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The meshless method is a new numerical technique presented in recent years.Ituses the moving least square(MLS)approximation as a shape function.The smoothness of theMLS approximation is determined by that of the basic function and of the weight function,and ismainly determined by that of the weight function.Therefore,the weight function greatly affectsthe accuracy of results obtained.Different kinds of weight functions,such as the spline function,the Gauss function and so on,are proposed recently by many researchers.In the present work,thefeatures of various weight functions are illustrated through solving elasto-static problems using thelocal boundary integral equation method.The effect of various weight functions on the accuracy,convergence and stability of results obtained is also discussed.Examples show that the weightfunction proposed by Zhou Weiyuan and Gauss and the quartic spline weight function are betterthan the others if parameters c and α in Gauss and exponential weight functions are in the rangeof reasonable values,respectively,and the higher the smoothness of the weight function,the betterthe features of the solutions.
The meshless method is a new numerical technique presented in recent years. It’s the moving least square (MLS) approximation as a shape function. The smoothness of theMLS approximation is determined by that of the basic function and of the weight function, and is primarily determined by that of the weight function.Therefore, the weight function greatly affectsthe accuracy of results obtained. Different kinds of weight functions, such as the spline function, the Gauss function and so on, are proposed recently by by many researchers.In the present work, thefeatures of various weight functions are illustrated through solving elasto-static problems using thelocal boundary integral equation method.The effect of various weight functions on the accuracy, convergence and stability of results obtained is also discussed. Examples show that the weight function proposed by Zhou Weiyuan and Gauss and the quartic spline weight function are betterthan the others if parameters c and α in Gauss and exponential weight fu nctions are in the range of reasonable values, respectively, and the higher the smoothness of the weight function, the betterthe features of the solutions.