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1.
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. 相似文献
2.
We consider a mathematical model of the stress-strain state of a plate with an inclined elliptic defect. We obtain approximate
formulas for the stress tensor, the displacements, and the principal stresses near the defect vertex. The obtained formulas
are compared with the results obtained by the holographic photoelasticity method. 相似文献
3.
W.B. Fraser 《International Journal of Solids and Structures》1975,11(4):501-518
In this paper, we consider the problem of finding the stress distribution in a highly stretched plate containing a circular hole that is eccentrically reinforced by thickening the plate, on one side only, in an annular region concentric with the hole. A solution of the nonlinear Kármán plate equations is obtained that is asymptotically valid for large membrane stresses. We show that, except for a narrow bending boundary layer in the neighbourhood of the boundary between the reinforced area and the rest of the plate, a state of plane stress prevails and the reinforced area undergoes a transverse deflection that brings its middle surface into the plane of the middle surface of the plate. 相似文献
4.
A method for the stress separation of interferometrically measured isopachics using an Airy stress function is proposed in
this study. A Poisson equation that represents the relationship between the sum of principal stresses and an Airy stress function
is solved using a finite element method. The Dirichlet boundary condition for solving the Poisson equation is determined by
the approximation of an assumed Airy stress function along the boundary of the model. Therefore, the distribution of the Airy
stress function is obtained from the measured isopachic contours. Then, the stresses are obtained from the computed Airy stress
function. The effectiveness of the proposed method is validated by applying the proposed method to the isopachic contours
in a perforated plate obtained by Mach-Zehnder interferometry. Results indicate that stress components around a hole in a
plate can be obtained from isopachics by the proposed method. 相似文献
5.
Numerical results for the stress state around a circular hole in a [0/±45/0]s boron-epoxy plate under tensile loading are presented. This serves as a model for the initial stress state around the hole during fatigue loading. Comparison is drawn with experimental results for a fatigued specimen obtained from thermography and radiography. Using these results, an interpretation of the effects of the initial stress state on the thermal behavior and on failure initiation is given. This interpretation shows that the circumferential normal stresses are responsible for the initial heat generation and failure initiation in the fatigued specimen. 相似文献
6.
7.
多层压电材料层合板的精确解 总被引:1,自引:0,他引:1
抛弃有关位移和应力的所有假设,直接从三维弹性力学理论的静电学理论,先导出正交各向异性压电材料板的状态方程,由此得到四边简支压电材料板的状态主程,再根据矩阵分析理论,建立了单层压电材料板的上下表面状态量之间的关系,进一步建立了多层压电板上,下表面状态量之间关系式,利用上下表面已知状态量,得到上表面未知状态的求解方程解。通过求解方程组,便得上表面未知状态量,最终可以得到任意位置处状态量,最后,同时给出了四边简支,两层不同压电材料组成,不同纵横比的层合板受正弦分布载荷作用下的精确解,其结果与现有解比较,吻合较好。 相似文献
8.
Based on Reddy's layerwise theory, the governing equations for dynamic response of viscoelastic laminated plate are derived by using the quadratic interpolation function for displacement in the direction of plate thickness. Vibration frequencies and loss factors are calculated for free vibration of simply supported viscoelastic sandwich plate, showing good agreement with the results in the literature. Harmonious transverse stresses can be obtained. The results show that the transverse shear stresses are the main factor to the delamination of viscoelastic laminated plate in lower-frequency free vibration, and the transverse normal stress is the main one in higher-frequency free vibration. Relationship between the modulus of viscoelastic materials and transverse stress is analyzed. Ratio between the transverse stress's maximum value and the in-plane stress's maximum-value is obtained. The results show that the proposed method, and the adopted equations and programs are reliable. 相似文献
9.
E. E. Gdoutos D. A. Eftaxiopoulos M. A. Kattis 《Theoretical and Applied Fracture Mechanics》1987,8(3)
The two-dimensional problem of a rigid rounded-off angle triangular inclusion partially bonded in an infinite elastic plate is studied. The unbonded part of the inclusion boundary forms an interfacial crack. Based on the complex variable method for curvilinear boundaries, the problem is reduced to a non-homogeneous Hilbert problem and the stress and displacement fields in the plate are obtained in closed form. Special attention is paid in the investigation of the stress field in the vicinity of the crack tip. It is found that the stresses present an oscillatory singularity and the general equations for the local stresses are derived. The singular stress field is coupled with the maximum circumferential stress and the minimum strain energy density criteria to study the fracture characteristics of the composite plate. Results are given for the complex stress intensity factors, the local stresses, the crack extension angles and the critical applied loads for unstable crack growth from its more vulnerable tip or two types of interfacial cracks along the inclusion boundary. 相似文献
10.
为研究金属-FGM-陶瓷 EFBF
复合板的稳态热应力,从热传导规律出发,结合热应力计算公式,建立了该复合板稳态热应
力的研究模型,用有限元和辛普生法分析了T_a=500K和T_b=1800K时,该
复合板的稳态热应力分布并与无梯度两层复合板的结果进行了比较.
结果表明:FGM梯度层的厚度、组分和孔隙率对该EFBF复合板的热应力有不同程度的影响,
此外,有梯度三层复合板的热应力比较缓和,最大拉应力减小29.18%.
此结果为该复合板的设计和应用提供了准确的计算依据. 相似文献
11.
12.
