孔洞裂纹问题的一种数值方法

研究孔洞与裂纹的相互作用问题,通过把适于单一裂纹的Bueckner原理扩充到含有多孔洞多裂纹的一般体系,将原问题分解为承受远处载荷不含裂纹不含孔洞的均匀问题,和在远处不承受载荷但在裂纹面上和孔洞表面上承受面力的多孔洞多裂纹问题.于是,以应力强度因子作为参量的问题可以通过考虑后者来解决,而利用笔者提出的杂交位移不连续法,这种多孔洞多裂纹问题是容易数值求解的.算例说明该数值方法对分析平面弹性介质中孔洞与裂纹的相互作用既简单又有效.     

内部压力作用下矩形板中源于椭圆孔的分支裂纹应力强度因子的一种数值分析

应用一种边界元方法来研究内部压力作用下矩形板中源于椭圆孔的分支裂纹。该边界元方法由Crouch与Starfied建立的常位移不连续单元和笔者最近提出的裂尖位移不连续单元构成。在该边界元方法的实施过程中,左、右裂尖位移不连续单元分别置于裂纹的左、右裂尖处,而常位移不连续单元则分布于除了裂尖位移不连续单元占据的位置之外的整个裂纹面及其它边界。本数值结果进一步证实这种数值方法对计算有限大板中复杂裂纹的应力强度因子的有效性,同时该数值结果可以揭示裂纹体几何对应力强度因子的影响。     

双轴载荷作用下源于椭圆孔的分支裂纹的一种边界元分析

利用一种边界元方法来研究双轴载荷作用下无限大板中源于椭圆孔的分支裂纹.该边界元方法由Crouch 与 Starfied 建立的常位移不连续单元和笔者提出的裂尖位移不连续单元构成.在该边界元方法的实施过程中,左、右裂尖位移不连续单元分别置于裂纹的左、右裂尖处,而常位移不连续单元则分布于除了裂尖位移不连续单元占据的位置之外的整个裂纹面及其它边界.文中算例说明本数值方法对计算平面弹性裂纹的应力强度因子是非常有效的.该文对双轴载荷作用下无限大板中源于椭圆孔的分支裂纹的数值结果进一步证实本数值方法对计算复杂裂纹的应力强度因子的有效性,同时该数值结果可以揭示双轴载荷及裂纹体几何对应力强度因子的影响.     

内部压力作用下无限大板中三角孔-边裂纹应力强度因子研究

利用已有文献中的杂交位移不连续边界元法,重点研究了内部压力作用下无限大板中三角孔-边裂纹问题;通过改变孔的几何参数,分析了孔的几何参数对应力强度因子的影响。结果表明:孔对源于其裂纹的应力强度因子具有屏蔽影响和放大影响;当尺寸参数ad ≥adc(adc为某一定值)时,三角孔对源于其裂纹的应力强度因子具有屏蔽影响,并且三角孔尺寸越接近裂纹尺寸,这种屏蔽影响越强烈;当参数 ad≤adc时,三角孔对源于其裂纹的应力强度因子具有放大影响,并且在参数 ad=adm(adm为某一定值)处,这种放大影响达到最大。本文所得结果在工程上具有重要意义。     

平面弹性介质多孔多裂纹问题的一种数值方法

提出了平面弹性介质中多孔洞多裂纹相互作用问题的一种数值计算方 法. 通过把适于单一裂纹的Bueckner原理扩充到含有多孔洞多裂纹的一般体系，将原问题 分解为承受远处载荷不含裂纹不含孔洞的均匀问题，和在远处不承受载荷但在裂纹面上和孔 洞表面上承受面力的多孔洞多裂纹问题. 于是，以应力强度因子作为参量的问题可以通过考 虑后者(多孔洞多裂纹问题)来解决，而利用提出的杂交位移不连续法，这种多孔 洞多裂纹问题是容易数值求解的. 算例说明该数值方法对分析平面弹性介质中多孔洞多裂纹 相互作用的问题既简单又有效.     

