扁球壳在均布压力与均匀温度场联合作用下的屈曲

根据扁壳几何非线性理论,推导了均布压力与均匀温度场联合作用下的扁球壳的位移型几何非线性控制方程.考虑夹紧边界条件,采用打靶法得到了扁球壳轴对称弯曲与屈曲的数值结果.讨论了壳体几何参数对平衡路径、临界荷载的影响.给出了壳体临界几何参数.当几何参数大于临界几何参数时,上、下临界荷载都随几何参数增加而增加.给定几何参数时,考察了不同均匀温度场对壳体上、下临界荷载、临界几何参数以及平衡构型的影响.均匀升温会使上临界荷载显著增加,会使下临界荷载略有减小.均匀变温会使临界几何参数改变.     

非线性边界滑移挤压膜流动

用一种包含初始滑移长度和临界剪切率的非线性边界滑移模型研究了两个球体间的挤压流体膜问题．研究发现初始滑移长度对低剪切率下的滑移行为起主要作用,而临界剪切率决定了高剪切率下的边界滑移程度．球体表面挤压流体膜的边界滑移量是与半径坐标相关的高度非线性函数．在挤压膜的中心点和远离中心点处由于低剪切率滑移量等于初始滑移长度,然而在高剪切率区域滑移长度迅速增加．球体挤压膜的流体动压力随着初始滑移长度的增加和临界剪切率的减小而减小,并且临界剪切率对流体动力的影响要比初始滑移长度大的多,当临界剪切率很小的情况下,流体动压随着最小膜厚的减小几乎不再增加．所用模型给出的理论预报和实验非常吻合．     

扁球壳在热-机械荷载作用下的稳定性分析

基于扁壳几何非线性理论,应用虚功原理和变分法推导了均匀变温场中圆底扁薄球壳在均布外侧压力作用下的位移型几何非线性控制方程.考虑周边不可移简支边界条件,运用打靶法计算获得了不同几何参数的扁球壳轴对称弯曲变形的数值结果.定义了壳体临界几何参数.考察了壳体几何参数对平衡路径和临界荷载的影响.当壳体几何参数大于壳体临界几何参数时,上临界荷载随几何参数的增加单调增加,下临界荷载在很小范围内随几何参数的增加而增加,之后随几何参数的增加而减小.给定几何参数时,考察了不同均匀温度变化对壳体临界几何参数、临界荷载和平衡构型的影响.均匀升温使上临界荷载显著增加,使下临界荷载和临界几何参数显著减小.     

集中荷载作用下组合梁剪切滑移计算分析

基于弹性理论,对钢-混凝土组合梁在竖向集中荷载作用下的剪切滑移应变差进行了理论分析,并与均布荷载作用下公认的理论解进行了计算对比．结果表明,所推导的在集中荷载作用下,钢-混凝土组合梁的剪切滑移应变差的计算公式是可信的．因为实际工程多为集中荷载作用,所以用该计算公式可以很方便的解决工程实际问题．     

翘曲空间曲线梁自然坐标精确解

基于现有空间曲线梁理论,考虑与扭转有关的翘曲变形和横向剪切变形的影响,建立了自然标架下空间曲线梁的内力和变形的解析解答．将该解答应用于受均布扭矩和竖向分布荷载的平面曲线梁的分析,将所得结果与Heins解答进行比较,证明了理论的正确．并应用该理论分析了解析式中翘曲和横向剪切变形项的影响．     

非均匀温度场中组合热超弹性球体的动态孔穴生成

在有限变形动力学的框架下,研究了在非均匀温度场中组合热超弹性球体,在表面均布拉伸死载荷作用下的动态孔穴的生成和增长问题．首先建立了相应的非线性数学模型,利用换元积分方法求得了孔穴半径与外加载荷之间的一个精确的微分关系,并进行了数值计算,得到了不同温度下球体中孔穴生成时的临界载荷和分叉曲线．考察了参数对孔穴生成与增长的影响,并与相应的静态结果进行了比较．结果表明孔穴是以一个有限的半径突然出现的,且随时间的演变孔穴半径呈现周期性的非线性振动;当温度升高,临界值降低,同时在相同的条件下动态临界载荷低于静态临界载荷．     

