Investigation of the Scattering of Harmonic Elastic Waves by Two Collinear Symmetric Cracks Using the Non-Local Theory

ＩｎｔｒｏｄｕｃｔｉｏｎＴｈｅｌａｓｔｆｏｕｒｄｅｃａｄｅｓｈａｖｅｗｉｔｎｅｓｓｅｄｔｈｅｉｎａｕｇｕｒａｔｉｏｎｏｆａｎｏｖｅｌｔｈｅｏｒｙｏｆｍａｔｅｒｉａｌｂｏｄｉｅｓ,ｎａｍｅｄｔｈｅｎｏｎ＿ｌｏｃａｌｍｅｃｈａｎｉｃｓ.ＴｈｉｓｗａｓｄｏｎｅｐｒｉｍａｒｉｌｙｄｕｅｔｏｔｈｅｅｆｆｏｒｔｓｏｆＥｄｅｌｅｎ[1],Ｅｒｉｎｇｅｎ[2 ],ＧｒｅｅｎａｎｄＲｉｖｌｉｎ[3].Ａｃｃｏｒｄｉｎｇｔｏｔｈｅｎｏｎ＿ｌｏｃａｌｔｈｅｏｒｙ ,ｔｈｅｓｔｒｅｓｓａｔａｐｏｉｎｔＸｉｎａｂｏｄｙｄｅｐｅｎｄｓｎｏ…     

The addendum for the generalized d'Alembert equations of motion

ＩｎｔｒｏｄｕｃｔｉｏｎＴｈｅｍｏｓｔｂａｓｉｃｃｏｎｄｉｔｉｏｎｓｆｏｒｆｅｅｄｂａｃｋｃｌｏｓｅｄ＿ｌｏｏｐｃｏｎｔｒｏｌｏｆｍａｎｉｐｕｌａｔｏｒｓａｒｅｔｈｅｆｉｎｅｓｔｒｕｃｔｕｒｅａｎｄｔｈｅｅｆｆｉｃｉｅｎｔｒｅａｌ＿ｔｉｍｅｃｏｍｐｕ...     

Generalized variational principle on nonlinear theory of naturally curved and twisted closed thin-walled composite beams

ＩｎｔｒｏｄｕｃｔｉｏｎＴｈｅｓｔａｔｉｃａｎｄｄｙｎａｍｉｃｎｏｎｌｉｎｅａｒａｎａｌｙｓｉｓｉｎｔｈｅｎａｔｕｒａｌｌｙｃｕｒｖｅｄａｎｄｔｗｉｓｔｅｄｃｌｏｓｅｄｔｈｉｎ＿ｗａｌｌｅｄｓｌｅｎｄｅｒｂｅａｍｓ(ａｂｂｒｅｖｃｕｒｖｅｄａｎｄｔｗｉｓｔｅｄｔｈｉｎ＿ｗａｌｌｅｄｃｏｍｐｏｓｉｔｅｂｅａｍｓ)ｏｆｔｈｅｆｉｂｒｅ＿ｒｅｉｎｆｏｒｃｅｄｃｏｍｐｏｓｉｔｅｍａｔｅｒｉａｌｓｉｓｃｏｍｍｏｎｌｙａｎｄｍａｉｎｌｙａｐｐｌｉｅｄｉｎｃｈｅｍｉｃａｌｉｎｄｕｓｔｒｙａｎｄａｅｒｏｎａｕｔｉ…     

THE MIXED BOUNDARY-VALUE PROBLEM FOR NON-LOCAL ASYMMETRIC ELASTICITY

ＩｎｔｒｏｄｕｃｔｉｏｎＩｔｉｓｗｅｌｌ＿ｋｎｏｗｎｔｈａｔｔｈｅｒｅｅｘｉｓｔｓｔｈｅａｒｇｕｍｅｎｔｂｅｔｗｅｅｎＡｔｋｉｎｓｏｎ（ｓｅｅ［１～４］）ａｎｄＥｒｉｎｇｅｎａｎｄｃｏ＿ｗｏｒｋｅｒｓ（ｓｅｅ［５～７］）ｏｖｅｒｔｈｅｎｏｎ＿ｌｏｃａ...     

