Twisting of an elastic plate containing a crack

The stress distribution caused by twisting an infinite plate containing a finite crack is analyzed in terms of Reissner's theory for the bending of thin plates. The singular character and the detailed structure of the stresses near the ends of the crack are determined in closed form. Numerical results are given for the magnitudes of the stress couples and stress resultants for a range of plate thicknesses.

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Zusammenfassung Due Spannungsvertcilung, hervorgerufen durch die Torsion einer unendlichen Platte mit einem Ri\ begrenzter Länge, wird mit Hilfe der Reissner-Theorie für die Biegebeanspruchung dünner Platten untersucht. Der singulare Charakter und die genauc Verteilung der Spannungen in Nähe der Ri\enden werden bestimmt. Zahlenmä\ige Ergebenisse für die Gro\e der Spannungsparre und ihrer Resultanten werden für eine Reihe von Plattenstärken angegeben.

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Résumé La distribution des contraintes dans une plague infinie comportant une fisure finic et soumise à torsion est analysée au moyen de la théorie de Reissner pour la flexion des tôles minces.Le caractère singulier, et la structure de détail des contraintes au voisinage des extrémités de la fisure sont explicités.Des résultats numériques sont fournis en ce qui regarde les grandeurs des couples de contraintes et de leurs résultantes, pour une certaine gamme d'éspaisseur de tôles.

     

Thermoelastic wave propagation in an elastic solid containing a finite crack

Investigated in this paper is the scattering of plane harmonic thermoelastic waves around the tip of a finite crack. Integral transform techniques are used to formulate the problem and reduce it to Fredholm integral equations of the second kind. The equations are solved numerically and the singular stress field near the crack tip is determined. In particular, the variation of the stress intensity factor with the frequency of the incoming wave is exhibited graphically. The peak in the magnitude of the stress intensity factor is of paramount interest in the application of fracture mechanics to thermal stress problems.     

Plastic zones in an orthotropic plate of finite width containing a Griffith crack

The problem of an orthotropic infinite plate of finite width containing a centrally located stressed Griffith crack is considered. The crack is located perpendicular to the edges of the orthotropic plate. The crack tips are fully yielded and in the inelastic zones the material carries only constant normal stresses equal to the yield stress. Dugdale's model is employed to find the effects of the material anisotropy on the size of the plastic zones around the crack tips. Graphical results showing the effects of anisotropy on the length of the plastic zone are also presented.     

Analysis of Rayleigh-Lamb wave scattering by a crack in an elastic plate

This paper considers the scattering of low-frequency elastic waves by a crack in a plate. A simple formula is derived for the reflection coefficient which serves as a lower bound to the reflection coefficient at higher frequencies.     

Vibration of non-ideal simply supported laminated plate on an elastic foundation subjected to in-plane stresses

In this paper, the effect of non-ideal boundary conditions and initial stresses on the vibration of laminated plates on Pasternak foundation is studied. The plate has simply supported boundary conditions and is assumed that one of the edges of the plate allows a small non-zero deflection and moment. The initial stresses are due to in-plane loads. The vibration problem is solved analytically using the Lindstedt–Poincare perturbation technique. So the frequencies and mode shapes of the plate with non-ideal boundary condition is extracted by considering the Pasternak foundation and in-plane stresses. The results of finite element simulation, using ANSYS software, are presented and compared with the analytical solution. The effect of various parameters like stiffness of foundation, boundary conditions and in-plane stresses on the vibration of the plate is discussed. Dependency of non-ideal boundary conditions on the aspect ratio of the plate for changing the frequencies of vibrations is presented. The relation between the shear modulus of elastic foundation and the frequencies of the plate is investigated.     

