Stresses in a 60° perforated wedge

This paper deals with the determination of stresses around a circular hole in a cantilevered wedge of uniform thickness subjected to end loading, using electrical resistance strain gauges. The authors have previously reported a similar investigation on a 45 wedge. The results obtained are compared with the theoretical analysis for an infinite perforated wedge given by Ling and Hsu. The stress concentration factors are calculated on the basis of nominal stress in the wedge at the hole boundary (using the theory for calculating stresses in a wedge without a hole). A maximum stress concentration factor of 3–2 was indicated for an end vertical load; and a maximum factor of 2 6 was indicated for an end horizontal load.     

Stress concentrations in a plate with two unequal circular holes

This paper contains an exact solution for stresses which are produced in an infinite plate with two unequal circular holes by a uniform tension, an internal pressure or uniform shearing forces along a hole. Bipolar coordinates are used in the solution. Expressions of the hoop stress at the edges of holes are explicitly derived and the stress concentration factors are calculated. The stresses in an infinite plate with two contacted unequal circular holes are also discussed.     

Inverse problems of material distributions for prescribed apparent fracture toughness in FGM coatings around a circular hole in infinite elastic media

This study is concerned with the inverse problem of calculating material distributions intending to realize prescribed apparent fracture toughness in functionally graded material (FGM) coatings around a circular hole in infinite elastic media. The incompatible eigenstrain induced in the FGM coatings after cooling from the sintering temperature, due to mismatch in the coefficients of thermal expansion, is taken into consideration. An approximation method of determining stress intensity factors is introduced for a crack in the FGM coatings in which the FGM coatings are homogenized simulating the nonhomogeneous material properties by a distribution of equivalent eigenstrain. A radial edge crack emanating from the circular hole in the homogenized coatings is considered for the case of a uniform pressure applied to the surfaces of the hole and the crack. The stress intensity factors determined for the crack in the homogenized coatings represent the approximate values of the stress intensity factors for the same crack in the FGM coatings, and are used in the inverse problem of calculating material distributions in the FGM coatings intending to realize prescribed apparent fracture toughness in the coatings. Numerical results are obtained for a TiC/Al₂O₃ FGM coating, which reveal that the apparent fracture toughness in FGM coatings around a circular hole in infinite elastic media can be controlled within possible limits by choosing an appropriate material distribution profile in the coatings.     

A weight function method for mixed modes hole‐edge cracks

A weight function approach is proposed to calculate the stress intensity factor and crack opening displacement for cracks emanating from a circular hole in an infinite sheet subjected to mixed modes load. The weight function for a pure mode II hole‐edge crack is given in this paper. The stress intensity factors for a mixed modes hole‐edge crack are obtained by using the present mode II weight function and existing mode I Green (weight) function for a hole‐edge crack. Without complex derivation, the weight functions for a single hole‐edge crack and a centre crack in infinite sheets are used to study 2 unequal‐length hole‐edge cracks. The stress intensity factor and crack opening displacement obtained from the present weight function method are compared well with available results from literature and finite element analysis. Compared with the alternative methods, the present weight function approach is simple, accurate, efficient, and versatile in calculating the stress intensity factor and crack opening displacement.     

芯棒锥面结构对孔冷挤压强化残余应力场的影响

为了在紧固孔周引入均匀的残余压应力,以延长紧固孔构件的疲劳寿命、提高其抗应力腐蚀性能,利用ANSYS有限元软件,建立了轴对称弹塑性有限元模型,对直接芯棒冷挤压强化过程进行了仿真,特别是对芯棒的前锥段曲线结构形式进行了设计与分析,研究了前锥段曲线形式对残余应力场分布的影响.结果表明:孔壁表面的周向残余应力分布复杂且不均匀,比较而言,外凸型正弦曲线型芯棒所产生的残余压应力沿孔壁深度方向分布更加均匀;几种曲线形式的芯棒在上表面近孔边区域均产生了径向残余拉应力,在孔的挤入段产生了轴向残余拉应力,但外凸型正弦曲线型芯棒在上述区域所产生的残余拉应力较小,且分布区域也较小.     

