A Coupling Magneto-Electro-Elastic(MEE)Node-based Smoothed Radial Point Interpolation Method(CM-NS-RPIM)was proposed to solve the free vibration and transient responses of Functionally Graded Magneto-Electro-Elastic(F...A Coupling Magneto-Electro-Elastic(MEE)Node-based Smoothed Radial Point Interpolation Method(CM-NS-RPIM)was proposed to solve the free vibration and transient responses of Functionally Graded Magneto-Electro-Elastic(FGMEE)structures.By introducing the modified Newmark method,the displacement,electrical potential and magnetic potential of the structures under transient mechanical loading were obtained.Based on G space theory and the weakened weak(W2)formulation,the equations of the multi-physics coupling problems were derived.Using triangular background elements,the free vibration and transient responses of three numerical examples were studied.Results proved that CM-NS-RPIM performed better than the standard FEM by reducing the overly-stiff of structures.Moreover,CM-NS-RPIM could reduce the number of nodes while guaranteeing the accuracy.Besides,triangular elements could be generated automatically even for complex geometries.Therefore,the effectiveness and validity of CM-NS-RPIM were demonstrated,which were valuable for the design of intelligence devices,such as energy harvesters and sensors.展开更多
In order to overcome the possible singularity associated with the Point Interpolation Method(PIM),the Radial Point Interpolation Method(RPIM)was proposed by G.R.Liu.Radial basis functions(RBF)was used in RPIM as basis...In order to overcome the possible singularity associated with the Point Interpolation Method(PIM),the Radial Point Interpolation Method(RPIM)was proposed by G.R.Liu.Radial basis functions(RBF)was used in RPIM as basis functions for interpolation.All these radial basis functions include shape parameters.The choice of these shape parameters has been and stays a problematic theme in RBF approximation and interpolation theory.The object of this study is to contribute to the analysis of how these shape parameters affect the accuracy of the radial PIM.The RPIM is studied based on the global Galerkin weak form performed using two integration technics:classical Gaussian integration and the strain smoothing integration scheme.The numerical performance of this method is tested on their behavior on curve fitting,and on three elastic mechanical problems with regular or irregular nodes distributions.A range of recommended shape parameters is obtained from the analysis of different error indexes and also the condition number of the matrix system.All resulting RPIM methods perform very well in term of numerical computation.The Smoothed Radial Point Interpolation Method(SRPIM)shows a higher accuracy,especially in a situation of distorted node scheme.展开更多
浸没光滑点插值方法(immersed smoothed point interpolation method,IS-PIM)是一种基于浸没类方法框架,采用光滑点插值方法(smoothed point interpolation method,S-PIM)作为固体求解器的流固耦合计算方法。在IS-PIM以及其它基于浸没...浸没光滑点插值方法(immersed smoothed point interpolation method,IS-PIM)是一种基于浸没类方法框架,采用光滑点插值方法(smoothed point interpolation method,S-PIM)作为固体求解器的流固耦合计算方法。在IS-PIM以及其它基于浸没类方法框架的方法中,流固耦合力是基于虚拟流体拉格朗日网格求解的,但这种求解方式忽略了流固边界节点的速度梯度,导致无法计算边界粘性力,尤其是在模拟低雷诺数流动时,会产生较大的数值误差。本文针对上面的问题,提出一种基于真实流体欧拉网格求解流固耦合力的新思路。经过算例证明,该方法无需额外修正即可有效计算流固边界的粘性力,提高了计算精度。展开更多
基金co-supported by the National Key R&D Program of China(Nos.2018YFF01012401-05)the National Natural Science Foundation of China(No.51975243)+2 种基金Jilin Provincial Department of Education(No.JJKH20180084KJ),Chinathe Fundamental Research Funds for the Central Universities and Jilin Provincial Department of Science&Technology Fund Project,China(Nos.20170101043JC and 20180520072JH)Graduate Innovation Fund of Jilin University,China(No.101832018C184).
文摘A Coupling Magneto-Electro-Elastic(MEE)Node-based Smoothed Radial Point Interpolation Method(CM-NS-RPIM)was proposed to solve the free vibration and transient responses of Functionally Graded Magneto-Electro-Elastic(FGMEE)structures.By introducing the modified Newmark method,the displacement,electrical potential and magnetic potential of the structures under transient mechanical loading were obtained.Based on G space theory and the weakened weak(W2)formulation,the equations of the multi-physics coupling problems were derived.Using triangular background elements,the free vibration and transient responses of three numerical examples were studied.Results proved that CM-NS-RPIM performed better than the standard FEM by reducing the overly-stiff of structures.Moreover,CM-NS-RPIM could reduce the number of nodes while guaranteeing the accuracy.Besides,triangular elements could be generated automatically even for complex geometries.Therefore,the effectiveness and validity of CM-NS-RPIM were demonstrated,which were valuable for the design of intelligence devices,such as energy harvesters and sensors.
文摘In order to overcome the possible singularity associated with the Point Interpolation Method(PIM),the Radial Point Interpolation Method(RPIM)was proposed by G.R.Liu.Radial basis functions(RBF)was used in RPIM as basis functions for interpolation.All these radial basis functions include shape parameters.The choice of these shape parameters has been and stays a problematic theme in RBF approximation and interpolation theory.The object of this study is to contribute to the analysis of how these shape parameters affect the accuracy of the radial PIM.The RPIM is studied based on the global Galerkin weak form performed using two integration technics:classical Gaussian integration and the strain smoothing integration scheme.The numerical performance of this method is tested on their behavior on curve fitting,and on three elastic mechanical problems with regular or irregular nodes distributions.A range of recommended shape parameters is obtained from the analysis of different error indexes and also the condition number of the matrix system.All resulting RPIM methods perform very well in term of numerical computation.The Smoothed Radial Point Interpolation Method(SRPIM)shows a higher accuracy,especially in a situation of distorted node scheme.
文摘浸没光滑点插值方法(immersed smoothed point interpolation method,IS-PIM)是一种基于浸没类方法框架,采用光滑点插值方法(smoothed point interpolation method,S-PIM)作为固体求解器的流固耦合计算方法。在IS-PIM以及其它基于浸没类方法框架的方法中,流固耦合力是基于虚拟流体拉格朗日网格求解的,但这种求解方式忽略了流固边界节点的速度梯度,导致无法计算边界粘性力,尤其是在模拟低雷诺数流动时,会产生较大的数值误差。本文针对上面的问题,提出一种基于真实流体欧拉网格求解流固耦合力的新思路。经过算例证明,该方法无需额外修正即可有效计算流固边界的粘性力,提高了计算精度。
