变宽度板在拉伸和弯曲作用下的三维应力集中

根据一种修正的余能原理，建立了具有一个无外力圆柱面的三维杂交应力元，元内假定应力场满足三维柱坐标表示的平衡方程及无外力圆柱面上的外力边界条件；当元退化为二维时，也满足协调条件。单元位移场选择与相邻单元协调。数值算例表明这种特殊杂交应力元在相当粗的网格下，能十分有效地分析变宽度薄／厚板在拉伸与弯曲作用下的三维(及二维)应力集中。     

拉伸偏心圆孔板的应力集中系数表达式

以半解析半经验的方法推导出拉伸偏心圆孔板应力集中系数的显式表达式,经验证该式具有足够的精度,目前文献中尚无类似表达式．     

含两个圆孔的正交异性板孔口补强应力分析

应用数学弹性力学和Ｆａｂｅｒ级数展开的方法，对于含有两个圆孔，且孔周各补强一弹性加强的正交异性板，给出了其在无限元处均布的外力作用下，环及板内的应力场解，其特例与前人结果一致。     

拉伸半无限圆孔板的应力集中系数表达式

首次推出拉伸半无限圆孔板孔边最大应力集中系数的显式表达式,此式不但形式简单而且具有良好的精度,目前献中尚无类似表达式。同时指出,Jeffery给出的仅有的几个具体理论值在圆孔比较靠近直线边界时误差较大。此外,采用本新定义的应力集中系数,当圆孔非常靠近直线边界时有一个极限值。     

弯曲波对含多圆孔薄板的散射与动应力集中

采用复变函数法和多极坐标方法,研究了弯曲波对含有多圆孔薄板的散射问题。通过板的弯曲波动方程和内力方程的推导,求出在入射弯曲波条件下该问题的一般解的函数逼近序列和边界条件的表达式。用展开正交函数的方法将待解的问题归结为对一组无穷代数方程组的求解。最后,给出了含3圆孔薄板的孔边动应力集中系数的结果,并分析了孔间距和波数对动应力分布的影响。     

SH波散射与界面圆孔附近的动应力集中

建立了求解含有界面圆孔的二种不同弹性组合介质中ＳＨ波的散射和界面圆孔附近的动应力集中问题的Ｇｒｅｅｎ函数法给出了一个具有半圆形缺口的弹性半空间水平表面上任意一点承受时间谐和的出平面线源荷载作用时位移函数的基本解取基本解作为Ｇｒｅｅｎ函数，建立起问题的定解积分方程最后给出了界面圆孔的动应力集中的算例和结果，并讨论了不同介质参数的组合对动应力集中的影响     

一类新的具有无外力圆柱表面的杂交应力元

根据Hellinger-Reissner原理,建立了进一步改进的具有一个无外力圆柱表面三维杂交应力元.元内假定应力场满足以柱坐标表示的平衡方程,及圆柱面上的无外力边界条件.当退化为二维时,也满足协调方程.数值算例表明,当分析带圆弧的槽孔板、块时,在稀疏的有限元网格下,这类单元即可提供较以前各类特殊元、一般假定位移元及一般假定应力元远为准确的三维及二维应力分布.     

带槽平板的三维应力集中效应

本文提供了用电阻应变片方法测量一组不同厚度的带有对称圆槽的拉伸平板在应力集中部位的应力分布情况。实验结果表明,应力集中系数不仅与板平面的几何尺寸有关,而且与板的厚度有关。     

含两个圆孔的正交异性板孔口补强应力分析

应用数学弹性力学和Ｆａｂｅｒ级数展开的方法，对于含有两个圆孔，且孔周各补强一弹性加强环的正交异性板，给出了其在无限远处均布的外力作用下，环及板内的应力场解；其特例与前人结果一致。     

Shape optimization of two equal holes in an infinite elastic plate

Abstract

The optimal design of the stress state in elastic plate structures with openings is a problem of great significance in engineering practice. Achieving proper shape of hole can reduce stress concentration around the boundaries remarkably. The optimal shape of a single hole in an infinite plate under uniform stresses has been obtained by complex variable method based on different optimal criteria. The complex variable method is particularly suitable for the hole shape optimization in infinite plate, in which the continuous hole boundary can be represented by the mapping function. It can also be used to solve the shape optimization problems of two or more holes. However, because of the difficulty of finding the mapping function for multi connected domain, the holes are mapped onto slits or separately mapped onto a circle. In this article, the two symmetrical and identical holes are mapped onto an annulus simultaneously by the newly found mapping function, which has a general form. The maximum tangential stress around the boundaries is minimized to achieve the optimal hole shape. And the coefficients of mapping function which describe the boundary are calculated by differential-evolution algorithm.     

