无网格伽辽金法中权函数效率的研究

无网格法是近年来出现的一种新的数值方法,它使用移动最小二乘近似(MLS)作为其形函数,并由基函数和权函数来决定,其中权函数起主要决定作用,并在很大程度上决定了计算结果的精确性,所以很多研究人员提出了不同的权函数,比如样条权函数,高斯权函数等等.通过分析几种权函数的特征曲线和对悬臂梁的实例计算,讨论了不同权函数对计算精度以及所消耗的CPU时间的影响.计算结果表明,四次样条权函数、Gaussian权函数和指数型权函数其参数处于一个较合理的范围时,更适合作为无网格的权函数,并且发现较高光滑度的权函数比较低的更合适.

Study on Weight Functions Efficiency of Element -free Galerkin Method

The element free method is a new numerical technique presented in recent years.It uses the moving least square(MLS) approximation as its shape function,and it is determined by the basic function and weight function.The weight function is the mainly determining factor,so it greatly affects the accuracy of the computational results.Different kinds of weight function,such as spline function,Gaussian function and exponential function,and so on,bave been proposed recently by many researchers.In this paper,the weight functions and various characteristic curves bave been analyzed,and the effect of weight function on accuracy and the consuming of CPU time have been also discussed by computing a cantilever beam.It shows that the Gaussian,quartic spline and exponential functions are better than others when employed as the weight function of element free method,if their parameters are in the range of reasonable values;the weight function of higher smoothness is better than that of the lowers.