Showing papers by "YuanTong Gu published in 2004"

Boundary meshfree methods based on the boundary point interpolation methods

Abstract: A group of meshfree methods based on Boundary Integral Equation have been developed in order to overcome drawbacks in the conversional boundary element method (BEM) that requires boundary elements in constructing shape functions. In this paper, the radial basis point interpolation is firstly used to formulate the boundary radial point interpolation method (BRPIM). Two boundary meshfree methods: the boundary point interpolation method (BPIM) using the polynomial PIM and the BRPIM, are then examined in detail. The numerical implementations of these two methods are studied to address several technical issues, including the size of the compact support domain, the convergence, the performance, and so on. These two boundary-type meshfree methods are also compared with the Boundary Node Method and the conventional BEM in terms of both efficiency and performance. Several numerical examples of 2D elastostatics are analyzed using BPIM and BRPIM. It is found that BPIM and BRPIM are very easy to implement, and very robust for obtaining numerical solutions for problems of computational mechanics with very good accuracy. Key issues related the future development of boundary meshfree methods are also discussed.

Assessment and applications of point interpolation methods for computational mechanics

Abstract: Two meshfree point interpolation methods (PIMs), which are based on the polynomial and the radial basis functions, have been proposed recently in addition to the earlier work with the moving least-squares (MLS) approximation for the field function approximation. However, it is found that PIMs cannot automatically ensure the compatibility of the solution when they are used together with the energy principles. In this paper, issues related to the compatibility of PIMs are studied. A technique of background cell-based nodal selections and a penalty method are proposed to enforce the compatibility of the solution of PIMs. The patch test is studied in great detail. The convergences and performances are investigated for both conforming and non-conforming PIMs. It is found that those methods of the PIM family are very easy to implement, and are very efficient in obtaining numerical solutions for problems of computational mechanics. Copyright © 2004 John Wiley & Sons, Ltd.

Analysis of microelectromechanical systems (mems) by meshless local kriging (lokriging) method

Abstract: A meshless Local Kriging (LoKriging) method is developed and used in this paper to analyze the behaviors of microelectromechanical system (MEMS) devices, which are simplified as thick beam systems subjected to dynamic non‐linear loading induced by applied voltages. In LoKriging, the Kriging interpolation technique is employed to obtain the shape function, which has a partition of unity and delta function properties. The local Petrov‐Galerkin weak form of the governing equations for MEMS devices is derived. The developed LoKriging method is used to analyze the behavior of microswitches and microtweezers, widely used for MEMS devices. Their static and dynamic characters are analyzed and compared with the results of experiments and other numerical methods. The computed results show that the present LoKriging method is easy to implement, efficient and accurate for the numerical simulation of MEMS devices. In addition, the method developed in this paper also has good potential for analysis of other co...