Fracture of Two-Layer Plates with Cracks in Tension with Regard for Local Buckling

The fracture of two-layer plates with cracks in tension, with regard for the preceding local buckling, is investigated experimentally. The critical stresses corresponding to the local buckling are determined for plates with various geometrical parameters. The effect of the local buckling on the fracture kinetics and strength of plates is estimated.     

二维瞬态热传导的PDDO分析北大核心CSCD

采用近场动力学微分算子(peridynamic differential operator, PDDO)理论求解了二维瞬态热传导问题.将热传导方程和边界条件由其局部微分形式重构为非局部积分形式,引入Lagrange乘数法,采用变分原理的概念,建立了二维瞬态热传导问题的非局部分析模型.通过误差与收敛性分析,与其他数值方法计算结果进行比较,验证了本模型的准确性.在此基础上,将本模型应用于计算不规则边界板和内部含微缺陷(裂纹和圆孔)板的二维瞬态热传导问题.结果表明该方法计算精度高、适用范围广、具有较好的收敛性,为计算二维瞬态热传导问题提供了新的思路.     

On the determination of stress concentration in a stretched plate with two holes

We present a short survey of studies of the elastic interaction of two holes in a stretched plate. Special attention is paid to the study of the concentration of stresses on the contours of closely positioned holes. For two identical elliptic holes, numerical results are obtained by the method of singular integral equations. With the help of the limit transition, we determined the stress intensity factors at the vertices of semi-infinite parabolic notches. A comparison of the numerical data with known analytic solutions for two circular holes and collinear cracks is performed.     

The stress state of an anisotropic plate with two arbitrarily located elliptic holes or cracks

Using Lekhnitskii's method of complex potentials we study the stress state of an anisotropic plate with two arbitrary elliptic holes. We consider the cases when one or both of the holes become narrow slit-cracks, when the cracks extend to the edge of the hole, and when two cracks intersect or form a broken two-link crack. We give the results of numerical studies. Translated fromTeoreticheskaya i Prikladnaya Mekhanika, No. 24, 1993, pp. 33–43.     

Evaluation of singular integrals for anisotropic elastic boundary element analysis

To improve the numerical evaluation of weakly singular integrals appearing in the boundary element method, a logarithmic Gaussian quadrature formula is usually suggested in the literature. In this formula the singular function is expressed in terms of the distance between source point and field point, which is a real variable. When an anisotropic elastic solid is considered, most of the existing fundamental solutions are written in terms of complex variables. When the problems with holes, cracks, inclusions, or interfaces are considered, to suit for the shape of the boundaries usually a mapping function is introduced and then the solutions are expressed in terms of mapped complex variables. To deal with the trouble induced by the complex variables, in this study through proper change of variables we develop a simple way to improve the evaluation of weakly singular integrals, especially for the problems of anisotropic elastic solids containing holes, cracks, inclusions, or interfaces. By simple matrix expansion, the proposed method is extended to the problems with piezoelectric or magneto-electro-elastic solids. By using the dual reciprocity method, the proposed method employed for the elastostatic fundamental solution can also be applied to the elastodynamic analysis.     

Opening of blind cracks in a plate

Integral equations are used to solve the problem of the limiting equilibrium state of plates with a system of parallel blind (surface) cracks, which are under tensile forces and bending moments, on the assumption that plastic deformations develop along the entire depth in the neighborhood of the cracks. The effect of the geometric and physicomechanical parameters on opening of the edges of the cracks is investigated.Translated from Matematicheskie Metody i Fiziko-mekhanicheskie Polya, No. 26, pp. 29–31, 1987.     

Fracture of plates,the compression of which is accompanied by cracking

The appearance of fracture shapes, analogous to fractures in the shape of a "Chinese lantern" in rectangular plates has been discussed, the compression of which is accompanied by cracking. It has been shown that one or two cracks can appear when rectangular hinged plates are subjected to compression. An arbitrary number of cracks can be formed when a cylindrical shell is subjected to compression.Paper presented at the 9th International Conference on the Mechanics of Composite Materials, Riga, October (1994).Translated from Mekhanika Kompozitnykh Materialov, Vol. 31, No. 3, pp. 326–329, May–June, 1995.     

