用伪应力函数法求解幂硬化材料柱体的扭转问题

本文引用伪应力函数使得幂硬化材料的任意形状等截面柱体和变直径圆截面柱体扭转问题的定解方程具有弹性柱体扭转问题的相应形式,从而可用类似于求解弹性柱体扭转的方法或直接利用已知的弹性解答求解对应的幂硬化材料柱体的扭转问题,本文用这种方法求得了幂硬化材料椭圆截面柱体及含球形空腔的圆轴扭转问题的解析解。     

用伪应力函数法求解幂硬化材料柱体的扭转问题

本文引用伪应力函数使得幂硬化材料的任意形状等截面柱体和变直径圆截面柱体扭转问题的定解方程具有弹性柱体扭转问题的相应形式,从而可用类似于求解弹性柱体扭转的方法或直接利用已知的弹性解答求解对应的幂硬化材料柱体的扭转问题,本文用这种方法求得了幂硬化材料椭圆截面柱体及含球形空腔的圆轴扭转问题的解析解。     

自平衡端头载荷问题衰减率的分析与计算

给出了自平衡端头载荷问题应力衰减率分析的一种方法．用边界单元法求得了在端面自平衡载荷作用下，具有椭圆截面和矩形截面的弹性柱体内应力场的最小衰减率。计算结果表明：当椭圆截面的长短轴之比和矩形截面的长宽之比变化时，最小衰减率变化很小．     

等腰三角形截面异质柱体在半无限弹性体内的热应力问题

1.引言文献[1]曾讨论了矩形截面异质柱体在半无限弹性体内的热应力问题.等腰三角形截面异质柱体在实用中实非罕见,本文就再扩展来讨论这个例子,以期能找出这一改变会引起应力分布和位移的哪些改变特征.2.含有等腰三角形截面异质柱体在无限弹性体内所引起的应力和位移如图1所示,在无限弹性体里镶进一个不同材料的等腰三角形截面柱体,柱轴平行于z 坐标轴,并设c>0;异质柱体的热胀系数α_i 大于无限弹性体材料的热胀系数α_(?),但两种材料有相同的弹性数据.为了照顾计算的便利而作此设想,当常温度等于零时,这个组合体里无应力存在,当其温度T_0大于零时,试求解这个组合体的热应力问题.     

均布载荷下含偏心裂纹椭圆盘的应力强度因子计算

本文用边界配置方法计算了不同情形下含偏心裂纹椭圆盘受均布载荷时的应力强度因子。在其特例——圆盘情形,用本文方法所得结果与Tweed等人用积分变换方法所得结果一致。本文结果也适用于含偏心裂纹椭圆轴的断裂分析。与其他方法相比。本文方法原理简明,计算量小,具有良好的计算精度和收敛性。同时,本文所采用的应力函数和计算过程可以推广到其他载荷下不同形状含偏心裂纹盘的断裂分析。     

椭圆截面侵彻弹体结构优化设计与结构响应

针对异型截面侵彻弹体的工程应用需求,围绕椭圆截面侵彻弹体结构响应及优化设计问题开展研究。引入无量纲壁厚系数,改进了椭圆截面弹体参数化表达式;以提高短轴惯性矩和静矩、降低短轴方向结构响应为目标,开展了椭圆截面弹体抗弯优化设计。基于152 mm口径轻气炮开展了椭圆截面弹体反弹道侵彻试验研究,获得了软回收试验弹体的弯曲挠度结果;开展了试验工况的数值模拟研究,提取了数值模拟中弹体的变形结果;建立了椭圆截面侵彻弹体弯曲结构响应计算模型,利用此模型对试验弹体变形情况进行了计算。与原椭圆截面弹体相比,优化后截面短轴惯性矩、静矩提高比例约为16%,试验弹体弯曲挠度降低比例约为25.3%,数值模拟及理论模型计算结果与试验结果较为相符,验证了本文优化设计方法的有效性,可为工程设计提供参考。     

多个椭圆柱波浪力的一种解析解

波浪在大尺寸结构表面产生不可忽略的散射波, 该散射波在多柱体体系中继续传播, 并在同体系中的其他柱体上产生高次散射波. 本文基于椭圆坐标系和绕射波理论首先推导了波浪作用下椭圆单柱体产生的散射波压力公式, 随后考虑该散射波在多柱体系中的传播, 将其视为第二次入射波, 推导出柱体上第二次散射波压力公式, 同理可以推导出高次散射波压力公式, 最后得到椭圆多柱体波浪力解析解, 并用数值解验证了本文解析方法的正确性. 本文以双柱体和四柱体体系为例, 分析了不同参数(波数、净距、波浪入射角度等)下, 高次散射波对柱体上波浪作用的影响. 结果表明: 波数较大的情况下, 高次散射波引起柱体上的波浪力不能忽略; 结构间距较大的情况下, 虽然高次波的作用有减小的趋势但仍然明显; 高次散射波来自多个柱体对入射波的散射, 柱体数目的增加后, 高次波的影响会增加, 结构所受的高次波作用因参数变化而起的波动会变剧烈; 高次波对上游柱体波浪力的贡献较对下游柱体的贡献大.      