考虑横向剪切的对称层合圆柱正交异性扁球壳的非线性稳定问题

本文建立了计及横向剪切的复合材料对称层合圆柱正交异性扁球壳的大挠度理论。应用修正迭代法,研究了均布压力作用下对称层合圆柱正交异性固定边扁球壳的非线性稳定问题,得到了临界荷载的解析解。此解可直接应用到工程设计中。     

夹层圆柱壳在移动内压作用下的临界速度研究

基于夹层壳理论和三维弹性动力学理论,研究了无限长夹层圆柱壳在移动内压作用下的临界速度．首先,基于夹层壳理论,考虑夹芯的压缩和剪切变形以及面板的剪切变形,研究了轴对称简谐波在无限长夹层圆柱壳中的传播问题;其次,基于三维弹性动力学理论,将位移变量用Legendre正交多项式系表示,同时引入位置相关函数,将求解导波问题化为简单的特征值问题．利用这两种方法得到了最低模态的频散曲线,最小相速便是内压移动的临界速度．最后,用算例和数值模拟来验证方法的有效性．结果表明,两种理论得到临界速度吻合得较好;当波数较小时,两种理论得到的频散曲线吻合得很好,当k→∞时,夹层壳理论和弹性动力学理论得到的极限相速分别趋于面板和夹芯的剪切波波速．波数较小时,两种理论分析夹层圆柱壳的导波问题是有效的．数值模拟预测的临界速度与理论分析的结果吻合得很好．     

扁壳压曲的蠕变效应

本文讨论了混凝土扁壳压曲的蠕变效应.基于弹性薄壳的非线性理论,发现椭圆抛物面扁壳,其荷载-挠度曲线的上临界荷载将随时间而降低,而下临界荷载则随时间而上升.至于扁壳的局部失稳问题,其临界荷载仅取决于压曲发生瞬间材料的弹性模量.     

夹层圆板轴对称非线性弯曲和屈曲的样条函数解法

以三次B样条函数为试函数,用配点法计算夹层圆板的非线性弯曲．支座可以是弹性的．夹层板采用Reissner模型．荷载可为多项式型的分布荷载、均布边缘力矩、均布径向压力或均布径向预应力及它们的组合．首次用非线性理论计算了夹层圆板的压曲临界荷载．在均布荷载作用下的结果同幂级数解的结果作了比较,说明样条配点法具有收敛范围大、精度高、编写程序通用的优点．     

The effect of transverse shear upon the buckling stability of inelastic orthotropic plates

The problem of buckling of inelastic orthotropic plates is analyzed. The phenomena associated with the transverse strains of the plate are considered in the framework of the Ambartsumyan theory of plates, which excludes the hypothesis of undeformed normals. The problem is solved with the aid of the localized strains theory, and it is shown that in the case of orthotropic materials, i.e., those characterized by a large E/G ratio, the effect of the transverse shear must be taken into account in determining the critical stress for a plate under compressive loads parallel to its surface.Mekhanika Polimerov, Vol. 1, No. 2, pp. 133–136, 1965     

Predicting the transverse strength of unidirectional composites under combination loading

This article presents a mathematical model for predicting the transverse strength of unidirectional fiber composites subjected to combination transverse loading under different conditions. The behavior of the matrix is described by nonlinear physical equations consistent with the strain theory of plasticity for the active loading section. The fibers are assumed to be isotropic and elastic. The boundary-value problem of micromechanics that is formulated includes strength criteria for the matrix and fibers that mark the beginning of their possible failure. The modeling of the fracture process is taken farther through the use of a scheme that reduces the stiffness of the matrix and fibers in the failed regions in relation to the sign of the first invariant of the stress tensor. The method of local approximation is used together with the finite-element method to calculate the stress and strain fields in unidirectional composites with cylindrical fibers in a tetragonal layup. The model is used to study the behavior of an epoxy-based organic-fiber-reinforced plastic subjected to transverse loading in different simple paths — including simultaneous compressive and tensile loads, as well as transverse shear.Paper to be presented at the Ninth International Conference on the Mechanics of Composite Materials (Riga, October 1995).Translated from Mekhanika Kompozitnykh Materialov, Vol. 31, No. 4, pp. 473–481, July–August, 1995.     

