动态扩展裂纹的若干反平面问题的研究

采用复变函数论,对反平面条件下的动态裂纹扩展问题进行研究。通过自相似函数的方法可以获得解析解的一般表达式。应用该法可以很容易地将所讨论的问题转化为Riemann—Hilbert问题,并可以相当简单地得到问题的闭合解。文中分别对裂纹面受均布载荷、坐标原点受集中增加载荷、坐标原点受瞬时冲击载荷以及裂纹面受运动集中载荷Px／t作用下的动态裂纹扩展问题进行求解,得到了裂纹扩展位移、裂纹尖端的应力和动态应力强度因子的解析解。应用该解并通过叠加原理,就可以求得任意复杂问题的解。     

柔性基层合柱瞬态响应的有限元分析

良好的尺寸设计可优化结构的力学性能,为了研究几何参数对柔性基底结构抗冲击性能的影响,本文运用ABAQUS软件,计算了柔性基底层合柱受冲击载荷时的瞬态响应,对比分析了不同基底厚度、截面尺寸的柔性基底层合柱的动态力学性能。给出了层合柱上端面中心点的位移、速度、加速度等响应,以及接触面中心点处的应力、应变响应,发现冲击过程中柔性基层合柱出现了大变形。结果表明:柔性基底对中间层的缓冲保护起到了较大的作用,减少了冲击力对中间层的破坏;柔性基层合柱瞬态响应随基底厚度的增加而减小。均布载荷冲击下,截面尺寸为10mm或7.5mm的层合柱瞬态响应平缓且出现一定幅度的波动;截面尺寸为4mm、5mm、5.2mm层合柱出现失稳现象,发生失稳的时刻分别为7.8ms、11.4ms、13.6ms。     

一种新型结构火炮身管膛线的计算分析

针对传统的火炮身管内弹道结构形式,提出了一种新型结构形式的火炮身管膛线——渐变截面结构膛线。以大口径火炮身管膛线作为研究对象,计算分析传统等截面结构膛线和渐变截面结构膛线的弹丸弹带挤进阻力、导转侧向力、膛线截面面积和膛线摩擦力的变化情况。计算结果表明,新型渐变截面结构膛线有利于增强弹丸弹带的挤入能力,减少膛线根部应力集中,减少弹丸弹带对膛线的冲击和磨损,有效提升弹丸弹带的闭气性能,同时渐变结构膛线可有效减小弹丸在膛内运动时受到的扰动,使得弹丸在膛内运行平稳,减少炮口章动,在保证射击精度的同时,有利于提高身管的使用寿命。     

裂纹表面承受均布载荷时的应力强度因子及裂纹张开位移的边界配…

本文针对裂纹表面承受载荷时的应力条件，提出了新的应力函数，对于各种裂纹模型，各种边界条件，各种边界形状，裂纹表面自由或承受均布载荷等均适用。并利用边界配位法，计算了裂纹表面承受均布载荷的方型板内中心裂纹的应力强度因子及裂纹的张开位移。     

动态光弹性方法的主应力分离的研究

本文提出了动态光弹性、动态焦散线实验方法同边界元法结合的混合法，并用这种方法解决了动态光弹性主应力分离的问题，首先对现有的多火花高速摄影系统进行了改造，在动态实验过程中，成功地得到了不同瞬时的清晰的动态光弹性的等差线条纹和动态焦散线系列图像，这样，便可提取不同瞬时的边界应力值、全场主应力差值及边界上的外载。继而提出用Ｌａｐｌａｃｅ变换域上的边界元法来求解在冲击载荷作用下二维弹性模型全场的主应力和。最后，以受冲击载荷作用的圆盘为例，进行实验及边界元法计算，得到了分离的主应力场。     

圆柱壳在两种非轴对称同步移动载荷作用下的动力响应

本文根据工程实例计算的需要,研究了有限长弹性圆柱薄壳在两种非轴对称同步移动载荷作用下的动力响应问题。两种非轴对称同步移动载荷作用是指非轴对称移动的集中载荷,以及同步移动且作用范围随移动位置增加的均布载荷的共同作用。建立了在上述两种不同类型载荷作用下的具有对称形式的动力学微分方程组;分别采用Dirac函数与Heaviside函数表示移动的均布载荷与集中载荷,设定位移函数的基础上,应用Galerkin法及Laplace变换,求得了圆柱薄壳应力与位移动态响应的解析解;通过具体算例,将所得到解析解的计算结果与ANSYS数值解进行了对比分析,验证了解析解的可靠性。     

三点弯曲试样动态冲击特性的有限元分析

本文使用动态有限元技术，对两种不同几何尺寸，两种不同材料的三点弯曲试样在三类七种不同冲击载荷作用下的动态响应进行了分析，求得了动态应力强度因子随时间的变化规律，并与准静态应力强度因子进行了比较，计算结果表明：半冲击载荷历史代入静态公式确定动态应力强度因子的做法是不正确的，要求得动态应力强度因子，必须对试样进行完全的动态分析，当材料的Ｅ／ρ值相同时，动态应力强度因子的响应曲线完全相同，而动态应力强度     

