Geometric elasticity problem of stress concentration in a plate with a circular hole

We use the geometric elasticity equations [1], which permit relating the medium stress state to the geometry of the Riemannian space generated by the stresses, to consider the plane problem of stress concentration near a circular hole in a thin unbounded plate loaded by normal and tangential stresses. The Riemannian space metric coefficient corresponding to the coordinate normal to the plate plane is treated as the variable thickness of the plate in three-dimensional Euclidean space, which determines the optimal law for the plate material distribution. We consider plates in uniaxial tension, biaxial tension, and shear. For the plate with thickness variation laws thus obtained, we construct direct numerical solutions of the corresponding classical elasticity problems and determine the stress concentration factors.     

On the stress concentration around a hole in a half-plane subject to moving contact loads

We study the stress concentration due to a pore in an elastic half-plane, subject to moving contact loading, in the entire range of possible geometrical parameters (contact area/hole diameter, hole depth/hole diameter). Since the number of cases is very large to study with FEM even with modern machines, the use of a recent simple approximate formula due to Greenwood based on the stress field in the absence of the hole is first attempted, and compared with a full FEM analysis in sample cases. To further distillate the effects of the hole distance from the free surface and of the contact area size, the limiting cases are studied of: (i) concentrated load perpendicular to the surface and aligned with the hole centre; (ii) constant unit pressure on the top surface of the half-plane and (iii) hydrostatic load. A full investigation is then conduced for the case of Hertzian load on the surface, and it is seen that the tensile stress concentration is significantly reduced with respect to that of the concentrated load, when the contact area size is of the same order of the hole radius. Results obtained with the approximate Greenwood formula are generally accurate however only if the hole distance from the surface is greater than two times the hole radius.     

Dynamic stress concentration around a circular hole due to SH-wave in anisotropic media

A new approach based on complex function to solve the SH-wave scattering problem around a circular hole in anisotropic media is introduced in this paper. It is found that the dynamic stress concentration factor is dependent on the incident wave number and the hole radius. Finally, some numerical results of dynamic stress concentration factor of a circular hole in anisotropic media are given. The Project Supported by National Natural Science Foundation of China     

On the stress distribution in a spherical shell with an off-center curvilinear hole

A numerical analysis is made of the joint effect of two factors of asymmetry—ellipticity and eccentricity—on the stress distribution near a free hole in a spherical shell. The nature of deformation is determined by the predominant factor. Whether there are “fixed” points on the graphs of stress distribution around a small hole at which they intersect depends on how rigidly the outer edge is fixed. As the rigidity of fixation is increased, the points smear __________ Translated from Prikladnaya Mekhanika, Vol. 42, No. 1, pp. 113–118, January 2006.     

The concentration of stress and strain in finite thickness elastic plate containing a circular hole

The elastic stress and strain fields of finite thickness large plate containing a hole are systematically investigated using 3D finite element method. It is found that the stress and strain concentration factors of the finite thickness plate are different even if the plate is in elasticity state except at notch root of plate surface. The maximum stress and strain do not always occur on the mid plane of plate. They occur on the mid plane only in thin plate. The maximum stress and strain concentration factors are not on mid plane and the locations of maximum stress and strain concentration factors are different in thick plate. The maximum stress and strain concentration factors of notch root increase from their plane stress value to their peak values, then decrease gradually with increasing thickness and tend to each constant related to Poisson’s ratio of plate, respectively. The stress and strain concentration factors at notch root of plate surface are the same and are the monotonic descent functions of thickness. Their values decrease rapidly and tend to each constant related to Poisson’s ratio with plate thickness increasing. The difference between maximum and surface value of stress concentration factor is a monotonic ascent function of thickness. The thicker the plate is or the larger the Poisson’s ratio is, the larger the difference is. The corresponding difference of strain concentration factor is similar to the one of stress concentration factor. But the difference magnitude of stress concentration factor is larger than that of strain concentration factor in same plate.     