各向异性板孔口补强应力分析

应用复变函数的方法，对于孔口被一圆形弹性环加强的各向异性板，给出了在无限远处任意均布力作用下，环及板内的应力场解；算例表明：随着环宽度的增加，环及板孔周的应力均有所降低；随着环刚度的增加，环内的应力随之增加，但板孔周的应力显著降低。     

具有衬砌圆形隧洞的弹塑性解

圆形隧洞是土木工程中常见的结构。但是,以往分析无限大均匀介质中轴对称圆形隧洞应力变形和屈服区的公式,是在Mohr-Coulomb 屈服条件中的第一主应力为径向应力的情况下导出的,这样做还不够全面。根据不同的工况和不同的地应力条件,正确选择Mohr-Coulomb 屈服条件中的第一主应力,导出衬砌和围岩的屈服范围和应力计算公式,提出第一和第二临界压力的概念,并根据临界压力给出屈服区和应力计算公式的适用范围。最后用算例比较了该方法和以往传统方法的不同。     

Effect of stacking sequence and thickness on the interlaminar stresses for quasi-isotropic laminated plates with a hole

This paper discusses the evaluation of interlaminar stresses, in the presence of in-plane stress gradients, for composite laminates by using three-dimensional equilibrium equations. The stress gradients are calculated by means of an improved finite difference scheme. A quasi-isotropic laminated plate with a circular hole subjected to a uniform tension stress is considered. The effects of stacking sequence and the thickness of the laminate on the interlaminar stresses have been studied.     

Longitudinal Shear of an Elastic Wedge with Cracks and Notches

We study the problem of longitudinal shear of an infinite wedge with cracks and notches. The integral representations of the complex stress potential are constructed in terms of the jumps of displacements and stresses on curvilinear contours identically satisfying the boundary conditions imposed on the faces of the wedge (stresses or displacements are equal to zero). By using these representations, we deduce singular integral equations of the analyzed problem for a wedge weakened by a system of cracks and holes of any shape. In some cases (a crack along the bisectrix of the wedge, a crack along a circular arc whose center is located at the edge of the wedge, and a circular notch near the edge of the wedge), we obtain exact closed solutions.     

The infinite sheet with cracked cylindrical hole under inclined tension or in-plane shear

The stress intensity factors are determined at the root of a radial crack emanating from a circular hole in an infinite sheet, under uniform tension in the direction at an arbitrary inclination with angle β and uniform in-plane shear, respectively. The stress analysis is carried out using the Muskhelishvili formulation and the conformal mapping. Numerical results of the stress intensity factors are obtained for varying crack length-to-hole radius ratio, L/R.     

Elastizitätstheoretische Lösung des kreisförmigen Einschlusses in unendlicher Scheibe mittels der Beziehungen zwischen Loch‐ und Einschlussproblem

The method applied for the derivation of an elastic solution of an infinite plate with a circular inclusion of mismatching stiffness under uniform remote tension stress is based on the special deformation characteristic of this inclusion geometry. Outgoing from the analysis of the plate with a circular hole is the exact solution of the general inclusion problem obtained by superposition of a specific inner stress field.     

Stresses in a thick plate with a circular hole under axisymmetric loading

An exact theoretical solution is given for the stresses and displacements in an infinite plate of finite thickness having a circular hole and subjected to axisymmetric normal leading. The solution is given in the form of Fourier-Bessel series and integral. Numerical results are given for stresses in plates having different thickness to hole diameter ratios and loadings. The results are compared with the available approximate theoretical and experimental results.     

Determination of crack surface displacements for cracks emanating from a circular hole using weight function method

Cracks emanating from a circular hole are of significant engineering importance, especially in aerospace industry. Accurate determination of key fracture mechanics parameters is essential for damage tolerance design and fatigue life predictions. The purpose of this paper is to provide an efficient and accurate closed‐form weight function approach to the calculation of crack surface displacements for radial crack(s) emanating from a circular hole in an infinite and finite‐width plate. Results were presented for two loading conditions: remote applied stress and uniform stress segment applied to crack surfaces, and extensively compared to recent studies using other methods in the literature. Both single and double radial cracks were considered, and also the effect of finite plate width on crack surface displacements has been investigated. A brief assessment was made on an engineering estimation of displacements based on a correction of stress intensity factor ratio. It has been demonstrated that the Wu‐Carlsson closed‐form weight functions are very efficient, accurate and easy‐to‐use for calculating crack surface displacements for arbitrary load conditions. The method will facilitate fatigue crack closure and other fracture mechanics analyses where accurate crack surface displacements are required.     

A circular inhomogeneity with mixed-type imperfect interface under in-plane deformations

We investigate the in-plane deformations of a circular inhomogeneity bonded to an infinite matrix through a mixed-type imperfect interface when the matrix is subjected to remote uniform stresses. The inhomogeneity and the matrix are endowed with separate and distinct Gurtin–Murdoch surface elasticities yet bonded together through a spring-type imperfect interface. This arrangement in which a soft interface (represented by the spring model) is bounded by two stiff interfaces (from the surface elasticities) is referred to as a ‘mixed-type imperfect interface’. A closed-form solution to the corresponding deformation problem is obtained via the use of complex variable methods, in particular, analytic continuation. We show that the introduction of the mixed-type imperfect interface leads to stress distributions in the composite which depend on six size-dependent parameters. In particular, the stress distribution inside the inhomogeneity is shown to be generally non-uniform except when a particular condition (which we identify explicitly) is satisfied by the material parameters, in which case the internal (size-dependent) stress distribution is uniform for any uniform remote loading. Finally, our solution is used to study the design of neutral and harmonic elastic inhomogeneities.     

