Analysis of Three-dimensional Problems with Coupled Multi-physics, Large Deformatioin and Irregular-shaped Geometry by Meshless Method

• Main Authors: Lee, Ming-Hsiao, 李銘孝
• Other Authors: Chen, Wen-Hwa
• Format: Others
• Language: en_US
• Published: 2010
• Online Access: http://ndltd.ncl.edu.tw/handle/11849263325972006887

博士 === 國立清華大學 === 動力機械工程學系 === 98 === The meshless method has a distinct advantage over other methods in that it requires only nodes without an element mesh which usually induces time-consuming work and inaccuracy when the elements are distorted during the analysis process. However, the element mesh can provide some geometry information for the numerical simulation, such as, the analysis domain is defined by the element’s edges or faces and the quadrature points are all inside the elements. Because the analysis model with only nodes for the meshless method lacks these types of geometry-related information, some difficulties are usually encountered during numerical simulations, especially in the cases with three-dimensional irregular-shaped analysis domains. To overcome these difficulties, two geometry schemes and check mechanisms are proposed. The check mechanisams can be used for determining if certain points are inside or outside the anayslis domain, when the situations are often encoutered in the analysis processes of the meshless method. Furthermore, on the analyses of extremely large deformation problems, the distortion of the distribution of nodes degrades the accuracy of the solution. A new three-dimensional meshless scheme with a uniform background grid is proposed herein. By this scheme, no matter how large the analysis domain deforms, the uniformly distributed nodes of the background grid will be selected to do the solution that the situation of the distortion of node distribution can be avoided and the accuracy of the solution can be maintained. An application to an electrostatic-structural problems encountered in many electrostatic driven MEMS devices is performed. In the type of cases, the electrostatic analysis domain is often extremely distorted due to the deflection of the structure of the electrode. This kind of problem is difficult to deal with by almost all kinds of available numerical methods. But, with the proposed background grid scheme and an iterative coupled-field analysis procedure, the electrostatic-structural problem can be solved without difficulties. Several demonstrative cases have been conducted to prove the effectiveness and advantages of the proposed techniques.