Photoelastic analysis of a thick plate with an elliptical hole subjected to simple out-of-plane bending

A three-dimensional photoelastic analysis using the stress freezing and slicing techniques was employed to study the stress distribution and the stress-concentration factors around an elliptical hole in a plate of finite thickness. The plate was subjected to simple out-of-plane bending. A special bending device was designed to produce uniform bending moment at the two opposite free edges of the plate. Six plates with various elliptical holes were studied. The stress variation across the plate thickness at the periphery of the elliptical hole was also investigated. The experimental results were correlated with the existing theoretical solutions.     

Photoelastic analysis of an asymmetrically reinforced circular cut-out in a flat plate subjected to uniform unidirectional stress

Three-dimensional photoelastic studies of stresses around an asymmetrically reinforced circular cut-out in a flat plate under uniform unidirectional stress are reported. The frozen-stress technique, with Hysol 4290 material, was used to determine the stress distribution through four critical points on the boundary of the reinforced hole. Included were models with different cross sections of reinforcement, with various interface fillet radii and with different plate widths. For the majority of models, the ratio of volume of reinforcement to volume of hole was unity. It is concluded that, for reducing the stress concentration, there is a limit on the effectiveness of increasing the fillet radius beyond half the plate thickness. It was found that a reinforcement having a thickness of approximately 40 percent of the plate thickness was optimum and that the stress concentration decreases with volume of reinforcement. The authors believe that, with judgment, some of the conclusions reached may be applied, for design purposes, beyond the specific dimensional ranges and loading conditions of the tests.     

Magneto elastic stress subjected to uniform magnetic field over a thin infinite plate containing an elliptical hole with an edge crack

Two dimensional solutions of the magnetic field and magneto elastic stress are presented for a magnetic material of a thin infinite plate containing an elliptical hole with an edge crack subjected to uniform magnetic field. Using a rational mapping function, each solution is obtained as a closed form. The linear constitutive equation is used for these analyses. According to the electro-magneto theory, only Maxwell stress is caused as a body force in a plate. In the present paper, it raises a plane stress state for a thin plate, the deformation of the plate thickness and the shear deflection. Therefore the magneto elastic stress is analyzed using Maxwell stress. No further assumption of the plane stress state that the plate is thin is made for the stress analysis, though Maxwell stress components are expressed by nonlinear terms. The rigorous boundary condition expressed by Maxwell stress components is completely satisfied without any linear assumptions on the boundary. First, magnetic field and stress analyses for soft ferromagnetic material are carried out and then those analyses for paramagnetic and diamagnetic materials are carried out. It is stated that those plane stress components are expressed by the same expressions for those materials and the difference is only the magnitude of the permeability, though the magnetic fields H_x, H_y are different each other in the plates. If the analysis of magnetic field of paramagnetic material is easier than that of soft ferromagnetic material, the stress analysis may be carried out using the magnetic field for paramagnetic material to analyze the stress field, and the results may be applied for a soft ferromagnetic material. It is stated that the stress state for the magnetic field H_x, H_y is the same as the pure shear stress state. Solutions of the magneto elastic stress are nonlinear for the direction of uniform magnetic field. Stresses in the direction of the plate thickness and shear deflection are caused and the solutions are also obtained. Figures of the magnetic field and stress distribution are shown. Stress intensity factors are also derived and investigated for the crack length.     

Normalized stresses around an elliptic hole in a finite plate of linear material subjected to large uniform in-plane loading

Stress-concentration factors associated with the large deformations of in-plane loaded plates with elliptic holes are presented in a form with which designers are familiar. An analytic expression to obtain the stress-concentration factor is included.     

Magneto-elastic stress in a thin infinite plate with an elliptical hole under uniform magnetic field

Two-dimensional magnetic field and magneto-elastic stress solutions are presented for a magnetic material of a thin infinite plate with an elliptical hole under uniform magnetic field. The linear constitutive equation is used for the magnetic field and the stress analyses. The magneto-elastic stress is analyzed using Maxwell stress since only Maxwell stress is caused as a body force according to the electro magneto theory. Except the approximation of the plane stress state in which the plate is thin, no further assumption is made for the stress analysis, though Maxwell stress components are expressed by nonlinear terms. The rigorous boundary condition expressed by Maxwell stress is completely satisfied without any linear assumptions on the boundary. First, magnetic field and stress for soft ferromagnetic material is analyzed and then those for paramagnetic and diamagnetic materials are analyzed. It is stated that the stress components are the same expressions for those materials and the difference is only the magnitude of the permeability, though the magnetic fields are different each other in the plates. If the analysis of magnetic field of paramagnetic materials is easier than that of soft ferromagnetic material, the stress analysis may be carried out using the magnetic field for paramagnetic material. Shear deflection as well as stress in the direction of the plate thickness arises and the solutions are also obtained. Figures of the magnetic field and stress distribution are shown. Stress intensity factors are also derived.     

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。     

Large deflection problem of a clamped elliptical plate subjected to uniform pressure

In this paper, the perturbation solution of large deflection problem of clamped elliptical plate subjected to uniform pressure is given on the basis of the perturbation solution of large deflection problem of similar clamped circular plate (1948), (1954). The analytical solution of this problem was obtained in 1957. However, due to social difficulties, these results have never been published. Nash and Cooley (1959) published a brief note of similar nature, in which only the case λ=a/b=2 is given. In this paper, the analytical solution is given in detail up to the 2nd approximation. The numerical solutions are given for various Poisson ratios v=0.25, 0.30, 0.35 and for various eccentricities λ=1, 2, 3, 4, 5, which can be used in the calculation of engineering designs.     

