应力边界元法解平面热弹性问题

本文提出了求解平面热弹性问题的应力边界元法。利用应力法由平面热弹性问题的基本方程出发,简要地叙述了边界积分方程的建立,给出了位移单值条件。这种方法适用于应力边界值问题。作为数值计算例,计算了圆形区域和具有偏心圆孔的圆形区域的热应力,得到了满意的结果。应力边界元法也可应用于平板弯曲问题。     

裂纹面荷载作用下多裂纹应力强度因子计算

该文基于比例边界有限元法计算了裂纹面荷载作用下平面多裂纹应力强度因子.比例边界有限元法可以给出裂纹尖端位移场和应力场的解析表达式,该特点可以使应力强度因子根据定义直接计算,同时不需要对裂纹尖端进行特殊处理.联合子结构技术可以计算多裂纹问题的应力强度因子.数值算例表明该文方法是有效且高精确的,进而推广了比例边界有限元法的...     

倾斜坡体中圆孔扩张的弹性应力分析

针对实际工程中遇到的斜坡边界下圆形孔扩张问题,提出了相应的计算方法。在考虑坡体自重应力的情况下,通过坐标变换将其转为水平边界半无限体中圆孔扩张,采用复变函数共形映射的方法得到应力解析。当圆形孔埋置较深时,将问题简化为无限体中圆孔的扩张,通过弹性力学的基本叠加得到最终应力解答。以一斜坡边界下圆形孔洞扩张为例,求解了圆孔周围径向正应力、环向正应力与切应力的分布。计算结果表明:斜坡倾角对坡体中应力分布影响显著,某点应力随距圆心距离的增大而减小,超过约4倍圆孔半径远处逐渐趋于稳定,其值接近于初始地应力场。当圆孔为深埋的情况时,与简化为无限平面的情况进行了对比,两种方法计算结果接近,距圆心2.5R远处岩体径向正应力和环向正应力均为负值,而切应力正负值间隔分布,各应力极值分布与斜坡倾向呈一定的相关性。     

应力强度因子计算的边界元法

本文利用非连续元离散边界的积分方程，推导了奇异积分的具体表达式，将非连续边界元和多域缩聚法用于二维弹性断裂应力强度因子计算，得到了合理的计算结果。     

应力强度因子计算的样条虚边界元法

含有裂纹的工程结构在荷载作用时在裂纹尖端会产生应力奇异的现象,其严重的程度可用应力强度因子来表征。采用基于Kelvin基本解的样条虚边界元法,结合位移外推法,给出了断裂问题应力强度因子的求解方法。通过对两个典型断裂问题的分析,对边界子段与虚边界元的划分、小单元的采用以及拟合点位置的确定等关键问题展开了讨论,获得了相关计算参数的选取规律,为该法在断裂问题的进一步应用打下良好的基础。     

基于坡面卸荷的土质边坡应力状态及稳定性分析

边坡稳定性分析中极限平衡法难以考虑土体应力状态,坡体滑面应力计算又长期停留在数值方法上。为解决这一问题,提出坡面卸荷应力等效思路,将坡面按半无限边界考虑后利用弹性理论求解坡体应力,并根据滑面应力进行稳定性安全系数计算,最后结合多个算例将潜在滑动面位置、滑面应力分布、安全系数与已有理论进行比较。研究结果表明:坡面卸荷应力等效思路概念清晰,符合边坡受力特征,且通过该思路求得的滑面应力与有限元分计算结果基本一致,搜索得到的潜在滑动面位置,以及对应的稳定性安全系数与有限元强度折减法、极限平衡法计算结果十分接近。此外,该计算方法还能有效与支护结构预应力结合,体现预应力的加固作用。     

动载荷下应力强度因子的边界元计算

用Ｎａｒｄｉｎｉ－Ｂｒｅｂｂｉａ边界元法计算了动载荷下的应力强度因子，与解析解及有限元解相比较，效果较好。最后对计算结果进行了分析讨论。     

正交异性光弹性应力分析方法研究

本文建立了正交异性光弹性应力分析的实验边界元混合解法并编制了相应的程序系统BE-MSC.该方法仅需模型边界结点处等差线一项实验数据即可实施应力的分离。它还十分适用于存在初应力的模型材料光弹性分析问题。最后对正交异性对径受压圆盘进行了光弹性应力实例分析。      