Surface tension-induced stress concentration around a nanosized hole of arbitrary shape in an elastic half-plane

This paper studies surface tension-induced stress concentration around a nanosized hole of arbitrary shape inside an elastic half-plane. Of particular interest is the maximum hoop stress on the hole’s boundary with relation to the point of maximum curvature and the distance between the hole and the free surface of the half-plane. The shape of the hole is characterized by a conformal mapping which maps the exterior of the hole onto the exterior of the unit circle in the image plane. On using the technique of conformal mapping and analytic continuation, the complex potentials of the half-plane are expressed in a series form with unknown coefficients to be determined by Fourier expansion method. Detailed numerical results are shown for elliptical, triangular, square and rectangular holes. Two basic conclusions are that the hoop stress increases with decreasing hole size and the maximum hoop stress generally appears nearby but not exactly at the point of maximum curvature. In addition, it is shown that the hoop stress nearby the point of maximum curvature on the hole’s boundary increases rapidly with decreasing distance between the hole and the free surface of the half-plane. On the other hand, if the distance between the hole and the free surface is more than three times the hole size, the effect of the free surface on the stress concentration around the hole is ignorable and the elastic half-plane can be treated approximately as an elastic whole plane.     

负压爆炸载荷和数据采集间隔对弹性开孔板动应力集中的影响

基于ANSYS 7.0/LS-DYNA程序,对3 m3 m四边简支,厚度0.025 m,中心开有0.3 m0.3 m方孔的弹性板,在正压和负压三角爆炸载荷作用下的应力响应进行了分析,利用能量密度时间分布函数（TDFED）确定了动应力集中因子,并给出其计算步骤。计算结果表明计算总时间和数据采集时间间隔对动应力集中因子影响较大,而负压荷载影响较小。     

Maximum stress in a tensile strip with a large hole

Measurements were made to decide between two solutions of the title problem. In question was the limiting value of the stress-concentration factor at the edge of a large hole in a tensile strip as the hole diameter approached the strip width. The results indicate that the stress-concentration factor is near two and support one of the solutions with a minor qualification.     

Surface tension-induced stress concentration around an elliptical hole in an anisotropic half-plane

We examine the surface tension-induced stress concentration around an elliptical hole inside an anisotropic half-plane with traction-free surface. Using conformal mapping techniques, the corresponding complex potential in the half-plane is expressed in a series whose unknown coefficients are determined numerically. Our results indicate that the maximum hoop stress around the hole (which appears in the vicinity of the point of maximum curvature) increases rapidly with decreasing distance between the hole and the free surface. In particular, for an elliptical or even circular hole in an anisotropic half-plane we find that, with decreasing distance between the hole and the free surface, the hoop stress can switch from compressive to tensile at certain points on the hole's boundary and from tensile to compressive at others. This phenomenon is absent in the case of an elliptical or even circular hole in the corresponding case of an isotropic half-plane.     

Photoviscoelastic stress analysis of a plate with a central hole

An epoxy resin containing excessive plasticizer was developed and characterized. The material, which deforms viscously at room temperature, has optical properties that depend on stress and strain. A tensile specimen was prepared from the epoxy resin so that the mechanical and optical properties of the epoxy resin could be characterized. The elastic and plastic behavior was determined at 37°C using tensile stresses between 4 and 26 MPa. The birefringence was also recorded as a function of time and stress. From these results, a photoviscoelastic constitutive equation was constructed to describe the dependence of the birefringence on stress and strain. The constitutive equation was then applied to study the deformation of a tensile specimen containing a central circular hole. By using the isochromatic fringes in combination with the isoclinic, the time-dependent variation of the stress field in the specimen was solved.     

The effect of transverse shear deformation on stress concentration factors for shallow shells with a small circular hole

Simplified equations are derived for the analysis of stress concentration for shear-deformable shallow shells with a small hole.General solutions of the equations are obtained,in terms of series,for shallow spherical shells and shallow circular cylindrical shells with asmall circular hole.Approximate explicit solutions and numerical results are obtianed forthe stress concentration factors of shallow circular cylindrical shells with a small hole onwhich uniform pressure is acting.