V. Vavourakis ¹

CMES-Computer Modeling in Engineering & Sciences, Vol.36, No.2, pp. 119-146, 2008, DOI:10.3970/cmes.2008.036.119

Abstract In this paper, a new meshless Local Hypersingular Boundary Integral Equation method is presented for the analysis of two-dimensional elastostatic problems. The elastic domain is discretized by placing arbitrarily nodes on its boundary and interior. Given this set of nodes, the corresponding map of background triangles is constructed through a common triangulation algorithm. The local domain of each node consists of the union of triangles that this point lies, thus, creating a polygonal line of its local boundary. The local boundary integral equations of both displacements and stresses of the conventional Boundary Elements Method are taken into account. The interpolation… More >

Wen-Hwa Chen¹, Cheng-Te Chi, Ming-Hsiao Lee

CMES-Computer Modeling in Engineering & Sciences, Vol.40, No.2, pp. 175-200, 2009, DOI:10.3970/cmes.2009.040.175

Abstract Based on an incremental formulation of element-free Galerkin method (EFGM), a highly efficient three-dimensional EFGM analysis procedure is proposed to deal with the structure with extremely large deformation. By this procedure, a fixed and uniform background grid, part of which coincides with the background cells employed in the conventional EFGM for numerical integration, is devised. The background grid is connected by uniformly distributed fictitious nodes which do not move during loading process even if extremely large deformation occurs. A deformable analysis domain, which is discretized by moving boundary nodes and interior nodes, is established for describing the deformation of the… More >

Yan Liu¹, Xiong Zhang¹, K. Y. Sze², Min Wang¹

CMES-Computer Modeling in Engineering & Sciences, Vol.20, No.3, pp. 177-192, 2007, DOI:10.3970/cmes.2007.020.177

Abstract In molecular simulations, the frequencies of the low-frequency modes are many orders of magnitude lower than those of the high-frequency modes. Compared with the amplitudes of the low-frequency modes, the amplitudes of the high-frequency modes are often negligible and, thus, least interesting. As dictated by the period of the highest frequency mode, the critical time step for stable time integration can be significantly increased by suppressing the negligible high-frequency modes yet the solution remains virtually intact. In this light, a smoothed molecular dynamics (SMD) approach is proposed to eliminate the high-frequency modes from the dynamical system through the use of… More >

Cheng-Te Chi¹, Ming-Hsiao Lee², Wen-Hwa Chen^1,3

CMC-Computers, Materials & Continua, Vol.24, No.3, pp. 239-256, 2011, DOI:10.3970/cmc.2011.024.239

Abstract A novel three-dimensional adaptive element-free Galerkin method (EFGM) based on a uniform background grid is proposed to cope with the problems with extremely large deformation. On the basis of this uniform background grid, an interior adaptive strategy through an error estimation within the analysis domain is developed. By this interior adaptive scheme, additional adaptive nodes are inserted in those regions where the solution accuracy needs to be improved. As opposed to the fixed uniform background grid, these inserted nodes can move along with deformation to describe the particular local deformation of the structure. In addition, a triangular surface technique is… More >

Ming-Hsiao Lee, Wen-Hwa Chen

CMC-Computers, Materials & Continua, Vol.11, No.1, pp. 59-78, 2009, DOI:10.3970/cmc.2009.011.059

Abstract On the analysis of electrostatic-structural coupled problems as encountered in many electrostatic driven MEMS devices, the electrostatic analysis domain is often extremely distorted due to the deflection of the structure. This kind of problem is difficult to be dealt with by almost all kinds of available numerical methods. A new three-dimensional meshless scheme with background grid is thus proposed herein. By this scheme, a three-dimensional fixed background grid with regularly-distributed nodes is utilized. Another set of discretized boundary grid is employed to describe the boundary surfaces of both the structure and the electrostatic field. The analysis electrostatic/structural domains are modeled… More >