Green's function for T-stress of semi-infinite plane crack

Green’s function for the T-stress near a crack tip is addressed with an analytic function method for a semi-infinite crack lying in an elastical, isotropic, and infinite plate. The cracked plate is loaded by a single inclined concentrated force at an interior point. The complex potentials are obtained based on a superposition principle, which provide the solutions to the plane problems of elasticity. The regular parts of the potentials are extracted in an asymptotic analysis. Based on the regular parts, Green’s function for the T-stress is obtained in a straightforward manner. Furthermore, Green’s functions are derived for a pair of symmetrically and anti-symmetrically concentrated forces by the superimposing method. Then, Green’s function is used to predict the domain-switch-induced T-stress in a ferroelectric double cantilever beam （DCB） test. The T-stress induced by the electromechanical loading is used to judge the stable and unstable crack growth behaviors observed in the test. The prediction results generally agree with the experimental data.

STUDY OF THE STRESS INTENSITY FACTOR OF PREFORMED V SHAPE FRACTURE TIP

In order to make the fracture cross-section of rock smooth in controlled cutting-blast, generally, two V-shape-notches on the inner wall of a shot hole are notched in symmetry along the design direction. A V-shape notch approximately be considered as V-shape-fracture under certain condition. This paper gave the complex stress function of preformed V-shape-fracture under a blasting load. The stress field and displacement field at the tip of a preformed V-shape-fracture were derived with Westergaard's method, hence its stressintensity factor was obtained. To verify the derived results, blasting tests were made with concrete samples of 400mm×400mm×300mm, and all having, in the center, a drilled hole of 25mm in diameter and 200mm in height. The test result showed that the formulas derived are correct and effective.

INTEGRAL EQUATION METHOD'S APPLICATION IN HOLE-EDGE STRESS OF COMPOSITE MATERIAL PLATE WITH DIFFERENT SHAPED HOLES

The strength of composite plate with different hole-shapes is always one of the most important but complicated issues in the application of the composite material. The holes will lead to mutations and discontinuity to the structure. So the hole-edge stress concentration is always a serious phenomenon. And the phenomenon makes the structure strength decrease very quickly to form dangerous weak points. Most partial damage begins from these weak points. According to the complex variable functions theory, the accurate boundary condition of composite plate with different hole-shapes is founded by conformal mapping method to settle the boundary condition problem of complex hole-shapes. Composite plate with commonly hole-shapes in engineering is studied by several complex variable stress fimction. The boundary integral equations are founded based on exact boundary conditions. Then the exact hole-edge stress analytic solution of composite plate with rectangle holes and wing manholes is resolved. Both of offset axis loadings and its influences on the stress concentration coefficient of the hole-edge are discussed. And comparisons of different loads along various offset axis on the hole-edge stress distribution of orthotropic plate with rectangle hole or wing manhole are made. It can be concluded that hole-edge with continuous variable curvatures might help to decrease the stress concentration coefficient; and smaller angle of outer load and fiber can decrease the stress peak value.

Dynamic thermal stress distribution in surface of two-dimensional cavity

Although we have had the problem of dynamic thermal stress distribution solved in the surface of a cavity in some special shapes, a general solution to this problem for an arbitrary shaped cavity was still not obtained. Using the complex function method, the present paper analyzed the dynamic thermal stress distribution in the surface of an arbitrary shaped cavity subjected to a steady temperature field. Actually, not only is a general solution of this problem represented by Hankle function obtained for an arbitrary shaped cavity, but also a process to calculate the coefficient of the dynamic thermal stress distribution in the surface of an arbitrary shaped cavity is derived. For illustration, some numerical results of a circular cavity, an elliptic cavity, a lining horseshoe cavity and a square cavity are given.

Dynamic stress concentration and scattering of SH-wave by interface elliptic cylindrical cavity

In this paper,the dynamic stress concentration and scattering of SH-waves by bi-material structures that possess an interface elliptic cavity are investigated.First,by using the complex function method,the Green's function is constructed.This yields the solution of the displacement field for an elastic half space with a semi-elliptic canyon impacted by an anti-plane harmonic line source loading on the horizontal surface.Then,the problem is divided into an upper and lower half space along the horizontal interface,regarded as a harmony model.In order to satisfy the integral continuity condition, the unknown anti-plane forces are applied to the interface.The integral equations with unknown forces can be established through the continuity condition,and after transformation,the algebraic equations are solved numerically.Finally,the distribution of the dynamic stress concentration factor(DSCF)around the elliptic cavity is given and the effect of different parameters on DSCF is discussed.

