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
A new model,called object model,for the simulation of cold roll-forming of tubes is presented.The model inherits the advantages of old models and is the embodiment of forming process that the strip is rolled step by s...A new model,called object model,for the simulation of cold roll-forming of tubes is presented.The model inherits the advantages of old models and is the embodiment of forming process that the strip is rolled step by step from feed rollers to last rolling pass.The elastic-plastic large deformation spline finite strip method based on updated Lagrangian method has been developed by improving the stiffness and transition matrix.Combined theory formulas and new analytical model,the forming process of a tube has been simulated successfully as an example.The analytical results are submitted and indicate that the proposed simulation method and new model are applicable.展开更多
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the National Natural Science Foundation of China (No. 50375135)the Talent Foundation of Beijing Jiaotong University (No. 2003RC059)
文摘A new model,called object model,for the simulation of cold roll-forming of tubes is presented.The model inherits the advantages of old models and is the embodiment of forming process that the strip is rolled step by step from feed rollers to last rolling pass.The elastic-plastic large deformation spline finite strip method based on updated Lagrangian method has been developed by improving the stiffness and transition matrix.Combined theory formulas and new analytical model,the forming process of a tube has been simulated successfully as an example.The analytical results are submitted and indicate that the proposed simulation method and new model are applicable.