A hybrid-Trefftz element containing an elliptic hole

Much work on special elements that simplify geometrical modelling of structures containing holes, cracks and/ or inclusions has been reported extensively in the literature. This paper presents a hybrid-Trefftz element containing elliptic hole formulated using Hellinger–Reissner principle by employing trial functions based on the mapping technique and the Cauchy integral method. The element presented in this paper could be regarded as an improved formulation over Piltner [Special finite elements with holes and internal cracks, Int. J. Numer. Methods Eng. 21 (1985) 1471–1485] element because the chosen trail functions in this paper have provided relatively more stable solutions. The use of the element with other ordinary displacement-based finite elements has also yielded very accurate solutions even when very coarse meshes relative to the size of the elliptic hole have been used.     

Growth and intersection of cracks using boundary-element analysis

Existing procedures which are available for the determinationof the path traversed by a crack growing in a two-dimensionallinear elastic body are limited to simple geometric configurationswhere the growth of all the crack tips is the same. In thispaper, an important advance has been made; a crack may intersectother cracks, while a crack growing from a boundary may intersectother boundaries. Simulations of crack growth and intersectionsare performed for a number of configurations and computationalprocedures are given which control the rate of crack growth.In order to assess the robustness of these new extensions, cracksat or near circular holes and multiple cracks growing into anedge crack are considered, and detailed results given.     

Electroelastic State of a Multiply Connected Piezoelectric Half Plane with Holes and Cracks

A method has been proposed [1] for solving two-dimensional electroelasticity problems using generalized complex potentials. General representations of complex potentials for a multiply coupled region have been studied [2] and a method for calculating the stress intensity factors and induction has been introduced. In this article, general expressions are obtained for the complex potentials for a multiply connected half plane with arbitrarily positioned holes and rectilinear cracks and the electroelastic state of a half plane with a single elliptical hole or rectilinear crack is studied.     

Crack initiation in elliptically notched plates

In this work, crack initiation in elliptically notched plates under uniaxial tension is studied by means of a Finite Fracture Mechanics analysis. The stress concentration factor changes with the aspect ratio of the half axes: from unity for slender ellipses in loading direction to infinity for crack-like ellipses normal to the loading. The closed-form solutions of the stress field and an approximate formulae of the stress intensity factor of mode I cracks allows for an efficient Finite Fracture Mechanics analysis of plates with elliptical notches with arbitrary aspect ratios. The results show that the transition from vanishing stress concentration to infinite (crack-like) stress concentration is rendered continuously by the present approach. A transition from strength of materials to Linear Elastic Fracture Mechanics is obtained that shows distinct size effects. A comparison to experimental results on size effects of notched plates shows good agreement. (© 2015 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Unsteady thermal stresses near a curvilinear hole in a plate with heat transfer under its warming by a heat flow

We describe an algorithm of determining quasistatic thermal stresses in multiply connected plates with heat transfer, induced by the disturbance of heat flow near holes. Our approach is based on the Laplace transformation and a modified relation of its numerical conversion. The boundary-value problems for the Helmholtz equation, from which the Laplace transform is determined, are solved using the method of boundary integral equations. We solve the integral equations by the method of mechanical quadratures. The results of calculation of nonstationary temperature fields and stresses induced by them in a strip with small holes of different shape are also presented. Translated from Matematychni Metody ta Fizyko-Mekhanichni Polya, Vol. 51, No. 1, pp. 105–111, January–March, 2008.     

An analytical formula for the effective conductivity of 2D domains with cracks of high density

We construct the conformal mapping of the square with circular non-overlapping holes onto the square with non-overlapping slits. It is constructed as a solution of the Riemann–Hilbert problem for a multiply connected domain in a class of double periodic functions. The Riemann–Hilbert problem is reduced to a system of functional equations which is solved with an arbitrary order of approximations. On the basis of this conformal mapping, an analytical formula for the effective conductivity of randomly distributed cracks in 2D media is deduced. This formula extends the known before formulae to high density fractures in 2D media.     

Solution of some two-dimensional problems of elasticity

Using the method of boundary elements, we obtain numerical solutions of two-dimensional (plane deformation) boundary-value problems on the elastic equilibrium of infinite and finite homogeneous isotropic bodies having elliptic holes with cracks and cuts of finite length. Translated from Sovremennaya Matematika i Ee Prilozheniya (Contemporary Mathematics and Its Applications), Vol. 51, Differential Equations and Their Applications, 2008.     