拉伸载荷作用下单边缺陷-边裂纹应力强度因子研究

利用杂交位移不连续法研究拉伸载荷作用下矩形板中单边缺陷-边裂纹(半圆孔裂纹和半方孔裂纹)问题,给出了这三种平面弹性裂纹问题的应力强度因子的详细数值解。通过半圆孔裂纹问题和半方孔裂纹问题与单边裂纹问题的应力强度因子的比较,发现半圆孔和半方孔对单边裂纹有屏蔽影响。此外,本文的研究结果表明,杂交位移不连续法用于分析平面弹性有限体中复杂裂纹问题的应力强度因子简单且又准确。     

复杂裂纹问题的多边形数值流形方法求解

数值流形方法是一种能统一处理连续和不连续问题的有效数值方法.该方法采用的数学覆盖系统可完全独立于物理域,能很好地求解各类裂纹问题,而n边形单元(n>4)则具有网格划分灵活,求解精度高等优点.论文基于数值流形方法,采用正六边形数学单元求解线弹性复杂裂纹问题.在导出相关方程的基础上对典型裂纹问题进行了分析,通过互能积分法得到了裂尖的应力强度因子,计算结果与参考解吻合得较好.除此之外,文中还对不同单元上的求解精度进行了比较,结果表明采用正六边形单元的求解精度较正四边形单元和正三角形单元上的精度均更高.     

一种计算三维裂纹应力强度因子的新方法

构造了一种新的三维奇异单元,提出了一种有效计算三维裂纹应力强度因子新的数值方法。该方法的计算结果与理论解和Newman解结果一致;与Panson等方法相比所使用的自由度数大大减小。结果表明该方法是一种高效、稳定可靠的计算方法。     

An effective boundary element method for analysis of crack problems in a plane elastic plate

A simple and effective boundary element method for stress intensity factor calculation for crack problems in a plane elastic plate is presented. The boundary element method consists of the constant displacement discontinuity element presented by Crouch and Starfield and the crack-tip displacement discontinuity elements proposed by YAN Xiangqiao. In the boundary element implementation the left or the right crack-tip displacement discontinuity element was placed locally at the corresponding left or right each crack tip on top of the constant displacement discontinuity elements that cover the entire crack surface and the other boundaries. Test examples (i. e. , a center crack in an infinite plate under tension, a circular hole and a crack in an infinite plate under tension) are included to illustrate that the numerical approach is very simple and accurate for stress intensity factor calculation of plane elasticity crack problems. In addition, specifically, the stress intensity factors of branching cracks emanating from a square hole in a rectangular plate under biaxial loads were analysed. These numerical results indicate the present numerical approach is very effective for calculating stress intensity factors of complex cracks in a 2-D finite body, and are used to reveal the effect of the biaxial loads and the cracked body geometry on stress intensity factors.     

An iterative integral equation formulation for the macrocrack — array of microcracks interaction problem

Summary The exact solution of the problem of a dislocation interacting with a crack has been used for the generation of integral equations on the microcracks only. A few discresation points are needed along the microcracks, due to their small length. The solution of the resulting system of linear algebraic equations is effected via interations for the time of computations to be further reduced. In several cases our results seem to be more accurate than the ones obtained in [3].     

A numerical analysis of perpendicular cracks under general in-plane loading with a hybrid displacement discontinuity method

In this paper, a numerical analysis of perpendicular cracks under general in-plane loading is performed by using a hybrid displacement discontinuity method which consists of the non-singular displacement discontinuity element presented by Crouch and Starfied and the crack tip displacement discontinuity elements by the author. In the boundary element implementation the left or the right crack tip displacement discontinuity element is placed locally at corresponding left or right crack tip on top of the ordinary non-singular displacement discontinuity elements that cover the entire crack surface and the other boundary. The present numerical results show that the numerical approach is simple, yet very accurate for calculating numerically stress intensity factors for perpendicular cracks under general in-plane loading.     

Computational‐Experimental Method for Determining Fracture Parameters of Cracked Structures

Computationalexperimental methods are proposed to estimate the mode I and II stress intensity factors, to determine the stresses acting at the location of a crack before its initiation, and to find the coordinates of the crack tips. The initial data are displacement discontinuities measured at several points at the crack edges. The methods are based on integral representations of the solution of the elastic equilibrium problem for anisotropic plates with a curved cut. Numerical examples are given to illustrate the efficiency of the methods.     

New type of dual bem and Green's-function-library strategy for fracture analysis in complex structures

A new type of dual boundary integral equations (DBIE) is presented first, through which, a smaller system of equations needs to be solved in fracture analysis. Then a non-conforming crack tip element in two-dimensional problems is proposed. The exact formula for the hypersingular integral over the non-conforming crack tip element is given next. By virtue of Green's-function-library strategy, a series of stress intensity factors (SIF) of different crack orientations, locations and/or sizes in a complicated structure can be obtained easily and efficiently. Finally, several examples of fracture analysis in two dimensions are given to demonstrate the accuracy and efficiency of the method proposed. Partially supported by the Aeronautical Science Foundation of China (No. 99C53026)