AbstractThe optimal design of the stress state in elastic plate structures with openings is a problem of great significance in engineering practice. Achieving proper shape of hole can reduce stress concentration around the boundaries remarkably. The optimal shape of a single hole in an infinite plate under uniform stresses has been obtained by complex variable method based on different optimal criteria. The complex variable method is particularly suitable for the hole shape optimization in infinite plate, in which the continuous hole boundary can be represented by the mapping function. It can also be used to solve the shape optimization problems of two or more holes. However, because of the difficulty of finding the mapping function for multi connected domain, the holes are mapped onto slits or separately mapped onto a circle. In this article, the two symmetrical and identical holes are mapped onto an annulus simultaneously by the newly found mapping function, which has a general form. The maximum tangential stress around the boundaries is minimized to achieve the optimal hole shape. And the coefficients of mapping function which describe the boundary are calculated by differential-evolution algorithm. 相似文献
13.
IntroductionHyper_elasticmaterials ,suchasrubberandpolyurethane ,havemanyexcellentpropertiesandhavebeenusedwidelyinalmostallregionsofevery_daylifeandindustrialmanufacturing .Thevoidformationandgrowthinhyper_elasticmaterialsduetotheinstabilityofmaterialsplayafundamentalroleinthemechanismsofmaterialfractureandfailure.SotheproblemhasgotacertaindevelopmentinthepasttwentyyearsandtherecentreviewisthatofHorgan[1] .Chou_WangandHorgan[2 ] ,RenandCheng[3 ,4] studiedthegrowthofacentervoidinthecylindero… 相似文献
14.
M. F. Selivanov 《International Applied Mechanics》2010,46(7):799-805
The time variation in the stresses around an elliptic hole in a composite plate is studied. Solutions that characterize the
effect of the time dependence of the relaxation moduli of the composite components on stresses are obtained. The solutions
in the time domain are obtained from the elastic–viscoelastic analogy and the corresponding elastic solutions for the effective
moduli of the composite and the stress field around an elliptic hole in an anisotropic plate. The inverse Laplace transformation
is carried out by an effective numerical method 相似文献
15.
Microstructural effects become important, when dimensions of the heterogeneous material are comparable to the length scale of microstructure and the state of stress needs to be defined in a non-local manner. Linear theory of elasticity, which is associated with the concept of homogeneity of material and local stresses, cannot describe the behavior of the materials with microstructures. In this study, Couple stress theory of elasticity has been employed to capture the size effects on the propagation of Lamb waves in an elastic plate with microstructure. Effects on the dispersion curves of Lamb waves are studied, when the characteristic length of the material is comparable to cell size. The governing equations of couple stress theory, involving stresses and couple stresses are solved to study the impact of different characteristic lengths, comparable with cell size. Since bone is a material with microstructure, so for numerical calculations and graphical representation of the results, the plate is considered to have mechanical properties typically used for bones. 相似文献
16.
Kenichi Okada 《Experimental Mechanics》1981,21(12):461-466
A method is proposed to determine stresses in acoustoelasticity by making use of orthotropic stress-acoustic relations and the equations of equilibrium. It is derived theoretically that shear stress is determined ny ultrasonic data ofB and ?, which denote a magnitude of acoustic birefringence and its principal direction, respectively. Other stress components are obtained by numerical integration of the equilibrium equation with the shear stress thus determined. Experiments were carried out to show the validity and usefulment of the method. This method was applied to the measurement of stress field on a plate with a circular hole subjected to axial tension. Ultrasonic measurements were made by a Y-cut quartz transducer with 5-MHz fundamental frequency. The specimen was cut out from 1100 aluminum plate of 4-mm thickness, which shows a slight orthotropy due to roll working. The values ofB and ? were measured in both stressed and unstressed state. Then, stress distributions were determined by the method proposed here, and are compared with the known theoretical distributions. 相似文献
17.
In this paper the general problem of a rectangular plate clamped along two parallel sides and containing a crack parallel to the clamps is considered. The problem is formulated in terms of a system of singular integral equations and the asymptotic behaviour of the stress state near the corners is investigated. Numerical examples are considered for a clamped plate without a crack and with a centrally located crack, and the stress intensity factors and the stresses along the clamps are calculated. 相似文献
18.
19.
《International Journal of Solids and Structures》1999,36(1):167-178
This paper presents an exact solution for the stresses in an infinite shape memory alloy plate with a circular hole subjected to biaxial tensile stresses applied at infinity. The solution obtained by assumption of plane stress is based on the two-dimensional version of the Tanaka constitutive law for shape memory materials. The plate is in the austenitic phase, prior to the application of external stresses. However, as a result of tensile loading, stress-induced martensite forms, beginning from the boundary of the hole and extending into the interior, as the load continues to increase. Therefore, in a general case, the plate consists of three annular regions: the inner region of pure martensite, the intermediate region where martensite and austenite coexist, and the outer region of pure austenite. The boundaries between these annular regions can be found as functions of the external stress. Two methods of solution are presented. The first is a closed-form approach based on a replacement of the actual distribution of the martensitic fraction by a piece-wise constant function of the radial coordinate. The second method results in an exact solution obtained by assuming that the ratio between the radial and circumferential stresses in the region where austenite and martensite coexist is governed by the same relationship as that in the encompassing regions of pure austenite and pure martensite. 相似文献
20.
The generalized differential quadrature (GDQ) method was used to determine the inter-laminar stresses and deflections in a laminated rectangular anisotropy plate under thermal bending involving the effect of shear deformation. We obtained the non-dimensional stresses and transverse center deflection in cross-ply and angle-ply anti-symmetric, anisotropic laminates subjected to thermal load with sinusoidal temperature distribution. We found that the shear deformation has significant effects on the stresses and deflections for laminated anisotropic plate with moderately side-to-thickness ratio under thermal load and bending state. 相似文献