INFLUENCE OF COUPLE-STRESSES ON STRESS CONCENTRATIONS AROUND THE CAVITY

The complex function method was used in the solution of micropolar elasticity theory around cavity in an infinite elasticity plane. In complex plane, the general solution of two dimension micropolar elasticity theory is given. The solution comes from analytic function and 'Zonal Function'. The boundary conditions of non-circular cavity are satisfied by using the conformal mapping method. Based on the method, a general approach solving the stress concentration in micropolar elasticity theory is established. Finally, the numerical calculation is carried out to the stress concentration coefficient of circular cavity.

Systematic Identification of Rice ABC1 Gene Family and Its Response to Abiotic Stress

Members of the activity of bc1 complex (ABC1) family are protein kinases that are widely found in prokaryotes and eukaryotes. Previous studies showed that several plant ABC1 genes participated in the abiotic stress response. Here, we present the systematic identification of rice and Arabidopsis ABC1 genes and the expression analysis of rice ABC1 genes. A total of 15 and 17 ABC1 genes from the rice and Arabidopsis genomes, respectively, were identified using a bioinformatics approach. Phylogenetic analyses of these proteins suggested that the divergence of this family had occurred and their main characteristics were established before the monocot-dicot split. Indeed, species-specific expansion contributed to the evolution of this family in rice and Arabidopsis after the monocot-dicot split. Intron/exon structure analysis indicated that most of the orthologous genes had similar exon sizes, but diverse intron sizes, and the rice genes contained larger introns, moreover, intron gain was an important event accompanying the recent evolution of the rice ABC1 family. Multiple sequence alignment revealed one conserved amino acid segment and four conserved amino acids in the ABC1 domain. Online subcellular localization predicted that nine rice ABC1 proteins were localized in chloroplasts. Real-time RT-PCR established that the rice ABC1 genes were primarily expressed in leaves and the expression could be modulated by a broad range of abiotic factors such as H2O2, abscisic acid, low temperature, drought, darkness and high salinity. These results reveal that the rice ABC1 gene family plays roles in the environmental stress response and specific biological processes of rice.

THERMAL STRESS FIELD WHEN CRACK ARREST IN AN AXIAL SYMMETRY METAL DIE USING ELECTROMAGNETIC HEATING

In order to solve the thermal stress field around crack tip in metal die when crack prevention using electromagnetic heating, a metal die with a half-embedded round crack was selected as the study object. The complex function method was used as a basis for the theoretical model of the space crack prevention in metal dies using electromagnetic heating. The crack arrest was accomplished by a pulse current discharge through the inner and outer. The theoretical analysis results show that the temperature around the crack tip rises instantly above the melting point of the metal. Small welded joints are formed at a small sphere near the crack tip inside the metal die by metal melting as a result of the heat concentration effect when the current pulse discharged. The thermal compressive stress field appears around the crack tip at the moment. The research results show that the crack prevention using electromagnetic heating can decrease the stress concentration and forms a compressive stress area around the crack tip, and also prevents the main crack from propagating further, and the goal of crack preventing can be reached.

Mode Stresses for the Interaction between Straight and Curved Cracks Problem in Plane Elasticity

In this paper, the complex variable function method is used to obtain the hypersingular integral equations for the interaction between straight and curved cracks problem in plane elasticity. The curved length coordinate method and suitable quadrature rule are used to solve the integrals for the unknown function, which are later used to evaluate the stress intensity factor, SIF. Three types of stress modes are presented for the numerical results.

围缘扁钢加强的开圆孔无限平板应力解析算法

为了研究围缘扁钢加强的开圆孔无限平板应力解析计算方法,近似认为围缘扁钢区域的平均应力处于广义平面应力状态。运用复变函数论的方法,将应力函数表示为两个待定的解析函数;列出围缘扁钢的边界条件、围缘扁钢与平板之间的应力连接条件和位移连接条件,求出应力函数,根据求出的应力函数便可求出应力。为了描述围缘扁钢减缓孔口应力集中的效果,提出围缘扁钢加强系数的定义。算例计算表明:本文提出的解析算法计算结果与有限元法计算结果吻合良好,围缘扁钢加强的开圆孔无限平板应力普遍小于开圆孔无限平板应力,围缘扁钢加强效果明显;相同体积的加强构件,围缘扁钢的加强效果优于环形加厚板。

General solutions of plane problem for power function curved cracks

A new exact and universal conformal mapping is proposed. Using Muskhelishvili＇s complex potential method, the plane elasticity problem of power function curved cracks is investigated with an arbitrary power of a natural number, and the general solutions of the stress intensity factors （SIFs） for mode I and mode II at the crack tip are obtained under the remotely uniform tensile loads. The present results can be reduced to the well-known solutions when the power of the function takes different natural numbers. Numerical examples are conducted to reveal the effects of the coefficient, the power, and the projected length along the x-axis of the power function curved crack on the SIFs for mode I and mode II.

