| The meshless method is an important mathematical method developed after scientific methods such as the finite element method,which develops rapidly in recent years.Because it does not need to be meshed when solving the problem,but only needs the relevant information at the nodes.Meanwhile,the nodes can be reduced or increased in a certain area according to its own needs during the calculation,so as to facilitate our calculation.The meshless method can be used to analyze problems such as structural failure process simulation,high-speed collision and blasting.Therefore,our research on meshless method has very important theoretical significance and research value.In this paper,the improved MLS method and the improved complex variable MLS method are derived and the selection of weight function is explained.Based on the MLS method,the EFG method of wave equation is derived,and the algorithm implementation process is explained.The cubic spline,the quadrature spline and the quintuple spline functions are selected as weight functions to analyze the specific examples.The primary basis and the quadratic basis are selected as basis functions,and the results in different examples are studied.Secondly,since the equations obtained by the IMLS method are neither ill-conditioned nor singular,nor need to solve the inverse of the matrix,the improved EFG method of wave equation is derived based on the improved MLS method.The EFG method of wave equation and the improved EFG method are analyzed,and their results are compared.At the same time,different spline functions are selected to study and discuss the specific examples.Then different parameters such as time step,weight function scale parameter dmaxand node distribution are selected to study.Finally,based on the improved complex variable MLS method,the improved complex variable EFG method of wave equation is derived.The rationality of this method is analyzed by several different examples,and it is analyzed and compared with IEFG method. |
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