The Researches And Applications On The Hermit-type Reproducing Kernel Particle Methods

In the recent years,meshless method is proposed.It uses nodes information instead of meshing.It has advantages of pre-processing and high precision.These features make it a hot point.Many scholars conduct in-depth research on it.The reproducing kernel particle method(RKPM)is widely applied in the research.It is a more mature meshless method,but there is a drawback that the node error is large on the boundary.In order to overcome the shortcoming of RKPM,the Hermit-type term is introduced to construct the Hermit-type RKPM,and apply it to solve the elasticity problem and the electromechanical problem.The main researches of the thesis are as follows.Based on the RKPM,this paper presents the Hermit-type RKPM.Comparing with the RKPM,the Hermit-type RKPM solve the approximate function,the terms of RKPM constructing by internal nodes in the domain and the normal derivatives of RBF constructing by nodes on the boundary.The method can decrease the errors on the boundary and improve computational accuracy.The Hermit-type RKPM is applied to elasticity problem.Discrete equations are derived.The essential boundary conditions are reinforced by penalty parameters.The advantages of this method are fast convergence and high calculation accuracy.The Hermit-type RKPM is applied to electromechanical problem.The governing equations are discretized by point collocation method,and the Hermit-type RKPM for electromechanical problem is constructed.The corresponding formulations are obtained.The method is a kind of pure meshless method.It only requires nodes information and does not need the integration of the background grid.Compared with the RKPM,the Hermit-type RKPM has higher precision when calculating the node values on the boundary.