Optimization Of The Radius Of Influence Of The Weight Function In The Mls Method And Its Applications

Comparing with conventional numerical methods, the advantage of Meshless methods lies in its approximation based on nodes. The main feature of the methods is that mesh can be eliminated wholly or partly, and reducing difficulty in mesh generation of the structure, and not like the traditional method in which mesh generation can be a very time-consuming and expensive task. Various kinds of meshless methods have been presented.In the passed several years, scholars have settled a lot of problems about meshless methods except for the influence domain of weight function , which is vital but always "ignored" by many scholars when they use the MLS method to approximate the functions. Therefore, this thesis aimed to study the influence on numerical results coming from domain of weight function , and the main contents are summarized as follows:The thesis discussed the keystones of the meshless methods and indicated that the influence radius of weight function is vital to result of numerical methods and the study about it is both important and necessary.For 3-dimension problem, this thesis studied the general principles on selecting the influence radius of weight function and established a practical mathematics model to compute the optimal influence radius of weight function, and then solved this model in the case of the linear basis and the quadratic basis. After considering the error estimates, the computing cost and the condition number etc., which are the key points of describing the performance of meshless methods in addition to many numerical tests results, the thesis concluded that the optimal radius of the weight function proposed here is correctt and efficient.As the application of the optimal model about the influence radius, this thesis accounted for the elastic mechanics problems by EFGM and solved this model in power weight function. This optimal result has been applied to the typital examples. By comparing the numerical result, the paper affirmed that the optimal model of the influence radius is applied and reliable.