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工程力学  2015 

基于欧拉插值的最小二乘混合配点法在弹性力学平面问题中的应用

DOI: 10.6052/j.issn.1000-4750.2014.01.0063

Keywords: 无网格法,配点法,欧拉插值,混合法,高斯权函数

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Abstract:

由于常规配点型无网格法存在求解不稳定、精度差和求解高阶导数等问题,提出了基于欧拉插值的最小二乘混合配点法。该方法同时以位移和应变作为未知量,通过欧拉插值将未知变量的导数表达出来,同时在插值中引入高斯权函数,并代入微分方程,从而形成以位移和应变为未知数的超定方程组,然后形成最小二乘意义下的法方程,法方程和相应的位移边界条件、应力边界条件一起形成定解体系。该方法不需要域积分,是一种真正的无网格法。一些典型的弹性力学平面问题表明本文方法具有良好的精度。

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