical solutions, it is concluded that for quasi-static analysis, there is no need to include unsymmetrical assumed modes in the calculation. If the shell is initially in the unstrained configuration, it will only be flattened smoothly when the edge tension is applied. No snap-through buckling is possible in this case. On the other hand, if the shell is initially in the strained position, it will be snapped back to the stable position on the other side of the base plane when the edge tension reaches a critical value. Experiment is conducted on several free brass shells of different initial heights to verify the theoretical predictions. Generally speaking, for the range of initial height H < 10 the experimental measurements of the deformation and the reverse snapping load agree well with theoretical predictions.     

Analysis of shallow spherical shell with circular base under eccentrically applied concentrated loads

In this paper,problems of a shallow sphericalshell with circular base under eccentrically appliedconcentrated loads are discussed.The solutions forsix cases of eccentrically applied concentrated loadsare given,namely:(1)Normal concentrated load,(2)Meridional tangential concentrated load,(3)Circumferential tangential concentrated load;(4)Concentrated moment in the tangential plane,(5)Concentrated moment in the meridional normalplane,(6)Concentrated moment in the circumferentialnormal plane.From the solutions of concentrated loads,thesolutions of distributed line loads in the form ofcosnθalong the circle are obtained.     

Determination of the perturbation parameter in large deflection of plates and shallow shells by means of the least square method

In this paper, the least square method of determination of the perturbation parameter is presented when the perturbation technique is used in the solution of large deflection of axisymmetrical plates and shallow shells. The examples of circular plates are calculated and compared with the exact solution and other perturbation solutions. The results show the best agreement with the exact solution among those perturbation solutions.     

Nonlinear bending of the shallow spherical shells with variable thickness under axisymmetrical loads

Based on the differential equation of the nonlinear bending of shallow sphericalshells with variable thickness under axisymmetrical loads,this paper studies thenumerical solution of the nonlinear differential equation by means of interpolatingmatrix method.The analysis of the results indicates that the suggested method is easyto implement and obtains the same high accuracy for both the displacements and theinternal forces.     

A rigorous solution for the axisymmetrical buckling of simply supported cylindrical sandwich shells under axial load

In this paper,based on ref[1],the axisymmetrical buckling of simply supportedcylindrical sandwich shells under the action of uniform axial load is solved by a rigorousmethod.The classical theory of shells is used for the two face sheets and the core isconsidered as a three-dimensional elastic body.A series of transcendental equations areobtained,from which the critical loads can be calculated by numerical methods.Numericalexamples are given to compare with the solutions of sandwich shell theories.     

Non-symmetrical large deformation of a shallow thin conical shell

I.IntroductionItisimportanttoresearchnon-symmetricalquestionsofshallowcollicalshellsintheoryoronapplication.Asonekindofpressurevessel'sparts,shallowconicalshellsareverycommonlyusedillellgineerillgpractice,becausethedifficultyofmanul\lctul.illgthemis'small.AlthotlghwelookupmanyChineseandtbreignperiodicalswhicharctlblctobefound,wehavenotyeth'ulldarticlesanddocumentsfornon-symmetricalandnolllinearquestionsofshitllowconictllshells.Oval'rccelltyears,ProlbssorWangXinzhiandhiscolleagueshavedonealot…     

The fundamental solution in the theory of shallow shells

A series representation for the fundamental solution of the shallow shell equations is obtained by means of a plane-wave decomposition of the Dirac δ-function. From this solution we can produce the singular solutions which correspond to concentrated forces, couples and thermal hot spots applied to a shallow shell with an arbitrary quadratic middle surface. The solutions converge for the entire range of the Gaussian curvature. Numerical results are presented for the case of a concentrated normal force acting on infinite shells having positive, zero or negative Gaussian curvature.