Thermo-stress concentration of an orthotropic plate weakened by multiple elliptical holes

A laminate weakened by multiple elliptical holes of arbitrary distribution, arbitrary orientation and arbitrary dimensions, is treated as an anisotropic, infinite, multiple connected thin plate. By Faber series expansion [1–6] and a complex potential method in the plane theory of thermo-elasticity of an anisotropic body, the general step to deduce the thermostress concentration in the laminate subjected to arbitrary mechanical and thermal loads is obtained.Supported by The Chinese Science Foundation of Aeronautics     

Elastoplastic state of flexible cylindrical shells with two circular holes

The elastoplastic state of thin cylindrical shells with two equal circular holes is analyzed with allowance made for finite deflections. The shells are made of an isotropic homogeneous material. The load is internal pressure of given intensity. The distribution of stresses along the hole boundary and in the stress concentration zone (when holes are closely spaced) is analyzed by solving doubly nonlinear boundary-value problems. The results obtained are compared with the solutions that allow either for physical nonlinearity (plastic strains) or geometrical nonlinearity (finite deflections) and with the numerical solution of the linearly elastic problem. The stresses near the holes are analyzed for different distances between the holes and nonlinear factors.Translated from Prikladnaya Mekhanika, Vol. 40, No. 10, pp. 107–112, October 2004.     

Diffraction of stress waves by a free or reinforced hole in an orthotropic plate

Photoelastic plates made of an orthotropic material are used to model the dynamic stress state near free and reinforced circular holes under blast loading. The diffraction of stress waves by holes in a thin-walled plate is studied. Experimental data are used to analyze the dynamic stress concentration in a plate with a hole in which quasilongitudinal and quasitransverse waves propagate __________ Translated from Prikladnaya Mekhanika, Vol. 43, No. 7, pp. 73–78, July 2007.     

Stress distribution around a circular cylindrical cavity in a prestressed plate

A system of equilibrium equations for nonthin transversely isotropic plates with a uniform prestress field is derived by expanding the unknown functions into Fourier-Legendre series. A method of finding the general solution of this system is expounded and used to determine the stress state of a plate with a circular cylindrical cavity __________ Translated from Prikladnaya Mekhanika, Vol. 44, No. 1, pp. 28–39, January 2008.     

Dynamic stress concentrations in thick plates with two holes based on refined theory

Based on complex variables and conformal mapping, the elastic wave scat- tering and dynamic stress concentrations in the plates with two holes are studied by the refined dynamic equation of plate bending. The problem to be solved is changed to a set of infinite algebraic equations by an orthogonM function expansion method. As examples, under free boundary conditions, the numerical results of the dynamic moment concen- tration factors in the plates with two circular holes are computed. The results indicate that the parameters such as the incident wave number, the thickness of plates, and the spacing between holes have great effects on the dynamic stress distributions. The results are accurate because the refined equation is derived without any engineering hypothese.     

3-D numerical study on the bending of symmetric composite laminates

３－ＤＮＵＭＥＲＩＣＡＬＳＴＵＤＹＯＮＴＨＥＢＥＮＤＩＮＧＯＦＳＹＭＭＥＴＲＩＣＣＯＭＰＯＳＩＴＥＬＡＭＩＮＡＴＥＳＣｈｉｅｎＷｅｉ－ｚａｎｇ（钱伟长）;ＨｕａｎｇＱｉａｎ（黄默）;ＦｅｎｇＷｅｉ（冯伟）（ＳｈａｎｇｈａｉＵｎｉｖｅｒｓｔｙｏｆＴｅｃ...     

On the stress distribution in a prestretched simply supported strip containing two neighboring circular holes under forced vibration

The three-dimensional linearized theory of elastic waves in initially stressed bodies under plane strain is used to study the influence of the initial stretching of a simply supported plate strip with two neighboring circular holes on the stress concentration around the holes caused by additional uniformly distributed dynamic (time-harmonic) normal forces acting on the upper face. The corresponding problem is formulated and solved by the finite-element method. Numerical results on the stress concentration around the holes and the influence of the initial stretching on this concentration are presented Published in Prikladnaya Mekhanika, Vol. 43, No. 10, pp. 135–140, October 2007.     

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。