Biaxial tension of a thick plate with an elliptical hole,from aging elastic-plastic material

Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 1, pp. 169–174, January–February, 1989.     

Magnetic field and magneto elastic stress in an infinite plate containing an elliptical hole with an edge crack under uniform electric current

Two-dimensional solutions of the electric current, magnetic field and magneto elastic stress are presented for a magnetic material of a thin infinite plate containing an elliptical hole with an edge crack under uniform electric current. Using a rational mapping function, the each solution is obtained as a closed form. The linear constitutive equation is used for the magnetic field and the stress analyses. According to the electro-magneto theory, only Maxwell stress is caused as a body force in a plate which raises a plane stress state for a thin plate and the deformation of the plate thickness. Therefore the magneto elastic stress is analyzed using Maxwell stress. No further assumption of the plane stress state that the plate is thin is made for the stress analysis, though Maxwell stress components are expressed by nonlinear terms. The rigorous boundary condition expressed by Maxwell stress components is completely satisfied without any linear assumptions on the boundary. First, electric current, magnetic field and stress analyses for soft ferromagnetic material are carried out and then those analyses for paramagnetic and diamagnetic materials are carried out. It is stated that the stress components are expressed by the same expressions for those materials and the difference is only the magnitude of the permeability, though the magnetic fields H_x, H_y are different each other in the plates. If the analysis of magnetic field of paramagnetic material is easier than that of soft ferromagnetic material, the stress analysis may be carried out using the magnetic field for paramagnetic material to analyze the stress field, and the results may be applied for a soft ferromagnetic material. It is stated that the stress state for the magnetic field H_x, H_y is the same as the pure shear stress state. Solving the present magneto elastic stress problem, dislocation and rotation terms appear, which makes the present problem complicate. Solutions of the magneto elastic stress are nonlinear for the direction of electric current. Stresses in the direction of the plate thickness are caused and the solution is also obtained. Figures of the magnetic field and stress distribution are shown. Stress intensity factors are also derived and investigated for the crack length and the electric current direction.     

Magneto-elastic stress induced by an electric current in an infinite thin plate with an elliptical hole

Two-dimensional magnetic field and stress analyses have been presented for soft ferromagnetic, paramagnetic, and diamagnetic materials of an infinite thin plate with an elliptical hole under steady electric current. The magnetic stress has been analyzed in the Maxwell Stress Model. Except for the approximation of the plane stress state since the plate is the thin plate, any assumption is not made for the stress analysis, though the Maxwell stress components are expressed by nonlinear terms. The boundary condition expressed by Maxwell’s stress is completely satisfied without any linear assumptions on the boundary. Two ways for the boundary condition are stated. The analysis of σ _z in the direction of the plate thickness is also carried out. Figures of the magnetic field and stress distribution are shown. Stress intensity factors are also derived, and the magnitude of the stress intensity factor for the magnetic stress and thermal stress due to the Joule heat caused by the electric current is discussed.     

Photoelastic stress analysis of orthtropic materials by using an isotropic plate

Based on the two-dimensional theory of elasticity for an orthotropic plate, relations between stress components produced in two different orthotropic plates are considered and the conditions to realize the similar stress fields in different orthotropic plates are studied. On the basis of the similarity law, a convenient photoelastic method to analyze stress fields in an orthotropic plate, using an isotropic plate, is presented. Two examples are treated. One deals with the stress-concentration problem around a circular hole in a strip with edges parallel to the symmetric axis of elasticity. In the second example, the edges of the strip are assumed to be inclined by 30 deg to the elastically symmetric axes. The experimental results are compared with theoretical calculations. Paper was presented at the SEM VII International Congress on Experimental Mechanics held in Las Vegas, NV on June 8–11, 1992.     

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。     

A numerical analysis of cracks emanating from an elliptical hole in a 2-D elasticity plate

This paper is concerned with the stress intensity factors (SIFs) of cracks emanating from an elliptical hole in an infinite or a finite plate under biaxial loads by using a boundary element method, which consists of the non-singular displacement discontinuity element presented by Crouch and Starfield and the crack-tip displacement discontinuity elements due to the author. In the boundary element implementation the left or the right crack-tip element is placed locally at the corresponding left or right crack tip on top of the constant displacement discontinuity elements that cover the entire crack surface and the other boundaries. A few numerical examples are included to show that the present approach is very efficient and accurate for the calculating the SIFs of crack problems in an infinite or a finite plate. The present numerical results of cracks emanating from an elliptical hole under biaxial loads can reveal the effect of the elliptical aspect ratio and the transverse load on the SIFs.     

Photoelastic analysis of an orthotropic plate on a nonlinear foundation

Frozen-stress techniques were used to analyze an orthotropic plate on a continuous, nonlinear foundation. A long-range objective of the investigation was to provide experimental results to compare with a future finite-element analysis of the same type problem. Data were presented to illustrate principal stress magnitudes and directions. Close agreement of a static equilibrium check of the nonlinear foundation with the applied load experimentally verified the procedure used for calculation of external pressure on the model-foundation interface. Paper was presented at 1969 Fall Meeting held in Houston, Tex. on October 14–17.