Levy-type solution for buckling analysis of thick functionally graded rectangular plates based on the higher-order shear deformation plate theory

In this article, an analytical approach for buckling analysis of thick functionally graded rectangular plates is presented. The equilibrium and stability equations are derived according to the higher-order shear deformation plate theory. Introducing an analytical method, the coupled governing stability equations of functionally graded plate are converted into two uncoupled partial differential equations in terms of transverse displacement and a new function, called boundary layer function. Using Levy-type solution these equations are solved for the functionally graded rectangular plate with two opposite edges simply supported under different types of loading conditions. The excellent accuracy of the present analytical solution is confirmed by making some comparisons of the present results with those available in the literature. Furthermore, the effects of power of functionally graded material, plate thickness, aspect ratio, loading types and boundary conditions on the critical buckling load of the functionally graded rectangular plate are studied and discussed in details. The critical buckling loads of thick functionally graded rectangular plates with various boundary conditions are reported for the first time and can be used as benchmark.     

Finite element dynamic analysis of unsymmetric composite laminated beams with shear effect and rotary inertia under the action of moving loads

The finite element dynamic response of an unsymmetric composite laminated orthotropic beam, subjected to moving loads, has been studied. One-dimensional finite element based on classical lamination theory, first-order shear deformation theory, and higher-order shear deformation theory having 16, 20 and 24 degrees of freedom, respectively, are developed to study the effects of extension, bending, and transverse shear deformation. The theories also account for the Poisson effect, thus, the lateral strains and curvatures can be expressed in terms of the axial and transverse strains and curvatures and the characteristic couplings (bend–stretch, shear–stretch and bend–twist couplings) are not lost. The dynamic response of symmetric cross-ply and unsymmetric angle-ply laminated beams under the action of a moving load have been compared to the results of an isotropic simple beam. The formulation also has been applied to the static and free vibration analysis.     

Effect of a local load on an orthotropic glass-reinforced plastic shell

The deformation of a layered orthotropic cylindrical shell under a local normal load is investigated on the basis of equations that do not depend on the hypothesis of straight normals. The solutions of the analogous classical problems were analyzed in [3]; a solution based on equations that take transverse shear strains approximately into account was proposed in [4]. The high degree of variability of the state of stress created by local loads indicates that it is quite important to take transverse shear strains rigorously into account in problems of this class. An attempt is made to estimate the error introduced by the hypothesis of straight normals and to calculate the load leading to debonding of the shell.S. Ordzhonikidze Moscow Aviation Institute. Translated from Mekhanika Polimerov, No. 1, pp. 95–101, January–February, 1970.     

Axisymmetric buckling of laminated thick annular spherical cap

Axisymmetric buckling analysis is presented for moderately thick laminated shallow annular spherical cap under transverse load. Buckling under central ring load and uniformly distributed transverse load, applied statically or as a step function load is considered. The central circular opening is either free or plugged by a rigid central mass or reinforced by a rigid ring. Annular spherical caps have been analysed for clamped and simple supports with movable and immovable inplane edge conditions. The governing equations of the Marguerre-type, first order shear deformation shallow shell theory (FSDT), formulated in terms of transverse deflection w, the rotation ψ of the normal to the midsurface and the stress function Φ, are solved by the orthogonal point collocation method. Typical numerical results for static and dynamic buckling loads for FSDT are compared with the classical lamination theory and the dependence of the effect of the shear deformation on the thickness parameter for various boundary conditions is investigated.     

Thermal buckling and post-buckling analysis of functionally graded beams based on a general higher-order shear deformation theory

In the present work, attention is focused on the prediction of thermal buckling and post-buckling behaviors of functionally graded materials (FGM) beams based on Euler–Bernoulli, Timoshenko and various higher-order shear deformation beam theories. Two ends of the beam are assumed to be clamped and in-plane boundary conditions are immovable. The beam is subjected to uniform temperature rise and temperature dependency of the constituents is also taken into account. The governing equations are developed relative to neutral plane and mid-plane of the beam. A two-step perturbation method is employed to determine the critical buckling loads and post-buckling equilibrium paths. New results of thermal buckling and post-buckling analysis of the beams are presented and discussed in details, the numerical analysis shows that, for the case of uniform temperature rise loading, the post-buckling equilibrium path for FGM beam with two clamped ends is also of the bifurcation type for any arbitrary value of the power law index and any various displacement fields.