Research on stability of interface of jet containing suspended solid particles

Ｎｏｍｅｎｃｌａｔｕｒｅ　αｓ:ｐａｒｔｉｃｌｅｖｏｌｕｍｅｆｒａｃｔｉｏｎ;　ｕｇ:ｇａｓｉｎｓｔａｎｔａｎｅｏｕｓｖｅｌｏｃｉｔｙｖｅｃｔｏｒ;　ｕｓ:ｐａｒｔｉｃｌｅｉｎｓｔａｎｔａｎｅｏｕｓｖｅｌｏｃｉｔｙｖｅｃｔｏｒ;　Ｕ :ｍｅａｎａｘｉａｌｖｅｌｏｃｉｔｙｏｆｔｗｏ＿ｐｈａｓｅｊｅｔ;　Ｕ0 :ｘ＿ａｘｉａｌｖｅｌｏｃｉｔｙｏｆｔｈｅｅｘｉｔ,ｃｈａｒａｃｔｅｒｉｓｔｉｃｖｅ ｌｏｃｉｔｙｏｆｆｌｏｗ＿ｆｉｅｌｄ;　ｐ:ｉｎｓｔａｎｔａｎｅｏｕｓｆｌｏｗ＿ｆｉｅｌｄｐｒｅｓｓｕｒｅ;　 ｐ:ｍｅａｎ…     

ROSSBY INERTIA GRAVITY SOLITARY WAVE AND THE REMOTE CORRELATION BETWEEN THE EAST-AND THE WEST-PACIFIC SUBTROPICAL HIGH

ＩｎｔｒｏｄｕｃｔｉｏｎＴｈｅａｂｎｏｒｍａｌｉｔｙｂｏｔｈｔｈｅＣｈｉｎａｗｅａｔｈｅｒａｎｄｔｈｅＷｅｓｔ＿Ｐａｃｉｆｉｃｓｕｂｔｒｏｐｉｃａｌｈｉｇｈ (ｍａｒｋｅｄＷＰＳＨ ,ｔｈｅｆｏｌｌｏｗｉｎｇｉｓｔｈｅｓａｍｅ)ａｒｅｃｌｏｓｅｌｙｃｏｒｒｅｌａｔｅｄｉｎｓｕｍｍｅｒｓｅａｓｏｎ .Ｉｎｒｅｃｅｎｔｙｅａｒｓ,ｓｏｍｅＷＰＳＨｓｅａｓｏｎａｌａｂｎｏｒｍａｌｉｔｙｓａｍｐｌｅｓｏｆｉｔｓｌｏｃａｔｉｏｎｐｅｒｓｉｓｔｉｎｇｌｅａｎｉｎｇｎｏｒｔｈｗａｒｄｏｓｏｕｔｈｗａｒｄｗｅｒｅｓｔｕ…     

Investigation of a griffith crack subject to uniform tension using the non-local theory by a new method

ＩｎｔｒｏｄｕｃｔｉｏｎＩｎｓｅｖｅｒａｌｐｒｅｖｉｏｕｓｐａｐｅｒｓ［１,２,３］,Ｅｒｉｎｇｅｎｄｉｓｃｕｓｓｅｄｔｈｅｓｔａｔｅｏｆｓｔｒｅｓｓｎｅａｒｔｈｅｔｉｐｏｆａｓｈａｒｐｌｉｎｅｃｒａｃｋｉｎａｎｅｌａｓｔｉｃｐｌａｔｅｓｕｂｊｅｃｔｔｏｕｎｉｆｏｒｍｔｅｎｓｉｏｎ,ｓｈｅａｒａｎｄａｎｔｉ＿ｐｌａｎｅｓｈｅａｒ．Ｔｈｅｆｉｅｌｄｅｑｕａｔｉｏｎｓｅｍｐｌｏｙｅｄｉｎｔｈｅｓｏｌｕｔｉｏｎｏｆｔｈｅｓｅｐｒｏｂｌｅｍｓａｒｅｔｈｏｓｅｏｆｔｈｅｔｈｅｏｒｙｏｆｎｏｎ＿ｌｏｃａｌｅ…     