端部切向载荷作用下的压杆失稳分析及其应用

细直杆件在压应力作用下会产生横向屈曲即失稳．直杆撞击刚性平面或拉断卸载后将形成压缩波，因承载压缩载荷的长度增加可以引起失稳．冲击速度转换的压应力沿着杆件切线方向，该处弯矩和剪力为零；而众多文献设定的失稳段固支边界条件并不准确．基于精确的杆件变形曲率方程得到端部载荷指向杆件中固定点时的受压失稳条件，得到其极限状态即载荷沿杆端切向作用时失稳长度相当于两端简支的1.5 倍．对于钢丝绳拉断形成的冲击失稳，载荷恒定而长度增加，可以产生高阶屈曲即在侧向出现多次曲折，并基于尼龙-橡胶带的模拟试验给出了定性说明．     

冲击法改善T91钢焊接残余应力的研究分析

基于焊后热处理可以降低T91钢焊接残余应力,但无法改变其应力状态的分布问题,本文模拟分析了冲击法对于改善焊接残余应力的影响情况。通过ANSYS软件平台,导入经焊后热处理后的残余应力为初始状态,分析了不同的冲击力度、冲击间隔、双点冲击情况对于T91钢中小径薄壁管焊接残余应力的影响。模拟结果表明:冲击处理可以在处理表面一定深度范围内引入一定区域占比的压应力,并且压应力区域随载荷的增加而加大;由于不经焊后热处理的最高应力集中在焊缝内表面区域,因此只通过冲击处理的机械方式不能得到良好的改善焊后残余应力效果。通过焊后热处理结合焊缝区外表面冲击处理,可以在降低焊接残余应力的同时引入一定比例的压应力,从而得到较好的应力状态。单点环向冲击间隔7.2°的0.2mm冲击位移载荷下,具有75%左右的外表面环向压应力产生,可作为改善T91钢中小径薄壁管焊接残余应力的方案。     

脆性岩石断裂破坏机理的边界配位法分析

针对裂纹表面承受载荷时的应力条件，提出了新的应力函数，该应力函数对于各种裂纹模型、各种边界条件、各种边界形状、裂纹表面自由或承受均布载荷等均适用．并利用边界配位法，计算了在压缩载荷下，岩石内部裂纹的应力强度因子（ＳＩＦ），给出了关于岩石断裂破坏的一些新结论     

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。     

Surface and non-local effects for non-linear analysis of Timoshenko beams

In this paper, we present a non-local non-linear finite element formulation for the Timoshenko beam theory. The proposed formulation also takes into consideration the surface stress effects. Eringen׳s non-local differential model has been used to rewrite the non-local stress resultants in terms of non-local displacements. Geometric non-linearities are taken into account by using the Green–Lagrange strain tensor. A C⁰ beam element with three degrees of freedom has been developed. Numerical solutions are obtained by performing a non-linear analysis for bending and free vibration cases. Simply supported and clamped boundary conditions have been considered in the numerical examples. A parametric study has been performed to understand the effect of non-local parameter and surface stresses on deflection and vibration characteristics of the beam. The solutions are compared with the analytical solutions available in the literature. It has been shown that non-local effect does not exist in the nano-cantilever beam (Euler–Bernoulli beam) subjected to concentrated load at the end. However, there is a significant effect of non-local parameter on deflections for other load cases such as uniformly distributed load and sinusoidally distributed load (Cheng et al. (2015) [10]). In this work it has been shown that for a cantilever beam with concentrated load at free end, there is definitely a dependency on non-local parameter when Timoshenko beam theory is used. Also the effect of local and non-local boundary conditions has been demonstrated in this example. The example has also been worked out for other loading cases such as uniformly distributed force and sinusoidally varying force. The effect of the local or non-local boundary conditions on the end deflection in all these cases has also been brought out.     

The determination of the elastic field of a polygonal star shaped inclusion

Recently we found that the elastic field is uniform in a pentagonal star (five-pointed star inclusion) [1], and in a triangular inclusion [2], when an eigenstrain is distributed uniformly in these inclusions. This result is similar to the famous result of Eshelby (1957) that the elastic field is uniform in an ellipsoidal inclusion in an infinitely body when an eigenstrain is distributed uniformly in the ellipsoidal inclusion. We also found that for a Jewish star (Star of David or six points star) or a rectangular inclusion subjected to a uniform eigenstrain, the stress field is not uniform in these inclusions. These results also hold for two dimensional plane strain cases. Furthermore these analytical results are confirmed experimentally by photoelasticity method. In this paper, we investigate a more general inclusion of an m-pointed polygonal inclusion subjected to the uniform eigenstrain. We conclude that the stress field is uniform when m is odd number. This conclusion agrees with the speculation made by B. Boley after the author's talk at Shizuoka [2].     