Elasto-plastic analysis for a finite thickness rectangular plate containing a through-thickness central crack

The objective of this work is to present a three-dimensional analysis of the elasto-plastic response of a center-cracked rectangular panel by using an alternate method, the method of lines (MOL). The problem of a finite thickness rectangular plate containing a through-thickness central crack under uniaxial tension is studied in detail. An incremental procedure is used to seek the 3-D elasto-plastic stress and strain distribution. The Prandtl-Reuss equations and the associated von Mises flow rule are employed. The material is assumed to be elastic-plastic with nonlinear work-hardening. Effective stress and effective strain concepts are used. The MOL is used to reduce the governing equations on displacements to a coupled set of ordinary differential equations (ODE) along x, y, z lines. These are integrated by Peano-Baker method. Since the ODE are of constant coefficient the coefficient matrix is diagonalized and the matrizon is easily evaluated. Numerical results on stresses, displacements, the growth of plastic zone and the crack surface opening displacements are reported and their variation along the thickness are presented in graphs. The variation of the stress intensity factor K ₁, along the thickness direction is given. It is found that the computation time needed for determining the distribution of stresses and strains is much less than what has been reported by using other methods. A comparison of results on SIF with those obtained by other methods is also given.

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Résumé L'objet du travail est de présenter une analyse tridimentionnelle de la réponse élastoplastique d'un panneau rectangulaire présentant une fissure centrale, et utilisant une méthode alternative, la méthode des lignes MOL. On étudie dans le détail le problème de la plaque rectangulaire d'épaisseur finie comportant une fissure centrale traversante et soumise à la contrainte uniaxiale. Une procédure incrémentale est utilisée en vue de rechercher la distribution des contraintes et des déformations élastoplastiques suivant les trois dimensions. On utilise les équations de Prandtl-Reuss et la règle d'écoulement de von Mises qui lui est associée. On suppose que le matériau est élastoplastique et qu'il présente un vieillissement non linéaire. On recourt au concept des contraintes effectives et des déformations effectives. Le MOL est utilisé en vue de ramener les équations gouvernant les déplacements à un ensemble d'équations différentielles ordinaires suivant les axes X, Y, Z; on fait appel à la méthode de Peano-Baker pour leur intégration. Comme les équations différentielles ont un coéfficient constant, la matrice de coéfficient peut être résolue par diagonales et le matriciel peut être aisément évalué. Les résultats numériques relatifs aux contraintes, aux déplacements, à la croissance de la zône plastique et aux déplacements d'ouverture de la surface de la fissure sont présentés, et leur variation sur l'épaisseur sont mises en graphiques. On fournit la variation du facteur d'intensité de contrainte K suivant la direction de l'épaisseur. On trouve que le temps de calcul nécessaire à la détermination de la distribution des contraintes et déformations est beaucoup moindre que celui nécessaire par l'utilisation d'autres méthodes. Une comparaison des résultats relatifs aux facteurs d'intensité de contraintes avec ceux obtenus par d'autres méthodes est également fournie.

     

Analysis of an internal crack in a finite anisotropic plate

In this paper the boundary collocation method is presented for computing the stress intensity factors for an internal crack in a finite anisotropic plate. The stress functions are assumed such that they can represent the stress singularity at the crack tips, satisfying not only the governing equations of the anisotropic plate theory in the domain, but also the stress-free conditions on the crack surfaces. Therefore, only the boundary conditions of the plate need to be considered, and they can be satisfied approximately by the Boundary Collocation Method. Numerical examples demonstrated that the proposed method gives satisfactory results compared with the existing solutions.     

Elasto-plastic finite element analysis of a crack in an infinite plate

The elastic support method was recently developed to simulate the effects of unbounded solids in the finite element analysis of stresses and displacements. The method eliminates all the computational disadvantages encountered in the use of `infinite' elements or coupled finite element boundary element methods while retaining all the computational advantages of the finite element method. In this paper, the method is extended to the elasto-plastic analysis of fracture in infinite solids by using the load increment approach and including the effects of strain hardening. Numerical tests and parametric study are conducted by analysing a straight crack in an infinite plate. Present results for J integrals and plastified zones are compared, respectively, with analytical solutions and available results obtained by using the body force method. The agreement between the results is found to be very good even if the truncation boundary of the finite element model is located very close to the crack tip or the plastified zone.     