基于复变函数理论的无中导连拱隧道应力与位移解析解

无中导连拱隧道由于后行洞衬砌搭接于先行洞衬砌拱腰之上,围岩与衬砌受力情况复杂,开展相应的围岩与衬砌应力和位移分析具有重要的工程意义。基于复变函数理论和Schwarz交替法,提出了深埋条件下考虑衬砌的无中导连拱隧道围岩与衬砌应力和变形的计算方法。针对无中导连拱隧道两洞具有共用边界的特点,在利用柯西积分法进行求解时,将单洞衬砌与围岩接触的边界积分条件转化为仅存在单洞时的完整边界积分与共用边界积分之差,对于Schwarz交替法中求解“附加面力”的过程亦进行类似处理。给出共用边界应力与位移的计算方法。通过算例,将上述解析结果和数值仿真结果进行对比,证明了方法的可行性和准确性。

基于复变函数不同规格矩形巷道围岩应力分布规律解析

鉴于矩形巷道应用的广泛性,为深入剖析矩形巷道尺寸、侧压力系数等因素变化对巷道围岩应力的影响程度及规律,将矩形巷道围岩应力求解视为弹性力学孔口问题,采用复变函数理论与Schwartz−Chistoffel映射函数,结合保角变换进行分析得到ζ复平面单位圆ζ的解析函数φ0(ζ)、ψ0(ζ),再进行Laurent级数展开后,求得复势函数φ(ζ)、ψ(ζ)。经过进一步推导最终确定矩形巷道围岩环向应力解析解,在此基础上通过环向应力的极坐标表达,深入剖析了矩形巷道尺寸与侧压力系数变化下矩形巷道周边围岩应力变化规律以及影响程度。结果表明:取映射函数前三项计算,映射巷道断面已逼近于理论断面,可保证精度要求;随着巷道宽高比增大,以宽高比等于1为分界点,巷道围岩周边应力峰值先增大后减小;巷道帮部围岩应力随宽高比的增大逐渐减小,巷道顶底板围岩应力随宽高比的增大逐渐增大;侧压力系数越大,侧帮围岩应力峰值越大,顶底板应力峰值越小;侧帮围岩应力随侧压力的增大而增大,两者呈正相关,顶底板应力随侧压力增大而减小,两者呈负相关。

浅埋三孔隧道开挖的复变函数解

为了分析浅埋三孔隧道施工对地层的影响,利用复变函数理论和Schwarz交替法,求解半无限平面内三孔圆形隧道开挖的弹性解。建立三孔隧道开挖数值计算模型,将得到的数值解与复变函数理论解进行对比分析。针对三孔隧道两种常见的布置方式(平行布置、“品”字形布置)进行参数分析,得到不同的隧道间距和埋深条件下地层变形的分布规律。结果表明:基于应力边界条件的复变函数解与数值解的吻合度较高,两种解得到的地表沉降变形的分布规律基本保持一致;在平行布置的条件下,随着隧道间径比的增大,三孔隧道之间的施工扰动随之减弱,当隧道的间径比为2时,地层的沉降曲线在三孔隧道各自洞室的上方形成相对独立的峰值;在“品”字形布置的条件下,随着三孔隧道埋深的增加,地层的竖向位移随之减少,而地层竖向位移等值线的影响范围却随之扩大。