Ishikawa Iterative Process in Uniformly Smooth Banach Spaces

ＬｅｔＥｂｅａｕｎｉｆｏｒｍｌｙｓｍｏｏｔｈＢａｎａｃｈｓｐａｃｅ ,ＫｂｅａｎｏｎｅｍｐｔｙｃｌｏｓｅｄｃｏｎｖｅｘｓｕｂｓｅｔｏｆＥ ,ａｎｄｓｕｐｐｏｓｅＴ :Ｋ→ＫｉｓａｃｏｎｔｉｎｕｏｕｓΦ＿ｓｔｒｏｎｇｌｙｐｓｅｕｄｏｃｏｎｔｒａｃｔｉｖｅｏｐｅｒａｔｏｒ.ＤｅｎｏｔｅｔｈｅｄｕａｌｓｐａｃｅｏｆＥｂｙＥ .ＷｅｄｅｎｏｔｅｂｙＪｔｈｅｄｕａｌｉｔｙｍａｐｆｒｏｍＥｔｏ 2 Ｅ ｄｅｆｉｎｅｄｂｙＪ(ｘ) =ｆ∈Ｅ :〈ｘ ,ｆ〉=‖ｘ‖2 =‖ｆ‖2 . ( 1 )Ｉｔｉｓｗｅｌｌ＿ｋｎｏｗｎｔｈａｔｉｆＥｉｓｕ…     

ORIENTATION DISTRIBUTION FUNCTIONS FOR MICROSTRUCTURES OF HETEROGENEOUS MATERIALS (Ⅰ) ──DIRECTIONAL DISTRIBUTION FUNCTIONS AND IRREDUCIBLE TENSORS

ＩｎｔｒｏｄｕｃｔｉｏｎＡｎａｔｕｒａｌｏｒａｒｔｉｆｉｃｉａｌｍａｔｅｒｉａｌｉｓｕｓｕａｌｌｙｍｉｃｒｏｓｃｏｐｉｃａｌｌｙｈｅｔｅｒｏｇｅｎｅｏｕｓａｎｄｏｗｎｓａｃｅｒｔａｉｎｍｉｃｒｏｓｔｒｕｃｔｕｒｅｃｏｍｐｒｉｓｉｎｇｔｈｅｍａｔｅｒｉａｌｃｏｎｓｔｉｔｕｔｉｏｎｓ (ｃｒｙｓｔａｌｌｏｉｄ ,ｄｉｓｌｏｃａｔｉｏｎｓ ,ｐｈａｓｅｔｒａｎｓｆｏｒｍａｔｉｏｎｓ,ｍｉｃｒｏ＿ｃｒａｃｋｓ,ｖｏｉｄｓ,ｆｉｂｅｒｓ,ｉｎｃｌｕｓｉｏｎｓ) .Ｉｔｉｓｎｏｔｓｕｒｐｒｉｓｉｎｇｔｈａｔａｎｕｍｂｅ…     

Forces and Moments of the Liquid Finite Amplitude Sloshing in a Liquid-Solid Coupled System

ＩｎｔｒｏｄｕｃｔｉｏｎＩｎｔｈｅｆｉｅｌｄｏｆｓｐａｃｅ,ｔｈｅｃｏｕｐｌｅｄｄｙｎａｍｉｃｓｒｅｌａｔｉｖｅｔｏｌｉｑｕｉｄｓｌｏｓｈｉｎｇｉｓｏｆｔｅｎｅｎｃｏｕｎｔｅｒｅｄ[1].Ｉｎａｓｐａｃｅｃｒａｆｔｄｙｎａｍｉｃａｌｓｙｓｔｅｍ ,ｔｈｅｌｉｑｕｉｄｓｌｏｓｈｉｎｇｕｓｕａｌｌｙｃｏｕｐｌｅｓｗｉｔｈｒｉｇｉｄｍｏｔｉｏｎｏｆｔｈｅｓａｔｅｌｌｉｔｅ ,ｖｉｂｒａｔｉｏｎｓｏｆｔｈｅｆｌｅｘｉｂｌｅａｐｐｅｎｄｉｘｅｓａｎｄｃｏｎｔｒｏｌｆｕｎｃｔｉｏｎ .Ｏｎｏｎｅｈａｎｄ ,ｔｈｅｍｏｔ…     

