复杂载荷作用下梁弯曲的重心插值配点法  

Barycentric interpolation collocation methodfor bending deformation problems of beams under complex loads

作　　者：赵晓伟[1] 王守波 李广惠[1] Zhao Xiaowei;Wang Shoubo;Li Guanghui(Shandong Jianzhu University,Jinan Shandong 250101,China;Shandong Construction and Construction(Group)Co.,Ltd.,Jinan Shandong 250014,China)

机构地区：[1]山东建筑大学,山东济南250101 [2]山东省建设建工(集团)有限责任公司第四分公司,山东济南250014

出　　处：《山西建筑》2023年第24期46-49,53,共5页Shanxi Architecture

基　　金：山东省住房与城乡建设厅项目(2021-K3-3)。

摘　　要：在材料力学中,梁上作用复杂载荷,且当载荷为非线性表达式时,求解过程烦琐复杂,在积分运算和积分常数确定方面花费很大工作量。重心Lagrange插值具有数值稳定性好、计算精度高的优点。采用重心Lagrange插值近似未知函数,采用配点法可将承受复杂载荷梁的控制方程表示为代数方程组。通过求解代数方程组,求得梁的各个离散点的挠度,进而利用微分矩阵可求得梁的转角和弯矩。数值算例表明,重心插值配点法原理简单,易于程序实现且数值计算精度很高。In the classroom teaching of mechanics of materals,when there are complex loads acts on the beam,especially when the distributed load is expressed in a nonlinear form,the integral operation becomes tedious,with a large amount of work in the integral calculation and the intefral constant determination.Barycentric Lagrange interpolation collocation method has excellent numerical stability and high accuracy.For the beam bending problem,this method was used in this paper to get the differentiation Matrix of unknown function.So the control equation of beams can be expressed as linear systems by the collocation method.According to those formulas,the deflection values of discrete points could be got.The principle of this method is simple and easy to be programmed.The accuracy and the numerical stability are very excellent.

关 键 词：重心Lagrange插值 配点法 复杂载荷 梁变形问题 

分 类 号：TU311[建筑科学—结构工程]