经皮肾镜联合输尿管软镜钬激光碎石术在复杂性肾结石患者治疗中的应用价值

目的:探究经皮肾镜联合输尿管软镜下实施钬激光碎石术在复杂性肾结石患者治疗中的应用价值。方法:前瞻性选取某院泌尿外科收治的104例复杂性肾结石患者,随机数字表法分为2组,各52例。实验组实施经皮肾镜联合输尿管软镜下钬激光碎石术,对照组采用经皮肾镜取石术治疗。比较2组结石清除率、手术相关指标、手术前后应激指标[皮质醇(COR)、去甲肾上腺素(NE)、促肾上腺皮质激素(ACTH)]、肾功能指标[肾损伤因子-1(KIM-1)、尿素(UREA)、胱仰素-C(Cys-C)]及并发症情况。结果:实验组结石清除率(94.23%)高于对照组(80.77%)(P<0.05);实验组手术时间、住院时间[(95.49±8.73)min、(5.53±0.78)d]短于对照组[(107.85±9.22)min、(6.48±0.91)d],术中出血量[(101.35±9.82)mL]少于对照组[(118.76±10.35)mL],差异均有统计学意义(P<0.05);实验组术后1、3 d COR、NE、ACTH水平[1 d:(254.78±22.71)ng/mL、(268.54±24.68)ng/mL、(28.95±3.26)pg/mL,3 d:(228.54±20.69)ng/mL、(232.41±21.59)ng/mL、(22.76±2.68)pg/mL]均低于对照组[1 d:(287.16±24.35)ng/mL、(309.52±25.77)ng/mL、(35.84±3.77)pg/mL,3 d:(251.38±21.36)ng/mL、(256.84±22.83)ng/mL、(29.62±2.71)pg/mL](P<0.05);实验组术后7、14 d KIM-1、UREA、Cys-C水平[7 d:(1.25±0.35)pg/mL、(5.02±0.81)μmol/L、(0.92±0.22)μg/L,14 d:(0.79±0.23)pg/mL、(4.39±0.65)μmol/L、(0.81±0.11)μg/L]均低于对照组[7 d:(1.66±0.47)pg/mL、(5.68±0.79)μmol/L、(1.12±0.24)μg/L,14 d:(0.92±0.24)pg/mL、(5.07±0.67)μmol/L、(0.95±0.17)μg/L](P<0.05);实验组并发症总发生率(5.66%)低于对照组(19.61%)(P<0.05)。结论:经皮肾镜及输尿管软镜联合模式下实施钬激光碎石术治疗复杂性肾结石,能提高结石清除效果,缩短术后恢复进程,且组织损伤较轻,能改善肾功能,降低并发症发生风险。

共线多孔边对称裂纹板的应力强度因子计算

阐明了复变应力函数方法及其近似迭加法的基本原理,并将其应用于无限板共线多裂纹应力强度因子的求解上,结合局部修正因子法得到共线多孔边对称裂纹板的应力强度因子,并利用此种方法计算了无限板共线双孔、三孔和四孔对称裂纹情况的数值算例。将计算结果与有限元结果比较可知,该计算结果精确、可靠,而且计算过程相对简单,易操作。因此,该解析方法能很好的解决无限板上对称分布与非对称分布的共线多孔对称裂纹问题,值得在工程断裂问题中得到推广。

有限板多孔MSD的应力强度因子计算

首先阐明组合法求解有限板多孔MSD(multiple site damage)应力强度因子的基本原理,然后就组合法运用中比较难以解决的多孔边裂纹间的修正系数问题,提出一种基于复变函数法的有效解决方法。将完善后的组合法应用于有限板多孔MSD应力强度因子的求解,计算某型飞机典型铆接壁板无主裂纹和含主裂纹两种情况的数值算例。通过与有限元结果的比较可知,该方法的计算结果精确、可靠,计算过程简单、易行。提出的近似解析方法能很好地应用于任意分布的有限板多孔MSD裂纹结构,在工程断裂问题中有较好的应用价值。

集中载荷作用下各向异性平面内的椭圆孔或裂纹问题

应用复变函数Cauchy积分的方法,对含有椭圆孔或裂纹的各向异性平面,系统地导出了当其在面内受任意集中载荷作用时的复应力函数解或裂纹应力强度因子解析解,即基本解;并通过基本解的迭加,得到了在椭圆孔周或裂纹表面作用一般外载时的解,其特例证实了上述解的正确性。

圆形隧道围岩附加应力场的解析解答

研究各向同性岩体中含一个圆形隧道围岩的附近应力问题。考虑全场的应力变形特征,运用复变函数的罗朗级数展开技术,构造合适的应力函数,结合隧道的边界条件和无穷远的性态,获得了全场应力复势的解析表达式。数值分析发现,应力集中程度最剧烈时,不一定总是发生在孔的附近;应力集中程度最弱时,不一定总是距离孔边较远;当隧道埋深为其半径的5倍以上时,可以作为无限大基体含一个圆形孔洞来处理。