残余应力下厚壁筒表面裂纹的应力强度因子计算

本文首先介绍了边界元法计算裂纹尖端应力强度因子的基本理论,接着利用边界元法计算了在残余应力下不同厚壁筒内表面椭圆裂纹的应力强度因子,研究了其大不随椭圆裂纹不同而变化的规律,为厚壁筒结构的设计,制造以及疲劳寿命分析提供了许多有价值的参考资料。     

集中载荷下含偏心裂纹椭圆盘的应力强度因子计算

本文采用边界配置方法计算了受集中载荷作用时椭圆盘中偏心裂纹两端的应力强度因子,其中包括椭圆两半轴不同比值。不同裂纹长度和不同偏心程度的情况,在其特例椭圆盘中心裂纹情形,本文结果与Isida一致;在圆盘偏心裂纹情形,本文给出比Rooke等人更好的结果。     

扇形截面杆扭转的应力分析

柱体扭转的基本方程为非齐次偏微分方程,在极坐标系下,利用分离变量法及傅立叶级数展开法,求出了扭转应力函数,进一步即可计算出扇形截面杆在外力偶作用下,扭转角和横截面上剪应力的精确解答。这种方法为精确解法,在各种机械及其他工程设备中,对受扭转作用的扇形截面杆设计,有一定实用价值。     

含椭圆刚性核有限大复合材料层板弯曲应力分析Bending problem of a finite composite laminated plate with elliptical rigid inclusions

基于经典的复合材料层板理论,将有限大复合材料层板等效成各向异性弹性平板。采用复变函数理论中的Faber级数分析方法,使用最小二乘边界配点法,对含多椭圆刚性核有限大各向异性板弯曲问题进行应力分析,得到了该问题的级数解形式,分析了含椭圆刚性核层板在弯曲载荷下的应力分布,并讨论了形状和结构参数对应力分布的影响。结果表明,本文方法对于分析含多个椭圆形刚性核有限大薄板弯曲应力问题非常有效,该方法具有精度高及计算方便等优点。     

Elliptical and circular FRP-confined concrete sections: A Mohr–Coulomb analytical model

An analytical stress–strain model is developed for predicting the compressive behavior of elliptical and circular fiber reinforced polymer (FRP)-confined concrete members. The model is based on a diagonal Poisson’s ratio formulation expressed as a function of the mechanical properties of the unconfined concrete and confining FRP jacket, the geometry of the concrete section, and the extent of internal damage in the confined concrete core. A Mohr–Coulomb yield criterion is introduced for analysis of the compressive behavior of confined concrete. Equilibrium and strain compatibility are used to obtain the ultimate compressive strength and strain of elliptical and circular FRP-confined concrete sections as a function of the effective confining stiffness of the FRP jacket. A simplified expression is derived for the FRP reinforcement ratio which precludes strain softening in elliptical and circular FRP-confined concrete sections.     

含多椭圆孔(核)复合材料加筋层板的应力集中研究

基于各向异性体平面弹性理论中的复势方法,应用杂交变分原理建立了一种与常规有限元相协调的含任意椭圆核各向异性板杂交应力有限元,采用该杂交应力有限元来描述层板的椭圆核区域,采用杆单元来描述加强筋(杆单元的刚度取为层板沿筋条方向的刚度),其余区域采用常规8节点等参单元进行模拟,建立起分析含多椭圆核复合材料加筋壁板问题的力学分析方法,详细讨论了椭圆核大小、位置、筋条尺寸、相对位置、铺层比例等诸参数的影响规律,得到了一些有益的结论。     

The solution of a crack emanating from an arbitrary hole by boundary collocation method

In this paper a group of stress functions has been proposed for the calculation of a crack emanating from a hole with different shape (including circular, elliptical, rectangular, or rhombic hole) by boundary collocation method. The calculation results show that they coincide very well with the existing solutions by other methods for a circular or elliptical hole with a crack in an infinite plate. At the smae time, a series of results for different holes in a finite plate has also been obtained in this paper. The proposed functions and calculation procedure can be used for a plate of a crack emanating from an arbitrary hole.     

