Browsing by Author "Singh, B. M."

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    Closed-form solution for piezoelectric layer with two collinear cracks parallel to the boundaries
    (2006-05-11) Singh, B. M.; Rokne, J.; Dhaliwal, R. S.
    We consider the problem of determining the stress distribution in an infinitely long piezoelectric layer of finite width, with two collinear cracks of equal length and parallel to the layer boundaries. Within the framework of reigning piezoelectric theory under mode III, the cracked piezoelectric layer subjected to combined electromechanical loading is analyzed. The faces of the layers are subjected to electromechanical loading. The collinear cracks are located at the middle plane of the layer parallel to its face. By the use of Fourier transforms we reduce the problem to solving a set of triple integral equations with cosine kernel and a weight function. The triple integral equations are solved exactly. Closed form analytical expressions for stress intensity factors, electric displacement intensity factors, and shape of crack and energy release rate are derived. As the limiting case, the solution of the problem with one crack in the layer is derived. Some numerical results for the physical quantities are obtained and displayed graphically.
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    Closed-Form Solutions for a Mode-III Moving Interface Crack at theInterface of Two Bonded Dissimilar Orthotropic Elastic Layers
    (2009-02-03) Singh, B. M.; Rokne, J.; Dhaliwal, R. S.
    An integral transform technique is used to solve the elastodynamic problem of a crack of fixed length propagating at a constant speed at the interface of two bonded dissimilar orthotropic layers of equal thickness. Two cases of practical importance are investigated. Firstly, the lateral boundaries of the layers are clamped and displaced inequal and opposite directions to produce antiplane shear resulting in a tearing motion along the leading edge ofthe crack, and secondly, the lateral boundaries of the layers are subjected to shear stresses. The analytic solutionfor a semi-infinite crack at the interface of two bonded dissimilar orthotropic layers has been derived. Closed-formexpressions are obtained for stressing the intensity factor and other physical quantities in all cases.
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    Contact problem for bonded nonhomogeneous materials under shear loading
    (2003-01-01) Singh, B. M.; Rokne, J.; Dhaliwal, R. S.; Vrbik, J.
    The present paper examines the contact problem related to shearpunch through a rigid strip bonded to a nonhomogeneous medium.The nonhomogeneous medium is bonded to another nonhomogeneousmedium. The strip is perpendicular to the y-axis and parallelto the x-axis. It is assumed that there is perfect bonding atthe common plane surface of two nonhomogeneous media. UsingFourier cosine transforms, the solution of the problem is reducedto dual integral equations involving trigonometric cosinefunctions. Later on, the solution of the dual integral equationsis transformed into the solution of a system of two simultaneousFredholm integral equations of the second kind. Solvingnumerically the Fredholm integral equations of the second kind,the numerical results of resultant contact shear are obtained andgraphically displayed to demonstrate the effect of nonhomogeneityof the elastic material.
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    Dual series equations involving generalized Laguerre polynomials
    (2005-01-01) Singh, B. M.; Rokne, J.; Dhaliwal, R. S.
    An exact solution is obtained for the dual series equationsinvolving generalized Laguerre polynomials.
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    The axisymmetric Boussinesq-type problem for a half-space under optimal heating of arbitrary profile
    (2004-01-01) Rokne, J.; Singh, B. M.; Dhaliwal, R. S.; Vrbik, J.
    A solution of the axisymmetric Boussinesq-type problem is derived for transient thermal stresses in a half-space under heating by using the Laplace and Hankel transforms. An analytical method is developed to predict the temperature field that satisfies the prescribed mechanical conditions. Several simple shapes of punches of arbitrary profile are considered and an expression for the total load is derived to achieve penetration. The numerical results for the temperature and the total load on the punch are shown graphically.
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    The Study of Triple Integral Equations with Generalized Legendre Functions
    (2008-11-09) Singh, B. M.; Rokne, J.; Dhaliwal, R. S.
    A method is developed for solutions of two sets of triple integral equations involving associated Legendre functions of imaginary arguments. The solution of each set of triple integral equations involving associated Legendre functions is reduced to a Fredholm integral equation of the second kind which can be solved numerically.
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    Two-Dimensional Electrostatic Problem in a Plane with Earthed Elliptic Cavity due to One or Two Collinear Charged Electrostatic Strips
    (2007-01-18) Singh, B. M.; Rokne, J. G.; Dhaliwal, R. S.
    A two-dimensional electrostatic problem in a plane with earthed elliptic cavity due to one or two charged electrostatic strips is considered. Using the integral transform technique, each problem is reduced to the solution of triple integral equations with sine kernels and weight functions. Closed-form solutions of the set of triple integral equations are obtained. Also closed-form expressions are obtained for charge density of the strips. Finally, the numerical results for the charge density are given in the form of tables.