基于裁剪造型的等几何分析方法求解波导本征值问题

doi:10.3969/j.issn.0372-2112.2016.10.038

电子学报 ›› 2016, Vol. 44 ›› Issue (10): 2548-2555.DOI: 10.3969/j.issn.0372-2112.2016.10.038

基于裁剪造型的等几何分析方法求解波导本征值问题

林皋¹, 李鹏¹, 刘俊^1,2, 张勇³, 王峰¹

1. 大连理工大学水利工程学院, 辽宁大连 116024;
2. 上海交通大学海洋工程国家重点实验室, 上海 200240;
3. 中国科学院合肥物质科学研究院核能安全技术研究所, 安徽合肥 230031

收稿日期:2015-03-09 修回日期:2015-06-16 出版日期:2016-10-25 发布日期:2016-10-25
通讯作者: 李鹏
作者简介:林皋,男,1929年1月出生,江西丰城人,大连理工大学水利工程学院教授、博士研究生导师,中国科学院院士.主要研究方向为大坝、核电结构、地下结构地震响应分析与安全评价,以及等几何分析在力学边值问题中的应用.E-mail:gaolin@dlut.edu.cn
基金资助:
国家自然科学基金（No.51409038，No.51138001）；中国博士后科学基金（No.2013M530919，No.2014T70251）；上海交通大学海洋工程国家重点实验室开放基金（No.1202）；中央高校基本科研业务费专项（No.DUT15RC（4）23）

Isogeometric Analysis with Trimming Technique for the Waveguide Eigenvalue Problem

LIN Gao¹, LI Peng¹, LIU Jun^1,2, ZHANG Yong³, WANG Feng¹

1. School of Hydraulic Engineering, Dalian University of Technology, Dalian, Liaoning 116024, China;
2. State Key Laboratory of Ocean Engineering, Shanghai Jiao Tong University, Shanghai 200240, China;
3. Hefei Institutes of Physical Science, Chinese Academy of Science, Hefei, Anhui 230031, China

Received:2015-03-09 Revised:2015-06-16 Online:2016-10-25 Published:2016-10-25

摘要/Abstract

摘要：

等几何分析方法使得几何模型和分析模型能够用NURBS统一表达，避免了模型转换过程，但由于其分析域是由张量积面片构成，很难处理截面形式复杂的多联通域问题.裁剪造型等几何分析方法通过背景曲面和裁剪曲线将复杂带孔结构作为一个被NURBS曲线裁剪后的参数区域直接映射而成，只需要一个参数空间就可以表示任意复杂的拓扑结构，该方法既保留了传统等几何分析方法的优点，又实现了对复杂多孔结构的处理.本文将裁剪造型的等几何分析方法扩展到TE波的波导本征值问题，对复杂多孔结构的截止波数进行有效求解，并通过相应的数值算例验证方法的有效性和高精度性.

关键词: 波导本征值, 等几何分析, NURBS, 裁剪, 背景曲面, 多孔结构

Abstract:

The geometric model and analysis model can be uniformly described by NURBS in isogeometric analysis method,so the model transformation process is avoided.However,since the analysis domain of IGA should be composed of tensor-product patches,it is difficult to deal with the issue of complex multiply connected domains.IGA based on trimming technique is constructed by NURBS geometric modeling of underlying surface and trimming curve,and then,directly map a parameter space trimmed by NURBS curve as the complicated holed structure,only one parameter space is sufficient to describe arbitrary complex topology.The advantages and properties of conventional IGA are maintained,and also,the range application of IGA is enlarged.In this paper,IGA based on trimming technique is expanded to the TE waveguide eigenvalue problem.With the solution of cutoff wave number for complicated multiholes structure,the effectiveness and high accuracy of proposed method are demonstrated by corresponding numerical examples.

Key words: waveguide eigenvalue, isogeometric analysis, non-uniform rational B-spline(NURBS), trimming technique, underlying surface, multiholes structure

中图分类号:

TN925

林皋, 李鹏, 刘俊, 张勇, 王峰. 基于裁剪造型的等几何分析方法求解波导本征值问题[J]. 电子学报, 2016, 44(10): 2548-2555.

LIN Gao, LI Peng, LIU Jun, ZHANG Yong, WANG Feng. Isogeometric Analysis with Trimming Technique for the Waveguide Eigenvalue Problem[J]. Acta Electronica Sinica, 2016, 44(10): 2548-2555.

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基于裁剪造型的等几何分析方法求解波导本征值问题

Isogeometric Analysis with Trimming Technique for the Waveguide Eigenvalue Problem

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