The analysis of crack problems with non-local elasticity

IntroductionTheclassicalconhnuummechanicshasbeenusedtosolvemanyproblemsinmacrofracturemechanics,butencountersdifficulheswhentheeffectofITilcrocharacteristicdimensionshouldbetakenintoaccount.Thestressfieldverynearthecracktipisstillnotclear.Somephenomenaofshortcrackscannotbeexplained["']andsomemechanismoffracturehasnotbeensolvedyet.Thenon-localelashcitytheoryseemsattractivetotheseproblems.Thetheoryofnon-localelasticity,establishedanddevelopedbyEringenetal[3),connectstheclassicalcontinuummechan…     

三维压电弹性体断裂分析的基本解

求解了在材料的特征方程有重根时，三维压电弹性体的单位集中不连续位移和不连续电势基本解。讨论了重根对断裂力学问题解的影响。     

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。     

Stress intensity factors for asymmetric branched cracks in plane extension by using crack-tip displacement discontinuity elements

Stress intensity factors are important in the analysis of cracked materials. They are directly related to the fracture propagation and fatigue crack growth criteria. Based on the analytical solution (Crouch, S.L., 1976. Solution of plane elasticity problems by displacement discontinuity method, Int. J. Numer. Methods Eng. 10, pp. 301–343; Crouch, S.L., Starfield, A.M., 1983. Boundary Element Method in Solid Mechanics, with Application in Rock Mechanics and Geological Mechanics, London, Geore Allon and Unwin, Bonton, Sydney) to the problem of a constant discontinuity in displacement over a finite line segment in the x, y plane of an infinite elastic solid, recently, the crack-tip displacement discontinuity element which can be classified as the left and right crack-tip displacement discontinuity elements are developed by the author Yan, X., (in press. A special crack-tip displacement discontinuity element, Mechanics Research Communications) to model the crack-tip fields to more accurately compute the stress intensity factors of cracks in general plane elasticity. In the boundary element implementation the left or the right crack-tip displacement discontinuity element is placed locally at the 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 boundaries. To prove further the efficiency of the suggested approach and provide more results of the stress intensity factors, in this study, analysis of an asymmetric branched crack bifurcated from a main crack in plane extension is carried out.     

The influence of elastic waves on dynamic stress intensity factors (three-dimensional problems)

Summary The fundamental solutions of the displacement discontinuity for three-dimensional problems in Laplace space are deduced in thsi paper. The displacement discontinuity method and the equivalent stress method were combined and used to determine dynamic stress intensity factors for three-dimensional time-dependent crack problems. The stress intensity factors were calcualted for dynamically loaded cracks with rectangular, circular, and elliptical crack fronts. The influence of elasticity waves (in particular surface waves) on the magnitude of the stress intensity factor and on the displacement of the crack surfaces was analysed.On leave from the Central-South University of Technology, Changsha, Hunan Province, P. R. China.     

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.     

The G2 constant displacement discontinuity method – Part I: Solution of plane crack problems

A new constant displacement discontinuity element was presented in a previous paper applied initially for the numerical solution of either isolated straight cracks or for co-linear cracks of the three fundamental deformation modes I, II and III due to the special form of the solution. It was based on the strain-gradient elasticity theory in its simplest possible Grade-2 variant. The assumption of the G2 expression for the stresses has resulted to a better average stress value at the mid-point of the straight displacement discontinuity compared to the classical elasticity solution. This new element gave considerably better predictions of the stress intensity factors compared to the constant displacement discontinuity element and the linear displacement discontinuity element. Moreover, it preserved the simplicity and hence the high speed of computations. In this Part I, the solution for this element is extended for the analysis of cracks of arbitrary shape in an infinite plane isotropic elastic body and it is validated against three known analytical solutions.