中厚圆柱壳在局部荷载下有限变形与屈曲分析

在柱壳的有限元计算中，采用Mindlin八结点杂交壳单元和增量荷载法，基于选择积分，缩减积分及完全积分三种积分模式编制了分层计算各种厚度板壳的有限元程序FEAM，并对中厚圆柱壳在局部法向均布荷载作用下的弹塑性有限变形和屈曲问题进行了分析和计算，算例表明，利用FEAM可对壳体屈曲的临界荷载及屈曲后结构的承载与形状改变作定性与定量的分析.     

域奇异积分的解析计算

本文讨论了r~1型及lnr型二维域奇异积分的解析计算。对多项式荷载给出了域奇异积分的正确公式。而对于一般荷载,利用泰勒展开化为多项式荷载进行积分,并给出了积分误差估计。计算结果表明,本文方法是有效的。     

基于Mindlin解的桩基础最终沉降计算的应力面积法

利用Ｍｉｎｄｌｉｎ竖向附加应力公式，通过积分得到地基内矩形面积上三角形分布荷载作用下角点下竖向附加应力解析式，并通过对地基内矩形面积上均布和三角形分布载荷作用下角点下竖向附加应力公式关于深度进行积分，得到了计算角点下竖附加应力面积的解析式，根据解析式制表格，可供运用应力面积法进行群桩实体基础等的最终沉降计算时查用。     

裂纹面受荷载作用的应力强度因子的计算

基于比例边界有限元法计算了裂纹面有荷载作用情况下裂纹尖端的应力强度因子,给出了有限介质裂纹面作用荷载的比例边界有限元方程的基本求解过程.对于随径向坐标任意变化的一类面荷载的积分能够显式计算,不需要引入额外的近似;并将计算结果与解析解和数值结果进行对比,结果表明比例边界有限元法在计算裂纹面作用荷载时的应力强度因子是有效且精确的.此外,该方法可方便地处理各向异性材料裂纹问题,本文给出了正交各向异性矩形盘裂纹面受均布荷载情况的应力强度因子.     

考虑几何与压电非线性行为压电层合轴对称圆板的精确解

研究可移简支及夹支边界条件下,轴对称压电层合圆板在强电场和机械荷载联合作用下的非线性变形.考虑电致伸缩的非线性压电效应及几何非线性的影响,导出轴对称压电层合圆板的控制方程.通过调整坐标轴的位置对控制方程进行简化,得到关于挠度和径向力的4阶非线性控制方程.再通过简单的积分并引入无量刚变量将控制方程等价地化为2阶非线性耦合微分方程组.利用幂级数法得到可移简支及夹支边界条件下强电场和均布荷载共同作用时的挠度、径向力及径向位移的幂级数精确解.通过对双、单压电晶片执行器的数值计算及分析,得到电场、外载对于位移、径向力的影响关系.     

加筋土强度的理论研究及试验验证

将加筋材料对土体强度提高的贡献等效成一种附加围压, 通过莫尔圆法, 求得小主应力增量, 并认为土体在破坏时处于极限平衡状态, 得到了黏聚力和内摩擦角同时变化时的加筋土强度表达式, 对该式作了详细讨论, 用该式计算了6 例典型加筋土在轴对称荷载下的大主应力, 结果表明计算所得大主应力值与三轴试验值比较吻合.     

受预张力或均布边缘径向荷载的圆薄板的大挠度问题

本文以幂函数为试函数,用配点法计算圆薄板的轴对称大挠度,圆板可先受预张力的作用。荷载为轴对称分布荷载、均布边缘力矩及径向力或它们的联合作用。计算结果表明,本法求解的收敛速度和收敛范围远远超过幂级数解法。     

人行荷载下梁式结构振动分析的DQ-IQ混合法

为了评估人行荷载作用下梁式结构的振动舒适度，利用微分求积-积分求积，即DQ-IQ混合法求解移动荷载作用下梁的振动响应。人行荷载作用下梁式结构的振动控制方程是含Dirac函数的偏微分方程，首先利用IQ法离散与时间相关的Dirac函数，再利用DQ法把控制方程转化为二阶常系数微分方程，最后利用Newmark算法求解微分方程。以某钢结构连廊为例，利用DQ法计算结构自振频率并与解析解进行对比，结果验证了节点选取和边界条件施加的合理性，再利用DQ-IQ混合法和振型叠加法分别计算了不同行走步频下连廊的响应，计算结果表明，DQ-IQ混合法具有较高的可靠性和精确性。DQ-IQ混合法也可以推广到诸如车辆荷载作用下路面或桥梁的动力响应等其他移动荷载下结构的振动分析。     