A hybrid method of studying the stress intensity factors at the tips of cracks in anisotropic plates

We propose an efficient new method of numerical analysis of the residual strength of finite plates weakened by cracks. The basis of the method is an alternating Schwartz procedure that makes it possible to achieve a successful combination of the algorithmicity and indifference to boundary conditions of the finite-element method and the application of the method of integral equations for studying singular stress fields. The numerical implementation of the scheme and the algorithm for determining the stress intensity factors at the tips of cracks is given as a software package written in FORTRAN. The efficiency of application of the computational methodology is illustrated by examples. Translated fromTeoreticheskaya i Prikladnaya Mekhanika, No. 23, 1992, pp. 34–40.     

Relative stiffness of irregularly perforated plates

Approximation of the average field is used in order to calculate the relative elastic properties of plates irregularly perforated with a large number of different hole. Relative properties are calculated for a plate perforated with a different kind of elliptical hole. It is shown that the Young's modulus and shear modulus of a plate perforated with identical round holes calculated in this approximation have values similar to those calculated accurately for the case of a regularly perforated plate.Translated from Dinamicheskie Sistemy, No. 5, pp. 3–11, 1986.     

Solution of the problem of the stressed state of a medium applied to the destruction of rock of nonuniform structure

We solve the two-dimensional problem of the distribution of stresses in a medium weakened by a system of cracks and elliptic holes loaded with a constant pressure. We obtain formulas that make it possible to determine the complex potentials of the two-dimensional problem of the theory of elasticity for the medium in question.Translated fromMatematicheskie Metody i Fiziko-Mekhanicheskie Polya, Issue 27, 1988, pp. 103–106.     

Modeling large amplitude vibration of matrix cracked hybrid laminated plates containing CNTR-FG layers

This paper presents the mathematical modeling of the nonlinear vibration behavior of a hybrid laminated plate composed of carbon nanotube reinforced functionally graded (CNTR-FG) layers and conventional fiber reinforced composite (FRC) layers. Three type symmetric distributions of single walled carbon nanotubes (SWCNTs) through the thickness of layers are considered. The cracks are modeled as aligned slit cracks across the ply thickness and transverse to the laminate plane. The distribution of cracks is assumed to be statistically homogeneous corresponding to an average crack density. The obtained partial differential equations are solved by the element-free kp-Ritz method, and the iteration process is dealt with using the linearized updated mode method. Detailed parametric studies are conducted investigate the effects of matrix crack density, CNTs distributions, CNT volume fraction, plate aspect ratio and plate length-to-thickness ratio, boundary conditions and number of layers on the frequency-amplitude responses of hybrid laminated plates containing CNTR-FG layers.     

Simulation of Rayleigh waves in cracked plates

The aim of this paper is to develop new numerical procedures to detect micro cracks, or superficial imperfections, in thin plates using excitation by Rayleigh waves. We shall consider a unilateral contact problem between the two sides of the crack in an elastic plate subjected to suitable boundary conditions in order to reproduce a single Rayleigh wave cycle. An approximate solution of this problem will be calculated by using one of the Newmark methods for time discretization and a finite element method for space discretization. To deal with the nonlinearity due to the contact condition, an iterative algorithm involving one multiplier will be used; this multiplier will be approximated by using Newton's techniques. Finally, we will show numerical simulations for both cracked and non‐cracked plates. Copyright © 2006 John Wiley & Sons, Ltd.     

Investigation of stress intensity factors near interacting cracks in linear viscoelastic plates

Stress intensity factors as a function of time near interacting cracks during creep in plates made of linear viscoelastic materials are investigated. The interaction of collinear as well as parallel cracks disposed on different levels perpendicular to the tensile stress was studied. It was found that during interaction of collinear cracks, the stress intensity factor K₁(t) grew in creep and varied mainly due to the change in the distance between the tips of interacting cracks. There was practically no increase in the length of the crack. During interaction of parallel cracks, the value of K₁(t) decreased slightly in time, which was also due to an increase in the distance between the tips of the cracks in creep.Institute of Mechanics, Lomonosov Moscow State University, Moscow, Russia. Translated from Mekhanika Kompozitnykh Materialov, Vol. 34, No. 5, pp. 643–650, September–October, 1998.