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An infinite plate containing an elliptic subregion in which a uniform eigencurvature is prescribed is analyzed. The problem is formulated by using the classical plate theory. Employing the Maysel's relation, an integral-type solut...
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An infinite plate containing an elliptic subregion in which a uniform eigencurvature is prescribed is analyzed. The problem is formulated by using the classical plate theory. Employing the Maysel's relation, an integral-type solution to the equilibrium equation is expressed in terms of the eigencurvature. Closed-form solutions of the displacement and corresponding resultant moment are obtained for int4rior points as well as for exterior points of the ellipse. An infinite plate containing an elliptic inhomogeneity in which a uniform eigencurvature is prescribed is also considered.
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An elliptic inclusion with prescribed polynomial eigenstrains in an infinite Kirchhoff plate is analyzed. The integral type general solutions for the in-plane and out-of-plane displacements on the mid-plane of the plate were deriv...
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An elliptic inclusion with prescribed polynomial eigenstrains in an infinite Kirchhoff plate is analyzed. The integral type general solutions for the in-plane and out-of-plane displacements on the mid-plane of the plate were derived. The integrals were simplified by using Green's function for the Kirchhoff plate. The integrals could be explicitly expressed by calculating two potential functions defined in this work. After some manipulation of Ferrers and Dyson's formula related to the integration of the harmonic potential for the three-dimensional ellipsoid, we evaluated the potential functions, which can be algebraically expressed by the I-integrals. The results were applied to the analysts of the thermal stress for an inclusion with non uniform temperature distribution that might be approximated by a polynomial. For mathematical convenience, we consider an inclusion with a linear temperature distribution. The expressions for the displacements were decomposed in order to separately investigate the effects of the constant and the first-order term of the temperature distribution. The elastic fields caused by an elliptic inhomogeneity with polynomial eigenstrains, which is called the inhomogeneous inclusion, were also determined by the equivalent eigenstrain method.
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We study the reduced parameter dependence in linear plane Cosserat elasticity with eigenstrains and eigencurvatures. The focus is on singly connected inhomogeneous materials. We find conditions on the eigenstrains and eigencurvatu...
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We study the reduced parameter dependence in linear plane Cosserat elasticity with eigenstrains and eigencurvatures. The focus is on singly connected inhomogeneous materials. We find conditions on the eigenstrains and eigencurvatures for the planar stress field to be invariant under a shift in area Cosserat compliances. The analysis can he extended to multiply connected inhomogeneous or multiphase materials. The special case is linear planar uncoupled micropolar thermoelasticity where eigenstrains represent the product of thermal expansion and temperature change.
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This paper proposes a simple method based on analytical continuation and conformal mapping to obtain an analytic solution for a two-dimensional arbitrarily shaped Eshelby inclusion with uniform main plane eigenstrains and eigencur...
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This paper proposes a simple method based on analytical continuation and conformal mapping to obtain an analytic solution for a two-dimensional arbitrarily shaped Eshelby inclusion with uniform main plane eigenstrains and eigencurvatures in an infinite or semi- infinite isotropic laminated plate. The main plane of the plate is chosen in such a way that the in-plane displacements and out-of-plane deflection on the main plane are decoupled in the equilibrium equations. Consequently, the complex potential formalism for the isotropic laminate can be readily and elegantly established. One remarkable feature of the present method is that simple elementary expressions can be obtained for the internal elastic field within the inclusion of any shape in an infinite laminated plate. Several examples are presented to illustrate the general method.
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We consider an Eshelby's inclusion of arbitrary shape with prescribed uniform mid-plane eigenstrains and eigencurvatures in an infinite, semi-infinite and in one of two bonded dissimilar semi-infinite Kirchhoff laminated anisotrop...
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We consider an Eshelby's inclusion of arbitrary shape with prescribed uniform mid-plane eigenstrains and eigencurvatures in an infinite, semi-infinite and in one of two bonded dissimilar semi-infinite Kirchhoff laminated anisotropic thin plates. The inclusion has the same extensional, coupling and bending stiffnesses as the surrounding material. The boundary of the semi-infinite plate can be described by free, rigidly clamped and simply supported edges. We derive solutions of simple form by using the new Stroh octet formalism for the coupled stretching and bending deformations of anisotropic thin plates and the method of analytic continuation. In particular, real solutions of the far-field elastic fields induced by an inclusion of arbitrary shape are obtained. Specific examples of an elliptical inclusion in an infinite, semi-infinite and in one of two bonded dissimilar semi-infinite anisotropic plates are presented to demonstrate the obtained general solutions.
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Within the framework of the Kirchhoff-Love isotropic and homogeneous plate theory, we obtain, in a unified manner, the analytic solutions to the Eshelby's problem of an inclusion of arbitrary shape with uniform eigencurvatures in ...
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Within the framework of the Kirchhoff-Love isotropic and homogeneous plate theory, we obtain, in a unified manner, the analytic solutions to the Eshelby's problem of an inclusion of arbitrary shape with uniform eigencurvatures in an infinite plate, a semi-infinite plate, one of two bonded semi-infinite plates or a circular plate by means of conformal mapping and analytical continuation. The edge of the semi-infinite plate can be rigidly clamped, free or simply supported, while that of the circular plate can be rigidly clamped, free or perfectly bonded to the surrounding infinite plate. Several examples of practical and theoretical interests are presented to demonstrate the general method. In particular, the elementary expressions of the internal elastic fields of bending moments and deflections within an (n + 1)-fold rotational symmetric inclusion described by a five-term mapping function, a symmetric airfoil cusp inclusion, a symmetric lip cusp inclusion and an inclusion described by a rational mapping function in an infinite plate are derived.
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An unsupported plate containing an embedded grind-out cavity repaired with a reinforcement bonded on one side may experience a considerable out-of-plane bending near a cavity due to the load-path eccentricity even when the geometr...
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An unsupported plate containing an embedded grind-out cavity repaired with a reinforcement bonded on one side may experience a considerable out-of-plane bending near a cavity due to the load-path eccentricity even when the geometrically nonlinear effect is taken into account. This out-of-plane bending causes stresses in the plate near the bottom of the cavity vary significantly through a remaining plate's thickness with inner wall fiber stresses in some cases at 20-30% higher than the corresponding plane-stress type results, i.e., those without considering the out-of-plane deflections. A plane-stress type analysis of a repair over a corrosion cavity had been presented in a previous paper by Duong et al. [Theoretical and Applied Fracture Mechanics 36 (2001a) 187] for a constant depth cavity repaired with an elliptical patch and most recently by Duong and Yu [International Journal of Engineering Science 40 (2002a) 347] for a spherical depth cavity repaired with a polygonal patch. Extension of these methods to include the effect of out-of-plane bending therefore will be delineated in the present paper. (C) 2003 Published by Elsevier Ltd. [References: 12]
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