比例边界有限元法分析静电场问题

摘要

基于拉普拉斯方程和边界条件，推导了比例中心选择在指定均一电位直线边界上的比例边界有限元公式，并将其应用到有限域和开域静电场分析中，当比例中心选择在指定均一电位直线边界或绝缘直线边界上时，可以只离散其余边界，使得数据准备工作量和计算量大大降低．数值解和理论解对比结果表明：比例边界有限元法具有精度高、数据准备量小、且处理开域静电场问题相当方便的特点。%Based on Laplace equation and boundary conditions, scaled boundary finite element formula with scaled center at the boundary of designated voltage is derived. Then this method is applied to the electrostatic analysis of finite or opening field. When the boundary center is chosen at the boundary of designated voltage or insulation, on-ly the other boundaries are to be made discrete, which can reduce the amount of data and computational capacity remarkably. The numerical results are compared with the exact solutions in this paper. It is proved that the scaled boundary finite element method has high precision as well as less amount of data, and that it is more convenient to solve opening electrostatic field.