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Y.z. Chen - One of the best experts on this subject based on the ideXlab platform.
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numerical solution for the degenerate scale problem in Plane Elasticity using null field cvbie
Engineering Analysis With Boundary Elements, 2016Co-Authors: Y.z. ChenAbstract:Abstract This paper provides a numerical solution for the degenerate scale problem in Plane Elasticity using the null field complex variable boundary integral equation (CVBIE). After performing the coordinate transformation, the CVBIE can be formulated in the normal scale. After making discretization, a linear algebraic equation is obtained. The influence matrix in the normal scale is invertible. By introducing two basic solutions, the degenerate scale problem is finally solved. Several numerical examples are given.
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Solution and Numerical Analysis for Thermal Elliptic Inclusion in Plane Elasticity
Journal of Thermal Stresses, 2015Co-Authors: Y.z. ChenAbstract:By using the conformal mapping technique and the continuity conditions along the interface, a general solution and numerical analysis for thermal elliptic inclusion in Plane Elasticity are presented. In the study, two types of temperature distributions in the inclusion, the constant distribution and the linear distribution, are assumed. In the first case, the strains and stresses in the inclusion remain constant. However, in the second case, the strains and stresses in the inclusion do not stay constant. For a particular case, a numerical example is carried out.
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collinear zener stroh crack problem in Plane Elasticity
Engineering Fracture Mechanics, 2008Co-Authors: Y.z. Chen, X Y LinAbstract:Abstract This paper investigates the collinear Zener–Stroh crack problem in Plane Elasticity. Two cracks in series are chosen as an example in analysis. Different to the Griffith crack problem, an initial displacement discontinuity exists in the Zener–Stroh crack problem, which in turn is the increment of displacement when a moving point goes around the crack in a closed loop. From the traction free condition along the cracks, the dislocation distribution function as well as the complex potential with undetermined coefficients is suggested. The involved undetermined coefficients can be evaluated from the condition of the assumed initial displacement discontinuity. Finally, a closed form solution for the problem is obtained and the calculated stress intensity factors at crack tips are presented. A problem for two collinear Zener–Stroh cracks with different lengths is also studied.
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Collinear Zener–Stroh crack problem in Plane Elasticity
Engineering Fracture Mechanics, 2008Co-Authors: Y.z. Chen, X Y LinAbstract:Abstract This paper investigates the collinear Zener–Stroh crack problem in Plane Elasticity. Two cracks in series are chosen as an example in analysis. Different to the Griffith crack problem, an initial displacement discontinuity exists in the Zener–Stroh crack problem, which in turn is the increment of displacement when a moving point goes around the crack in a closed loop. From the traction free condition along the cracks, the dislocation distribution function as well as the complex potential with undetermined coefficients is suggested. The involved undetermined coefficients can be evaluated from the condition of the assumed initial displacement discontinuity. Finally, a closed form solution for the problem is obtained and the calculated stress intensity factors at crack tips are presented. A problem for two collinear Zener–Stroh cracks with different lengths is also studied.
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On the equivalence of types of damage in Plane Elasticity
Philosophical Magazine Letters, 2006Co-Authors: Y.z. Chen, X Y LinAbstract:In this paper, a model for the equivalence of types of damage in Plane Elasticity is suggested. The model is based on the evaluation of additional work done by the existing damage. Analysis has been carried out for four particular cases of damage: (a) an ellipse, (b) a line crack, (c) a triangular hole and (d) a square hole. These cases are equivalent to that of a circular hole with appropriate radius.
X Y Lin - One of the best experts on this subject based on the ideXlab platform.