多层地基上轴对称受荷刚性圆板问题

利用刚性圆板表面各点位移相等,并结合刚性圆板与地基表面的位移相容条件与光滑接触条件,经由Hankel变换,推导出了刚性圆板与分层地基表面接触应力的对偶积分方程;求解该对偶积分方程,再由多层地基应力与位移的传递矩阵解,并经Hankel逆变换,得到了多层地基上轴对称受荷刚性圆板问题的解.编制了计算程序,并进行了数值分析与计算.计算结果表明:对均匀地基而言,实际工程的计算分析可只考虑4倍刚性圆板直径以内深度范围内的应力与位移;而地基的分层性对地基的位移和应力有着较大的影响,简单地将均匀地基的结论推广到分层和非均匀地基是不恰当的.     

人行荷载下梁式结构振动分析的DQ-IQ混合法

为了评估人行荷载作用下梁式结构的振动舒适度,利用微分求积-积分求积,即DQ-IQ混合法求解移动荷载作用下梁的振动响应。人行荷载作用下梁式结构的振动控制方程是含Dirac函数的偏微分方程,首先利用IQ法离散与时间相关的Dirac函数,再利用DQ法把控制方程转化为二阶常系数微分方程,最后利用Newmark算法求解微分方程。以某钢结构连廊为例,利用DQ法计算结构自振频率并与解析解进行对比,结果验证了节点选取和边界条件施加的合理性,再利用DQ-IQ混合法和振型叠加法分别计算了不同行走步频下连廊的响应,计算结果表明,DQ-IQ混合法具有较高的可靠性和精确性。DQ-IQ混合法也可以推广到诸如车辆荷载作用下路面或桥梁的动力响应等其他移动荷载下结构的振动分析。     

Analysis and calculation of stresses and displacements in layered elastic systems

The general formulae for the stresses and displacements in layered elastic systems subjected to external loads are derived in this paper. On the basis of these formulae the practical formulae for calculation of the stresses and displacements in layered elastic systems under the action of vertical, centripetal-horizontal, unidirectional-horizontal and rotational-horizontal loads distributed on circular areas and compressed by rigid circular plates are further derived, and the corresponding computer programs have been worked out.     

Thermal stresses in infinite circular cylinder subjected to rotation

The present investigation is concerned with the effect of rotation on an infinite circular cylinder subjected to certain boundary conditions.An analytical procedure for evaluation of thermal stresses,displacements,and temperature in rotating cylinder subjected to thermal load along the radius is presented.The dynamic thermal stresses in an infinite elastic cylinder of radius a due to a constant temperature applied to a variable portion of the curved surface while the rest of surface is maintained at zero temperature are discussed.Such situation can arise due to melting of insulating material deposited on the surface cylinder.A solution and numerical results are obtained for the stress components,displacement components,and temperature.The results obtained from the present semi-analytical method are in good agreement with those obtained by using the previously developed methods.     

Fatigue growth modeling of cracks emanating from a circular hole in infinite plate

This paper presents a numerical approach of fatigue growth analysis of cracks emanating from a hole in infinite elastic plate subjected to remote loads. It involves a generation of Bueckner’s principle and a hybrid displacement discontinuity method (a boundary element method) proposed recently by the senior author of the paper. Because of an intrinsic feature of the boundary element method, a general crack growth problem can be solved in a single region formulation. In the numerical simulation, for each increment of crack extension, remeshing of existing boundaries is not necessary. Crack extension is modeled conveniently by adding new boundary elements on the incremental crack extension to the previous crack boundaries. As an example, fatigue growth process of an inclined crack in an infinite plate under uniaxial cycle load is modeled to illustrate the effectiveness of the numerical approach. In addition, fatigue growth of cracks emanating from a circular hole in infinite elastic plate subjected to remote loads is investigated by using the numerical approach. Many numerical results are given     

Equivalent inhomogeneity method for evaluating the effective elastic properties of unidirectional multi-phase composites with surface/interface effects