Determination of thermal stress intensity factors for an interface crack under vertical uniform heat flow

In the case where an interface crack exists in an infinite two-dimensional elastic bimaterial, the crack surface is insulated under traction-free conditions and the uniform heat flow vertical to the crack from an infinite boundary is given, temperature and stress potentials are obtained by using the complex variable approach to solve Hubert problems, and the results are used to obtain thermal stress intensity factors. The mode II thermal stress intensity factor only occurs if both the shear moduli, as well as the Poisson's ratios in the upper and lower material, are the same. Otherwise, mode I and II thermal stress intensity factors exist but the value of the mode I thermal stress intensity factor is much smaller than that of mode II.     

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。     

Global/local analysis of composite plates with cutouts

 The study focuses on the development of a simple and accurate global/local method for calculating the static response of stepped, simply-supported, isotropic and composite plates with circular and elliptical cutouts. The approach primarily involves two steps. In the first step a global approach, the Ritz method, is used to calculate the response of the structure. Displacement based Ritz functions for the plate without the cutout are augmented with a perturbation function, which is accurate for uniform thickness plates only, to account for the cutout. The Ritz solution does not accurately satisfy the natural boundary conditions at the cut-out boundary, nor does it accurately model the discontinuities caused by abrupt thickness changes. Therefore, a second step, local in nature is taken in which a small area in the vicinity of the hole and encompassing other points of singularities is discretized using a fine finite element mesh. The displacement boundary conditions for the local region are obtained from the global Ritz analysis. The chosen perturbation function is reliable for circular cutout in uniform plates, therefore elliptical cutouts were suitably transformed to circular shapes using conformal mapping. The methodology is then applied to the analysis of composite plates, and its usefulness successfully proved in such cases. The proposed approach resulted in accurate prediction of stresses, with considerable savings in CPU time and data storage for composite flat panels.     

Catalogue of photoelastic fringes for a biaxially loaded infinite plate with a hole

This paper presents a typical catalogue of "virtual" photoelastic isochromatic fringes around the hole of a biaxially loaded infinite plate for two problems. Problem 1 relates to an infinite plate in which the circular hole is drilled first and then the loads are applied. Problem 2 is the residual stress problem in which the hole is drilled after the biaxial load is applied to the infinite plate. Use of this catalogue allows visualisation of the stress distribution around the hole, and a first approximation to the solution of the inverse problem using photoelasticity.     

Stress analysis of multilayered plates around circular holes

In this paper, a technique to study the 3-dimensional stress state around a circular hole in laminated plates is developed. First, the 3-dimensional elasticity problem for a thick plate with a circular hole is formulated in a systematic fashion by using the z-component of the Galerkin vector and that of Muki's harmonic vector function. This problem was originally solved by Alblas[1]. The reasons for reconsidering it are to introduce a technique which may be used in solving the elasticity problem for a multilayered plate and to verify and extend the results given by Alblas. Among the additional results of particular interest, one may mention the significant effect of the Poisson's ratio on the behavior and the magnitude of the stresses. Secondly, the elasticity problem for a laminated thick plate, which consists of two bonded dissimilar layers and which contains a circular hole, is considered. The problem is formulated for arbitrary axisymmetric tractions on the hole surface. Through the expansion of the boundary conditions into Fourier series, the problem is reduced to an infinite system of algebraic equations which is solved by the method of reduction. Of particular interest in the problem are the stresses along the interface as they relate to the question of delamination failure of the composite plate. These stresses are calculated and are observed to become unbounded at the hole boundary. An approximate treatment of the singular behavior of the stress state is presented, and the stress intensity factors are calculated. It is also observed that, the results compare rather well with those obtained from the finite element method.     

On the elasto-plastic stress concentration at a circular hole in an anisotropic sheet

Summary The classical problem of determining the stress concentration factor at a circular hole embedded in an infinite sheet subjected to remote uniform tension is investigated. A finite strain elasto-plastic deformation theory based on Hill's new anisotropic flow theory [7] is used. It is shown that the governing field equations can be reduced to a single first order differential equation from which the stress concentration factor is obtained by a standard numerical method. The solution covers the entire elasto-plastic range and is valid for any strain hardening function. Comparison with experimental results, for a few materials, shows good agreement.With a pure power hardening law and within the framework of small strain plasticity, our results agree with those obtained from a more general solution discovered by Budiansky [8].With 3 Figures