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collinear zener stroh crack problem in Plane Elasticity
Engineering Fracture Mechanics, 2008Co-Authors: Y.z. Chen, X Y LinAbstract:Abstract This paper investigates the collinear Zener–Stroh crack problem in Plane Elasticity. Two cracks in series are chosen as an example in analysis. Different to the Griffith crack problem, an initial displacement discontinuity exists in the Zener–Stroh crack problem, which in turn is the increment of displacement when a moving point goes around the crack in a closed loop. From the traction free condition along the cracks, the dislocation distribution function as well as the complex potential with undetermined coefficients is suggested. The involved undetermined coefficients can be evaluated from the condition of the assumed initial displacement discontinuity. Finally, a closed form solution for the problem is obtained and the calculated stress intensity factors at crack tips are presented. A problem for two collinear Zener–Stroh cracks with different lengths is also studied.
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Collinear Zener–Stroh crack problem in Plane Elasticity
Engineering Fracture Mechanics, 2008Co-Authors: Y.z. Chen, X Y LinAbstract:Abstract This paper investigates the collinear Zener–Stroh crack problem in Plane Elasticity. Two cracks in series are chosen as an example in analysis. Different to the Griffith crack problem, an initial displacement discontinuity exists in the Zener–Stroh crack problem, which in turn is the increment of displacement when a moving point goes around the crack in a closed loop. From the traction free condition along the cracks, the dislocation distribution function as well as the complex potential with undetermined coefficients is suggested. The involved undetermined coefficients can be evaluated from the condition of the assumed initial displacement discontinuity. Finally, a closed form solution for the problem is obtained and the calculated stress intensity factors at crack tips are presented. A problem for two collinear Zener–Stroh cracks with different lengths is also studied.
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On the equivalence of types of damage in Plane Elasticity
Philosophical Magazine Letters, 2006Co-Authors: Y.z. Chen, X Y LinAbstract:In this paper, a model for the equivalence of types of damage in Plane Elasticity is suggested. The model is based on the evaluation of additional work done by the existing damage. Analysis has been carried out for four particular cases of damage: (a) an ellipse, (b) a line crack, (c) a triangular hole and (d) a square hole. These cases are equivalent to that of a circular hole with appropriate radius.
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solution of zener stroh arc crack problem in Plane Elasticity
Mechanics Research Communications, 2005Co-Authors: Y.z. Chen, X Y Lin, Z X WangAbstract:Abstract In this paper, solution of the Zener–Stroh arc crack in Plane Elasticity is present. The problem is reduced to a solution of singular integral equation. After using some formulae and equations in complex variable function a closed form solution is obtained.
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Solution of Zener–Stroh arc crack problem in Plane Elasticity
Mechanics Research Communications, 2005Co-Authors: Y.z. Chen, X Y Lin, Z X WangAbstract:Abstract In this paper, solution of the Zener–Stroh arc crack in Plane Elasticity is present. The problem is reduced to a solution of singular integral equation. After using some formulae and equations in complex variable function a closed form solution is obtained.
A. Venkatesh - One of the best experts on this subject based on the ideXlab platform.
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Hybrid trefftz Plane Elasticity elements with p ‐method capabilities
International Journal for Numerical Methods in Engineering, 1992Co-Authors: J. Jirousek, A. VenkateshAbstract:A family of p-method Plane Elasticity elements is derived based on the hybrid Trefftz formulation.1 Exact solutions of the Lame-Navier equations are used for the intra-element displacement field together with an independent displacement frame function field along the element boundary. The final unknowns are the parameters of the frame function field consisting of the usual degrees of freedom at corner nodes and an optional number of hierarchic degrees of freedom associated with the mid-side nodes. Since the element matrices do not involve integration over the element area, the elements have a polygonal contour with an optional number of curved sides. The quadrilateral element has the same external appearance as the conventional p-method Plane Elasticity element.2,3 But unlike in the conventional p-method approach, suitable special-purpose Trefftz functions are generally used to handle the singularity and/or stress concentration problems rather than a local mesh refinement. The practical efficiency of the new elements is assessed through a series of examples.
