An element-free Galerkin method(EFGM) is used to solve the two-dimensional(2D) ground penetrating radar(GPR)modelling problems, due to its simple pre-processing, the absence of elements and high accuracy. Different fr...An element-free Galerkin method(EFGM) is used to solve the two-dimensional(2D) ground penetrating radar(GPR)modelling problems, due to its simple pre-processing, the absence of elements and high accuracy. Different from element-based numerical methods, this approach makes nodes free from the elemental restraint and avoids the explicit mesh discretization. First, we derived the boundary value problem for the 2D GPR simulation problems. Second, a penalty function approach and a boundary condition truncated method were used to enforce the essential and the absorbing boundary conditions, respectively. A three-layered GPR model was used to verify our element-free approach. The numerical solutions show that our solutions have an excellent agreement with solutions of a finite element method(FEM). Then, we used the EFGM to simulate one more complex model to show its capability and limitations. Simulation results show that one obvious advantage of EFGM is the absence of element mesh, which makes the method very flexible. Due to the use of MLS fitting, a key feature of EFM, is that both the dependent variable and its gradient are continuous and have high precision.展开更多
The element-free method is a new numerical technique presented in recent years.It uses the moving least square(MLS) approximation as its shape function,and it is determined by the basic function and weight function.Th...The element-free method is a new numerical technique presented in recent years.It uses the moving least square(MLS) approximation as its shape function,and it is determined by the basic function and weight function.The weight function is the mainly determining factor,so it greatly affects the accuracy of the computational results.The element-free Galerkin method(EFGM) was applied for the solution to plastic large deformation.The simulation of metal rheological forming was successfully done by programming and its results were visualized by using the plotting and data analyses software Tecplot.Then plastic strain under different stages during rheological forming and the three principal stresses at the last deformation were obtained.The example shows the feasibility of EFGM used for metal rheological forming and provides a new method for numerical simulation of rheological forming of complex parts.展开更多
Possessing the unique and highly valuable properties, graphene sheets(GSs) have attracted increasing attention including that from the building engineer due to the fact that Graphene can be utilized to reinforce concr...Possessing the unique and highly valuable properties, graphene sheets(GSs) have attracted increasing attention including that from the building engineer due to the fact that Graphene can be utilized to reinforce concrete and other building materials. In this work, the nonlocal elastic theory and classical plate theory(CLPT) are used to derive the governing equations. The element-free framework for analyzing the buckling behaviors of double layer circular graphene sheets(DLCGSs) relying on an elastic medium is proposed. Pasternak-type model is adopted to describe the elastic medium. Accordingly, the influences of boundary conditions, size of GSs and nonlocal parameters on the buckling behavior of DLCGSs are investigated. The results show that the OP buckling modes are only sensible to the van der Waals forces.展开更多
基金Project(41074085)supported by the National Natural Science Foundation of ChinaProject(NCET-12-0551)supported by the Funds for New Century Excellent Talents in University,ChinaProject supported by Shenghua Yuying Program of Central South University,China
文摘An element-free Galerkin method(EFGM) is used to solve the two-dimensional(2D) ground penetrating radar(GPR)modelling problems, due to its simple pre-processing, the absence of elements and high accuracy. Different from element-based numerical methods, this approach makes nodes free from the elemental restraint and avoids the explicit mesh discretization. First, we derived the boundary value problem for the 2D GPR simulation problems. Second, a penalty function approach and a boundary condition truncated method were used to enforce the essential and the absorbing boundary conditions, respectively. A three-layered GPR model was used to verify our element-free approach. The numerical solutions show that our solutions have an excellent agreement with solutions of a finite element method(FEM). Then, we used the EFGM to simulate one more complex model to show its capability and limitations. Simulation results show that one obvious advantage of EFGM is the absence of element mesh, which makes the method very flexible. Due to the use of MLS fitting, a key feature of EFM, is that both the dependent variable and its gradient are continuous and have high precision.
基金Key project(02103) supported by National Education Department of ChinaKey project(02A008) supported by the Education Department of Hunan Province,China+3 种基金Project(2005090) supported by Central South University of Forestry and TechnologyProject(03JJY3007) supported by the Natural Science Foundation of Hunan Province,ChinaProject supported by the Rewarding Project for Excellent PhD Thesis of Hunan Province,ChinaProject(07031B) supported by Scientific Research Fund of Central South University of Forestry and Technology
文摘The element-free method is a new numerical technique presented in recent years.It uses the moving least square(MLS) approximation as its shape function,and it is determined by the basic function and weight function.The weight function is the mainly determining factor,so it greatly affects the accuracy of the computational results.The element-free Galerkin method(EFGM) was applied for the solution to plastic large deformation.The simulation of metal rheological forming was successfully done by programming and its results were visualized by using the plotting and data analyses software Tecplot.Then plastic strain under different stages during rheological forming and the three principal stresses at the last deformation were obtained.The example shows the feasibility of EFGM used for metal rheological forming and provides a new method for numerical simulation of rheological forming of complex parts.
基金Project(30917011339)supported by the Fundamental Research Funds for the Central Universities,ChinaProject(BK20170820)supported by the Natural Science Foundation of Jiangsu Province,China+2 种基金Projects(61472267,71471091,71271119)supported by the National Natural Science Foundation of ChinaProject(17KJD110008)supported by the Natural Science Fund for Colleges and Universities in Jiangsu Province,ChinaProject(BE2017663)supported by the Key Research & Developement Plan of Jiangsu Province,China
文摘Possessing the unique and highly valuable properties, graphene sheets(GSs) have attracted increasing attention including that from the building engineer due to the fact that Graphene can be utilized to reinforce concrete and other building materials. In this work, the nonlocal elastic theory and classical plate theory(CLPT) are used to derive the governing equations. The element-free framework for analyzing the buckling behaviors of double layer circular graphene sheets(DLCGSs) relying on an elastic medium is proposed. Pasternak-type model is adopted to describe the elastic medium. Accordingly, the influences of boundary conditions, size of GSs and nonlocal parameters on the buckling behavior of DLCGSs are investigated. The results show that the OP buckling modes are only sensible to the van der Waals forces.