A new technique is presented for evaluating the effective properties of linearly elastic, multi-phase unidirectional composites. Various effects on the fiber/matrix interfaces (perfect bond, homogeneously imperfect interfaces, uniform interphase layers) are allowed. The analysis of nano-composite materials based on the Gurtin and Murdoch model of material surface is also included. The basic idea of the approach is to construct a circular inhomogeneity in an infinite plane whose effects on the displacements and stresses at distant points are the same as those of a finite cluster of inhomogeneities (fibers of circular cross-section) arranged in a pattern representative of the composite material in question. The elastic properties of the equivalent inhomogeneity then define the effective elastic properties of the material. The volume ratio of the composite material is found after the size of the equivalent circular inhomogeneity is defined in the course of the solution procedure. This procedure is based on a semi-analytical solution of a problem of an infinite plane containing a cluster of non-overlapping circular inhomogeneities subjected to loading at infinity. The method works equally well for periodic and random composites and – importantly – eliminates the necessity for averaging either stresses or strains. New results for nano-composite materials are presented.     

Bending of rectangular plates carried by vacuum cups

In order to carry thin plates, vacuum cups are frequently used. When the over-hang is large, the deflections and stresses of the plate have considerably large values. In this paper, the rectangular plate hung by circular vacuum cups is treated. The analysis is carried out for the plate, which is subjected to line loads and radial bending moments at the inner circular boundary and free at the outer rectangular boundary. In addition to these boundary conditions, the plate is subjected to different distributed loads on inner and outer domains. First, the general solutions for the deflections on each domain are obtained by using infinite series, which are expressed by the polar coordinate system. The several undetermined constants in these equations are decreased by the conditions of continuity at the inner boundaries. Satisfying the boundary conditions at the finite points on the outer edges of the plate, the deflections and stresses of the plate and the contact pressures between the plate and the vacuum cup are calculated. Typical results are presented in dimensionless graphical form for different parameters and vacuum cup edge conditions.     

Large Deflection of a Circular Plate on Elastic Foundation under Symmetrical Load

ABSTRACT

The large deflection of a clamped circular plate on elastic foundation under nonuniform but symmetrical loads has been investigated following Berger's approximate method. The deflections are obtained in the form of an infinite series involving Bessel functions. Graphs are plotted for deflections, bending moments, and bending stresses for various values of foundation modulus and load functions.     

浅埋隧道围岩应力场的解析解

隧道围岩应力和变形分析是隧道设计的重要内容。对深埋隧道的研究已取得了很多结果。但对于受地表边界和地面荷载的影响，浅埋隧道围岩分析在数学处理上仍存在一定的困难。一般采用边界元或有限元等数值方法，未见有解析解的报导。本文采用复变函数解法研究地面荷载作用下浅埋圆形隧道围岩的平面弹性问题，该解法利用复变函数保角变换将物理平面上的研究域映射到像平面上的圆环域内。将复势函数进行罗伦级数展开，通过边界条件得到罗伦级数展开式系数的递推公式，并由复势函数确定应力分量和位移分量。最后通过算例给出了围岩应力分布和沉降曲线。所得结果适用于任意分布荷载的情况，具有通用性。     

厚圆板轴对称振动的弹性力学解

本文以轴对称三维弹性力学基本方程为基础,导出厚圆板强迫振动的状态方程式。利用Ｍａｃｌａｕｒｉｎ级数和Ｓｙｌｖｅｓｔｅｒ定理,厚圆板的位移和应力可以用中面位移和应力的微分算子表示。通过载荷分解和圆板表面条件,可以得到厚圆板在对称载荷与反对称载荷作用下的振动控制方程。求解了厚圆板在周边固支和简支条件下的对称与反对称的自由振动问题。通过数值计算得到了这两类自由振动的固有频率。本文的方法适用于求解厚圆板在     

梯度弹性基础上正交异性薄板的弯曲

基于能量法和变分原理，采用双参数弹性基础模型，研究了梯度弹性基础上正交异性薄板在分布载荷作用下的弯曲问题。首先，根据能量法与变分原理，给出了梯度弹性基础上正交异性薄板的弯曲微分平衡方程，并得到了梯度弹性基础刚度系数 与 的计算表达式；进而，假设 向正应力在厚度方向上均匀分布，推导了弹性基础 向位移衰减函数 的计算式。在算例中，通过将梯度弹性基础退化为均质基础，并与Vlazov模型对比，证明了本文理论的正确性；最后，求解了弹性模量呈幂律分布的梯度基础上薄板的挠度分布，分析了基础上下表层材料弹性模量比 与体积分数指数 对薄板挠度分布的影响。