EFGM在固体力学应用中的误差影响研究

Study on the error influence of EFGM in the application of solid mechanics

本文针对固体力学平面问题,采用全局误差能量范数作为误差衡量标准,分别采用线性基条件和二次基条件时的无网格伽辽金法(EFGM)进行误差影响参数研究。当采用线性基时,支持域的无量纲尺寸(α_(s))最优的取值区间建议取为1.8—3.0;当采用二次基时,αs在3.1附近出现了能量范数突变现象(即计算结果严重失真),并在进一步的研究当中找到解决该问题的办法—增加背景网格的高斯积分点数;α_(s)最优取值区间建议取为2.2—4.0,为避免能量范数突变现象,最好不要在3.1—3.2附近取值。在布点时,全局总积分高斯点数宜大于场节点的4倍,在提高精度时,最好优先考虑增加高斯积分点数,再考虑增加场节点数,并且在增加场节点时,同时增加高斯积分点,使之和场节点数相匹配。

Aiming at the plane problem of solid mechanics,this paper studies the error influence parameters of EFGM with linear basis and quadratic basis respectively by using the global error energy norm as the error measurement standardand.When the linear basis is used,the optimal value interval of α_(s) is suggested to be 1.8 to 3.0.When using the quadratic basis,it is found that there is an abrupt change in the energy norm ofαs near 3.1(that is,the calculation results are seriously distorted).And in further research,a way has been found to overcome this phenomenon—to increase the number of Gaussian integral points of the background grid;the optimal value interval of α_(s) is suggested to be 2.2 to 4.0 in order to avoid the abrupt change of energy norm,and it is best not to take the value near 3.1 to 3.2.When arranging points,the number of global total integral Gaussian points should be more than 4 times of the field nodes.When improving the accuracy,it is best to give priority to increasing the number of Gaussian integral points,and then consider increasing the number of field nodes.While increasing the number of field nodes,it is necessary to increase the Gaussian integral points to match the number of field nodes.