Stress concentration factor expression for tension strip with eccentric elliptical hole

Two explicit expressions of the stress concentration factor for a tension finite-width strip with a central elliptical hole and an eccentric elliptical hole, respectively, are formulated by using a semi-analytical and semi-empirical method. Accuracy of the results obtained from these expressions is better, and application scope is wider, than the results of Durelli’s photo-elastic experiment and Isida’s formula. When eccentricity of the elliptical hole is within a certain range, the error is less than 8%. Based on the relation between the stress concentration factor and the stress intensity factor, a stress intensity factor expression for tension strips with a center or an eccentric crack is derived with the obtained stress concentration factor expressions. Compared with the existing formulae and the finite element analysis, this stress intensity factor expression also has sufficient accuracy.     

A small-scale magnetic-yielding model for an infinite magnetostrictive plane with a crack-like flaw

The effect of an external magnetic field on the fracture toughness of magnetostrictive materials has been investigated by determining the local stress fields around the tip of a very slender elliptical flaw embedded in an infinite magnetostrictive plane subjected to magnetic loading, based on the assumption of linear magnetization. In this paper, the above-mentioned analytical approach is extended to develop a small-scale magnetic-yielding model. The magnetic saturation zone is constructed and the distributions of magnetic field and magnetization are obtained around the tip of a slender elliptical crack. Based on the complex potential theory, the stress field is obtained in the vicinity of the tip of the slender elliptical crack by implementing the continuity conditions of displacement and resultant force at the interface between the magnetic saturation and magnetoelastic zones. The stress fields near the tip of the slender elliptical crack are obtained for two kinds of soft ferromagnetic materials each with a small induction magnetostrictive modulus. The theoretical results obtained show that the stresses in the neighborhood of a crack-tip are finite even when the elliptical crack reduces to a sharp crack, and are much smaller than the yield stress or the nominal fracture stress of the material. This suggests that, generally, the magnetic field has no obvious effects on the apparent fracture toughness of soft ferromagnetic materials, which is in agreement with the existing experimental results published in the existing literature. In addition, the theoretical analysis illustrates that no crack is magnetically impermeable, and the corresponding boundary conditions are inappropriate for fracture analysis of soft ferromagnetic materials.     

Green's function of a point dislocation for the bending of a composite infinite plate with an elliptical hole at interface

Summary  The problem of a hole at bimaterial interface is of practical importance in providing a good understanding of the debonding phenomenon and for determining factors that affect the mechanical properties of composite elements of structures. The problem of a point dislocation in bending bonded dissimilar semi-infinite plates with an elliptical hole at interface is tackled in this paper. Based on the method of analytic continuation and the rational mapping function technique, the problem of obtaining the stress functions in the upper and lower plates is decoupled, and reduced to two Riemann–Hilbert problems. The closed-form solution is obtained. The stress distributions at the bimaterial interface, as well as the debonding at both vertices of the elliptical hole are studied. The stress intensities of debonding are depicted for various parameters. Received 16 March 2000; accepted for publication 12 July 2000     

一种新型后装式垃圾车结构优化设计

首先对后装式压缩垃圾车的车厢截面形状进行优化,设计出一种具有椭圆截面车厢的新型后装式垃圾车.给出椭圆截面车厢的自重、惯性、压缩、挤入、推出等压缩垃圾载荷的数学表达.而后对车厢与填科器结构进行多种危险工况的有限元分析,采用导重法对结构构件尺寸进行优化设计,在保证结构应力小于许用应力的前提下,本新型椭圆截面后装武垃圾车结构质量比原来的矩形截面压缩垃圾车减少了33.5%,是同类后装武压缩垃圾车中的最轻者.     

Stress-strain state of an inclined elliptical defect in a plate under biaxial loading

A mathematical model for the stress-strain state of a plate with an inclined elliptical defect under biaxial loading is considered. Exact formulas for stresses in polar coordinates, displacements, principal stresses, maximum shear stress, and stress intensity in the case of a plane stress state of the plate were obtained by the Kolosov-Muskhelishvili method. Simulation results are compared with experimental data obtained by holographic interferometry.     

半空间内含有部分脱胶的椭圆夹杂及圆孔对SH波的散射

采用复变函数法,结合"保角映射"技术及Green函数法,研究SH波作用下半空间内含有部分脱胶的椭圆夹杂以及圆形孔洞的散射问题。首先,利用"保角映射"技术将椭圆夹杂映射为圆夹杂,求出散射波位移场,同时,利用Green函数法与"虚设点源"的方法,求出半空间内椭圆夹杂以及圆孔的位移及应力场;然后,根据椭圆夹杂周围位移、应力连续、圆孔周围应力自由的边界条件,建立无穷线性代数方程组,求解出波函数中的未知系数;最后,在脱胶部分施加大小相等、方向相反的应力,构造出"脱胶模型",得到半空间内含有部分脱胶的椭圆夹杂以及圆形孔洞的总位移场。数值算例表明,入射角度、入射波频率、缺陷之间的距离、夹杂埋深及脱胶角度等对动应力集中因子有较大影响。