保角映射法求解渐开线直齿轮齿根应力

目前国际上确定渐开线齿轮齿廓保角映射函数的方法均为数值回归法,计算复杂,映射精度的提高受到限制．为此,本文给出了渐开线齿轮齿廓保角映射函数的解析解,计算方便,使映射精度大幅度提高。以上述工作为基础,笔者给出了渐开线直齿轮齿根应力的解析公式,并由算例证实了计算结果和边界元法计算值之间的一致性。     

逆随机边界元法预测残余应力和接触应力

本文提出了用于预测残余应力和接触应力的逆随机边界元法。将滤波算法引入随机边界元法,根据某些内点的应变的随机分布,建立量测值的边界元解析灵敏度矩阵和解析量 测矩阵,从而可能预测边界上的随机残余应力和随机接触载荷的分布和结构可靠度的分布。 最后,两个算例表明了本方法的有效性。     

On the calculation of boundary stresses with the Somigliana stress identity

The computation of boundary stresses by Boundary Element Method (BEM) is usually performed either by expressing the boundary tractions in a local co-ordinate system, calculating the remaining stresses by shape function differentiation and inserting into Hooke's law or recently also by solving the hypersingular integral equation for the stresses. While direct solution of the hypersingular integral equation, the so-called Somigliana stress identity, has been shown to be more reliable, the interpretation and numerical treatment of the hypersingularity causes a number of problems. In this paper, the limiting procedure in taking the load point to the boundary is carried out by leaving the boundary smooth and the contributions of all different types of singularities to the boundary integral equation are studied in detail. The hypersingular integral in the arising boundary integral equation is then reduced to a strongly singular one by considering a traction free rigid body motion. For the numerical treatment, an algorithm for multidimensional Cauchy Principal Value (CPV) integrals is extended that is applicable for the calculation of boundary stresses. Moreover, the shape of the surrounding of the singular point is studied in detail. A numerical example of elastostatics confirms the validity of the proposed method.     

On the evaluation of hyper-singular integrals arising in the boundary element method for linear elasticity

The boundary element method (BEM) for linear elasticity in its curent usage is based on the boundary integral equation for displacements. The stress field in the interior of the body is computed by differentiating the displacement field at the source point in the BEM formulation, via the strain field. However, at the boundary, this method gives rise to a hypersingular integral relation which becomes numerically intractable. A novel approach is presented here, where hyper-singular kernels for stresses on the boundary are made numerically tractable through the imposition of certain equilibrated displacement modes. Numerical results are also presented for benchmark problems, to illustrate the efficacy of the present approach. Solutions are compared to the commonly used boundary stress algorithm wherein the boundary stresses are computed from known boundary tractions, and derivatives of known displacements tangential to the boundary. An extension of this approach to solve linear elasticity problems using the traction boundary integral equation (TBIE) is also discussed.     

On the calculation of boundary stresses in boundary elements

The discontinuity of boundary stresses evaluated using discretized boundary elements is discussed, and stress error bound is derived. A new procedure for calculating interelement stress is proposed to overcome stress discontinuity at the interelement boundary. By employing two middle nodes of the two adjacent elements and the interelement node, a new quadratic element is formed, which leads to a more accurate interelement stress. Two examples are used to study error distributions of displacements and stresses. The comparison study indicates that the new procedure provides a better solution for interelement stresses than the conventional method.     

Stresses near Crack Tips on the Boundary of Two Media in the Presence of Plastic Strips

Under the conditions of plane deformation, we study stresses in a piecewise-homogeneous isotropic body near the tip of a mode I crack appearing at the angular point on the boundary of two media. It is assumed that plastic strips (modeled by plastic slip lines) are formed on the boundary of the media. To determine the stresses, we use the Mellin integral transformation and the Wiener–Hopf method. The angular point is a stress concentrator with power singularity and, therefore, immediately after the appearance of lateral plastic strips (zones), a new plastic zone begins to develop from this point. We study the dependence of the power of singularity of stresses on the angle made by the boundary and the elastic characteristics of the media.     