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hybrid trefftz Plane Elasticity elements with p method capabilities
International Journal for Numerical Methods in Engineering, 1992Co-Authors: J. Jirousek, A. VenkateshAbstract:A family of p-method Plane Elasticity elements is derived based on the hybrid Trefftz formulation.1 Exact solutions of the Lame-Navier equations are used for the intra-element displacement field together with an independent displacement frame function field along the element boundary. The final unknowns are the parameters of the frame function field consisting of the usual degrees of freedom at corner nodes and an optional number of hierarchic degrees of freedom associated with the mid-side nodes. Since the element matrices do not involve integration over the element area, the elements have a polygonal contour with an optional number of curved sides. The quadrilateral element has the same external appearance as the conventional p-method Plane Elasticity element.2,3 But unlike in the conventional p-method approach, suitable special-purpose Trefftz functions are generally used to handle the singularity and/or stress concentration problems rather than a local mesh refinement. The practical efficiency of the new elements is assessed through a series of examples.
Z X Wang - One of the best experts on this subject based on the ideXlab platform.
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solution of zener stroh arc crack problem in Plane Elasticity
Mechanics Research Communications, 2005Co-Authors: Y.z. Chen, X Y Lin, Z X WangAbstract:Abstract In this paper, solution of the Zener–Stroh arc crack in Plane Elasticity is present. The problem is reduced to a solution of singular integral equation. After using some formulae and equations in complex variable function a closed form solution is obtained.
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Solution of Zener–Stroh arc crack problem in Plane Elasticity
Mechanics Research Communications, 2005Co-Authors: Y.z. Chen, X Y Lin, Z X WangAbstract:Abstract In this paper, solution of the Zener–Stroh arc crack in Plane Elasticity is present. The problem is reduced to a solution of singular integral equation. After using some formulae and equations in complex variable function a closed form solution is obtained.
Wei Lin - One of the best experts on this subject based on the ideXlab platform.
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the natural integral equations of Plane Elasticity problem and its wavelet methods
Applied Mathematics and Computation, 2004Co-Authors: Youjian Shen, Wei LinAbstract:In this paper, we apply interpolatory Hermite-type trigonometric wavelet to investigate the numerical solution of the natural boundary integral equation of Plane Elasticity problem by Galerkin method. In our fast algorithm, the computational formulae of entries of the stiffness matrix yield simple close-form and for one 2^j^+^3x2^j^+^3 stiffness matrix, we only need to compute 2(2^j^+^2+2^j-1) entries. The error estimates of the approximate solution are given and the test examples are presented in the end.
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wavelet algorithm for the numerical solution of Plane Elasticity problem
Lecture Notes in Computer Science, 2001Co-Authors: Youjian Shen, Wei LinAbstract:In this paper, we apply Shannon wavelet and Galerkin method to deal with the numerical solution of the natural boundary integral equation of Plane Elasticity probem in the upper half-Plane. The fast algorithm is given and only 3 entries need to be computed for one 4K × 4K stiffness matrix.
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WAA - Wavelet Algorithm for the Numerical Solution of Plane Elasticity Problem
Wavelet Analysis and Its Applications, 2001Co-Authors: Youjian Shen, Wei LinAbstract:In this paper, we apply Shannon wavelet and Galerkin method to deal with the numerical solution of the natural boundary integral equation of Plane Elasticity probem in the upper half-Plane. The fast algorithm is given and only 3 entries need to be computed for one 4K × 4K stiffness matrix.
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Wavelet Solutions to the Natural Integral Equations of the Plane Elasticity Problem
Proceedings of the Second ISAAC Congress, 2000Co-Authors: Wei Lin, Y. J. ShenAbstract:In this paper, we apply interpolatory Hermite-type trigonomet-ric waveletsand Galerkin methods to get the numerical solutions of the natural boundaryintegral equations of the Plane Elasticity problem. Error estimates for the approximation solutions are given. We also give a fast algorithm and for one 2 j +3 × 2 j +3 stiffness matrix, we only need to compute 2(2 j +2 + 2 j − 1) entries.
