重心插值Galerkin法求解梁弯曲变形问题

doi:10.3976/j.issn.1002-4026.2013.03.012

J4 ›› 2013, Vol. 26 ›› Issue (3): 60-65.doi: 10.3976/j.issn.1002-4026.2013.03.012

重心插值Galerkin法求解梁弯曲变形问题

綦甲帅,王兆清

山东建筑大学工程力学研究所，山东济南 250101

收稿日期:2012-10-18 出版日期:2013-06-20 发布日期:2013-06-20
作者简介:綦甲帅(1987-)，男，硕士研究生，研究方向为结构优化设计与工程弹塑性理论。Email：549085469@qq.com

The solution of beam bending problem with barycentric rational interpolation Galerkin method

QI Jia-Shuai, WANG Zhao-Qing

Institute of Engineering Mechanics, Shandong Jianzhu University, Jinan 250101, China

Received:2012-10-18 Online:2013-06-20 Published:2013-06-20

摘要/Abstract

摘要：

本文运用广义函数建立非连续载荷作用下梁弯曲变形的控制方程，采用重心有理插值函数作为试函数，利用Delta函数的积分筛选性，建立重心有理插值Galerkin法求解梁弯曲变形问题的计算公式。数值算例表明，该方法原理简单，易于程序实现，数值计算精度高。

关键词: 重心有理插值, 广义函数, 梁弯曲变形问题, Galerkin法

Abstract:

We employ a generalized function to construct the governing equation of beam bending under discrete loads. We also present the formula for solving beam bending problem by barycentric interpolation Galerkin method with barycentric rational interpolation as a test function and integral filtering of a Delta function. Numerical calculation examples demonstrate that the presented method has such positives as simplicity principle, easy programming and high accuracy.

Key words: barycentric rational interpolation, generalized function, beam bending problem, Galerkin method

中图分类号:

TU311

綦甲帅,王兆清. 重心插值Galerkin法求解梁弯曲变形问题[J]. J4, 2013, 26(3): 60-65.

QI Jia-Shuai, WANG Zhao-Qing. The solution of beam bending problem with barycentric rational interpolation Galerkin method[J]. J4, 2013, 26(3): 60-65.

[1]	庄美玲，王兆清，张磊，纪思源. 极坐标下薄板弯曲问题的重心有理插值法[J]. 山东科学, 2016, 29(2): 82-87.
[2]	马燕，王兆清，唐炳涛. 波动问题的高精度重心有理插值配点法[J]. J4, 2012, 25(3): 80-87.
[3]	李淑萍. 基于重心型插值的数值计算方法[J]. J4, 2010, 23(4): 13-16.

重心插值Galerkin法求解梁弯曲变形问题

The solution of beam bending problem with barycentric rational interpolation Galerkin method

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