The Research And Application Of The Radial Basis Reproducing Kernel Particle Method

Meshless method is a new method developed in recent decades and has become a powerful tool for solving numerical analysis in engineering and scientific problems.The reproducing kernel particle method(RKPM)is one of the meshless methods,which is relatively mature and widely used in numerical analysis.The radial basis function(RBF)is introduced into the RKPM,and proposed the radial basis function reproducing kernel particle method(RRKPM).The method is applied to solve the potential problem and the piezoelectric materials problem.In this paper,the RBF is introduced on the basis of the RKPM,the formula is deduced.In the process of constructing approximation function,all the nodes in the problem domain are used to construct the reproducing kernel function,and the nodes in the problem domain are used to construct the RBF.This method can improve the accuracy of calculation when dealing with internal problems.In this paper,the RRKPM is applied to solve potential problems.The RRKPM for potential problems is established,and the corresponding calculation formula is deduced.When dealing with potential problems,this method can make the numerical results converge quickly and improve the calculation accuracy.In this paper,the RRKPM is applied to solve the electromechanical coupling problem.The collocation method is used to discretize the governing equation.The RRKPM for the electromechanical coupling problem is constructed,derived the corresponding calculation formula is.Compared with the RKPM,it can improve the accuracy of the calculation in the problem domain.