Propagation of a transient shear wave from a crack in an elastic plate

A simple analytical technique based on the methods of transverse resonance and group velocity is developed in order to predict the propagation of shear (SH) waves emitted from a crack in elastic plates. Since a total solution of the Rayleight Lamb waves propagation inside the plate is very complicated, the simple SH mode was used to demonstrate the argument of this paper. The effects of varying distances between the crack and the sensor are also discussed.

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Résumé On développe une technique analytique simple basée sur les procédés de résonance transversale et de vitesse de trains d'onde en vue de prédire la propagation d'ondes SH émises à partir d'une fissure dans une plaque élastique.Comme une solution complète pour la propagation des ondes de Rayleight-Lamb est très compliquée à mettre en oeuvre, on s'est restreint à utiliser le mode SH pour démontrer la validité de l'étude.On discute également des effets d'une distance variable entre la fissure et le palpeur.

     

Edge crack in an elastic layer resting on Winkler foundation

The paper deals with the stress analysis near a crack tip in an elastic layer resting on Winkler foundation. The edge crack is assumed to be normal to the lower boundary plane. The upper surface of the layer is loaded by given forces normal to the boundary. The considered problem is solved by using the method of Fourier transforms and dual integral equations, which are reduced to a Fredholm integral equation of the second kind. The stress intensity factor is given in the term of solution of the Fredholm integral equation and some numerical results are presented.     

On the dynamic propagation of a griffith crack in a finite rectangular plate

A preliminary analysis of crack initiation and dynamic crack propagation of a Griffith crack in a finite rectangular plate is performed. The problem is simulated using an improved two-dimensional finite difference code—the SMF2D code—thus yielding more accurate and reliable results. The results are then presented and discussed.     

Anti-plane shear problem for an edge crack in a finite orthotropic plate

The problem of an edge crack in a finite orthotropic plate under anti-plane shear is considered. The boundary collocation method is used to calculate the mode III stress intensity factor (SIF). For the case in which the material is isotropic, the present results agree very well with those obtained by using the integral equation method. Furthermore, the method can be extended readily for general cases with arbitrary geometrical and boundary loading conditions and material properties.     

Integral representations of the solutions for a bending plate on an elastic foundation

Summary The existence of distributional solutions is investigated for boundary integral equaitons associated with the bending of an elastic plate with transverse shear deformation on an elastic foundation.     

The stress intensity factor of an edge crack in a finite elastic disc

In this paper, a Mellin transform technique is used to express the stress intensity factor and the crack energy of an edge crack in a finite elastic disc directly in terms of the solution of a Fredholm integral equation of the second kind. The constant loading case is considered in detail and the results given in graphical form.     

Energy trapping in power transmission through an elastic plate by finite piezoelectric transducers

We study transmission of electric energy through an elastic plate by acoustic wave propagation and piezoelectric transducers. Our mechanics model consists of an elastic plate with finite piezoelectric patches on both sides of the plate. A theoretical analysis using the equations of elasticity and piezoelectricity is performed. Energy trapping that describes the confinement and localization of the vibration energy is examined.     

An effective numerical method for an interfacial crack in a finite bi-material plate

In this paper an effective numerical method is presented for analyzing the stress intensity factors associated with the stress field near a partially debonded interface in a finite bi-material plate. The strees functions are assumed such that they can represent the stress singularity at the crack tips, satisfying not only the equilibrium equations in the domain, but also the stress and displacement conditions on the crack surfaces and across the interface. Therefore, only the boundary conditions of the plate need be considered, and they can be satisfied approximately by the Boundary Collocation Method. Numerical examples demonstrated that the proposed method gives satisfactory results and has many advantages compared to other methods.