Evaluation of K-factors and weight functions for 2-d mixed-mode multiple cracks by the boundary element alternating method

The concept of the Schwartz-Neumann alternating method, in conjunction with the boundary element method to solve for the stresses in an uncracked body and an analytical solution for an embedded 2-D crack subjected to arbitrary crack face loading in an infinite domain, is used to detennine the mixed-mode K-factors and weight functions for cracks in finite bodies. Situations of edge-cracks, as well as multiple cracks, all under mixed mode loading, are considered. The boundary element method is better suited for these problems since, pointwise evaluation of stresses at the location of the crack in the uncracked body is more accurate and simple once the tractions and displacements on the boundary are determined. It is expected that the above method would yield highly accurate results in the least expensive way, even compared to the finite element alternating method.     

Warping shear stresses in nonuniform torsion by BEM

 In this paper a boundary element method is developed for the nonuniform torsion of simply or multiply connected prismatic bars of arbitrary cross section. The bar is subjected to an arbitrarily distributed twisting moment, while its edges are restrained by the most general linear torsional boundary conditions. Since warping is prevented, beside the Saint–Venant torsional shear stresses, the warping normal and shear stresses are also computed. Three boundary value problems with respect to the variable along the beam angle of twist and to the primary and secondary warping functions are formulated and solved employing a BEM approach. Both the warping and the torsion constants using only boundary discretization together with the torsional shear stresses and the warping normal and shear stresses are computed. Numerical results are presented to illustrate the method and demonstrate its efficiency and accuracy. The magnitude of the warping shear stresses due to restrained warping is investigated by numerical examples with great practical interest. Received: 13 November 2001 / Accepted: 2 October 2002     

A new space marching method for solving inverse heat conduction problems

A new space marching method is presented for solving the one-dimensional nonlinear inverse heat conduction problems. The temperature-dependent thermal properties and boundary condition on an accessible part of the boundary of the body are known. Additional temperature measurements in time are taken with a sensor located in an arbitrary position within the solid, and the objective is to determine the surface temperature and heat flux on the remaining part of the unspecified boundary. The temperature distribution throughout the solid, obtained from the inverse analysis, is then used for the computation of thermal stresses in the entire domain, including the boundary surfaces. The proposed method is appropriate for on-line monitoring of thermal stresses in pressure components. The three presented example show that the method is stable and accurate.     

正交各向异性平面问题边界元素法研究

边界元素法是近年来受到国内外广泛重视并得到迅速发展的一种计算方法。本文系统地研究了正交各向异性平面问题边界元素法的有关基本问题,包括基本解,C矩阵、G_ii矩阵和域内应力的表达式等,并在此基础上建立了常值边界元素和线性边界元素的计算公式。所述理论和公式适用于各类边值问题。最后,按本文所述理论和公式计算了含孔正交各向异性板的应力,数值结果与解析解相符甚好。      

梯度功能材料薄板瞬态热弹性弯曲有限元分析

用层合板有限元法分析了由ZrO2和Ti-6Al-4V组成的新型梯度功能材料薄板的瞬态热弹性弯曲应力问题,并对本方法的正确性进行了检验。讨论了加热、 冷却热边界条件以及两种力学边界条件(固支和简支)对梯度功能材料薄板的瞬态热弹性弯曲应力分布的影响。发现：(1) 在加热过程中,简支板低温金属侧出现较大压应力;在冷却过程中,简支板高温陶瓷侧出现较大拉应力; 且其拉、压应力会随着板上、下表面温差的增大而增大。(2) 无论是简支板还是固支板, 在冷却过程中,沿整个厚度板内部压应力均较大。(3) 在本文的相同条件下,固支板比简支板更适合高温、大温差的使用环境。