The stress concentration problem in structures with a circular or elliptic hole can be investigated by analytical methods. For the problem with a rectangular hole, only approximate results are derived. This paper dedu...The stress concentration problem in structures with a circular or elliptic hole can be investigated by analytical methods. For the problem with a rectangular hole, only approximate results are derived. This paper deduces the analytical solutions to the stress concentration problem in plates with a rectangular hole under biaxial tensions. By using the U-transformation technique and the finite element method, the analytical displacement solutions of the finite element equations are derived in the series form. Therefore, the stress concentration can then be discussed easily and conveniently. For plate problem the bilinear rectangular element with four nodes is taken as an example to demonstrate the applicability of the proposed method. The stress concentration factors for various ratios of height to width of the hole are obtained.展开更多
The spline finite strip method （FSM） is one of the most popular numerical methods for analyzing prismatic structures. Efficacy and convergence of the method have been demonstrated in previous studies by comparing on...The spline finite strip method （FSM） is one of the most popular numerical methods for analyzing prismatic structures. Efficacy and convergence of the method have been demonstrated in previous studies by comparing only numerical results with analytical results of some benchmark problems. To date, no exact solutions of the method or its explicit forms of error terms have been derived to show its convergence analytically. As such, in this paper, the mathematical exact solutions of spline finite strips in the plate analysis are derived using a unitary transformation approach （abbreviated as the U-transformation method herein）. These exact solutions are presented for the first time in open literature. Unlike the conventional spline FSM which involves assembly of the global matrix equation and its numerical solution, the U-transformation method decouples the global matrix equation into the one involving only two unknowns, thus rendering the exact solutions of the spline finite strip to be derived explicitly. By taking Taylor＇s series expansion of the exact solution, error terms and convergence rates are also derived explicitly and compared directly with other numerical methods. In this regard, the spline FSM converges at the same rate as a non-conforming finite element, yet involving a smaller number of unknowns compared to the latter. The convergence rate is also found superior to the conventional finite difference method.展开更多
In this paper, the Geometry/G/1 queueing model with inter-arrival times generated by a geometric（parameter p） distribution according to a late arrival system with delayed access and service times independently distr...In this paper, the Geometry/G/1 queueing model with inter-arrival times generated by a geometric（parameter p） distribution according to a late arrival system with delayed access and service times independently distributed with distribution {gj }, j≥ 1 is studied. By a simple method （techniques of probability decomposition, renewal process theory） that is different from the techniques used by Hunter（1983）, the transient property of the queue with initial state i（i ≥ 0） is discussed. The recursion expression for u -transform of transient queue-length distribution at any time point n^＋ is obtained, and the recursion expression of the limiting queue length distribution is also obtained.展开更多
基金supported by the National Natural Science Foundation of China (No.10772202)the Chinese PostdoctoralScience Foundation (No.20060400757).
文摘The stress concentration problem in structures with a circular or elliptic hole can be investigated by analytical methods. For the problem with a rectangular hole, only approximate results are derived. This paper deduces the analytical solutions to the stress concentration problem in plates with a rectangular hole under biaxial tensions. By using the U-transformation technique and the finite element method, the analytical displacement solutions of the finite element equations are derived in the series form. Therefore, the stress concentration can then be discussed easily and conveniently. For plate problem the bilinear rectangular element with four nodes is taken as an example to demonstrate the applicability of the proposed method. The stress concentration factors for various ratios of height to width of the hole are obtained.
基金Project supported by the Division Research Grant from City University of Hong Kong(No.DRG 13/08-09)
文摘The spline finite strip method （FSM） is one of the most popular numerical methods for analyzing prismatic structures. Efficacy and convergence of the method have been demonstrated in previous studies by comparing only numerical results with analytical results of some benchmark problems. To date, no exact solutions of the method or its explicit forms of error terms have been derived to show its convergence analytically. As such, in this paper, the mathematical exact solutions of spline finite strips in the plate analysis are derived using a unitary transformation approach （abbreviated as the U-transformation method herein）. These exact solutions are presented for the first time in open literature. Unlike the conventional spline FSM which involves assembly of the global matrix equation and its numerical solution, the U-transformation method decouples the global matrix equation into the one involving only two unknowns, thus rendering the exact solutions of the spline finite strip to be derived explicitly. By taking Taylor＇s series expansion of the exact solution, error terms and convergence rates are also derived explicitly and compared directly with other numerical methods. In this regard, the spline FSM converges at the same rate as a non-conforming finite element, yet involving a smaller number of unknowns compared to the latter. The convergence rate is also found superior to the conventional finite difference method.
基金This work was supported by the Scientific Research Fund of Southwestern University of Finance and Economics and the Science Foundation of Sichuan Normal University.
文摘In this paper, the Geometry/G/1 queueing model with inter-arrival times generated by a geometric（parameter p） distribution according to a late arrival system with delayed access and service times independently distributed with distribution {gj }, j≥ 1 is studied. By a simple method （techniques of probability decomposition, renewal process theory） that is different from the techniques used by Hunter（1983）, the transient property of the queue with initial state i（i ≥ 0） is discussed. The recursion expression for u -transform of transient queue-length distribution at any time point n^＋ is obtained, and the recursion expression of the limiting queue length distribution is also obtained.