Mechanics of adhesive joints

Summary Taking into consideration both the pulling and bending actions of the external force, the differential equations for bending of a partly attached tape in a peeling test have been derived. The equations relating the peeling load to the adhesive force were derived under the assumption that the peeling may proceed step by step from the attached end when the adhesive force is overcome by either the tensile stress along the interface (shearing peeling) or that which is perpendicular to the interface (tensile peeling). To verify the validity of the obtained equations, the dependence of the peeling load P on the angle between the direction of the action of the load and the adhering surface has been investigated using plasticized polymer films. In view of the elementary mechanics, the results were satisfactory, while a modification was attempted by introducing the stress concentration factor.     

Interfacial de-bonding caused by a screw dislocation pile-up at a circular cylindrical rigid inclusion

An array of continuously-distributed screw dislocations piled up against a circular cylindrical rigid inclusion is analyzed by the complex-variable method. Both uniformly applied shearing load at infinity and internal friction stress opposing the movement of dislocations are taken into account. The pile-up tip is away from the matrix-inclusion interface, its distance from the interface being determined by the condition that the stresses should be finite everywhere in the solid. Stress distributions on the interface are determined, and de-bonding of the interface, namely the formation of initial voids or cracks, is discussed. Stress and displacement near the tip of these initial voids are then analyzed. This analysis is combined with the virtual work argument of A.A. Griffith (1920) to yield a criterion for the initial voids to grow along the interface. The critical void-growth load is expressed by the sum of two terms, one proportional to the friction stress and the other inversely proportional to the square-root of the inclusion radius.     

Experimental estimation of the load distribution in bearings by the method of caustics

The objective of this paper is the experimental estimation of the load distribution in roller-bearing by the metrhod of caustics. Contact problems have many practical and important applications¹. For the solution of such problems, besides mechanical analysis, the experimental method of caustics² can also be applied. The optical method of caustics is suitable for the experimental study of singularities in stress fields created either by discontinuities or by loading. Previously, caustics has been applied to the study of singular stress fields developed near concentrated or uniformly distributed loads which are applied along straight boundaries.^3,4 In this work, it is applied to study the load distribution in rollerbearings.     

基于高斯过程回归的有限元应力解的改善研究

本文应用高斯过程回归方法对有限元应力解进行了改善研究．考题是一简化为平面应力问题的各向同性且受均布载荷的等截面悬臂深梁，应力考察量取Mises 应力，高斯积分点为样本点，单元角结点为改善点．4结点单元有限元模型和8 结点单元有限元模型的计算结果表明：(1)改善点的总体误差比样本点的总体误差都小，且4 结点明显、8 结点不明显；(2)边界结点的改善效果均较传统整体应力修匀的效果显著；(3)改善点应力具有置信区间；(4)较传统分片应力修匀方法，高斯过程回归方法可将所选取区域内的所有角结点的应力同时给予改善，且边界角结点改善效果好．     

变宽截面箱梁剪力滞效应研究

将变宽度截面箱梁的剪力滞翘曲位移函数定义为三次抛物线形式,用能量变分原理建立了分析变宽截面箱梁剪力滞效应的控制微分方程,并用差分法求解此方程。分别计算了简支箱梁在集中荷载和均布荷载作用下的正应力,并用有限元法作了验证。将计算结果与等截面箱梁的应力进行对比,总结变宽箱梁剪力滞效应的分布规律。结果表明,均布荷载作用下,相对于等截面梁,变宽箱梁的顶板应力变化幅度更大,峰值更高,箱梁的顶板宽度变化对剪力滞效应影响较大;在集中荷载作用下,等截面与变宽度箱梁跨中截面的应力相近,应力分布曲线吻合较好,说明顶板宽度变化对剪力滞效应影响较小;分别在集中和均布荷载作用下,箱梁跨中截面应力均为正剪力滞分布状态。当箱梁顶板、底板和悬臂板宽度相等时,剪力滞效应控制微分方程也适用于等截面箱梁。     

Unbonded contact between a circular plate and an elastic half-space

The paper concerns the unbonded contact between a thin circular plate of finite radius, governed by Kirchhof or Reissner theory, pressed by means of rotationally symmetric distributed load and its own weight against the surface of an elastic half-space. The contact is assumed frictionless and unbonded. A Hankel transform solution is used for the half-space and the plate deflection is found by inverting the plate equation. The coefficients in a power expansion are obtained by equating plate and half-space deflections at a number of points in the contact region. The variation of contact radius with plate radius, the radius of the uniformly applied load, and the relative stiffness of plate and foundation, is displayed in a series of figures.