摘要
One of major difficulties in the implementation of meshfree methods using the mov- ing least square （MLS） approximation, such as element-free Galerkin method （EFG）, is the im- position of essential boundary conditions as the approximations do not pass through the nodal parameter values. Another class of meshfree methods based on the radial basis point interpola- tion can satisfy the essential boundary conditions exactly since its approximation function passes through each node in an influence domain and thus its shape functions possess the properties of delta function. In this paper, a coupled element-free Galerkin（EFG）-radial point interpola- tion method （RPIM） is proposed to enhance their advantages and avoid their disadvantages. Discretized equations of equilibrium are obtained in the RPIM region and the EFG region, respectively. Then a collocation approach is introduced to couple the RPIM and the EFG method. This method satisfies the linear consistency exactly and can maintain the stiffness matrix symmetric. Numerical tests show that this method gives reasonably accurate results consistent with the theory.
One of major difficulties in the implementation of meshfree methods using the mov- ing least square （MLS） approximation, such as element-free Galerkin method （EFG）, is the im- position of essential boundary conditions as the approximations do not pass through the nodal parameter values. Another class of meshfree methods based on the radial basis point interpola- tion can satisfy the essential boundary conditions exactly since its approximation function passes through each node in an influence domain and thus its shape functions possess the properties of delta function. In this paper, a coupled element-free Galerkin（EFG）-radial point interpola- tion method （RPIM） is proposed to enhance their advantages and avoid their disadvantages. Discretized equations of equilibrium are obtained in the RPIM region and the EFG region, respectively. Then a collocation approach is introduced to couple the RPIM and the EFG method. This method satisfies the linear consistency exactly and can maintain the stiffness matrix symmetric. Numerical tests show that this method gives reasonably accurate results consistent with the theory.
基金
supported by the National Natural Science Foundation of China (No. 11172192)
the College Postgraduate Research and Innovation Project of Jiangsu Province (No. CX10B 029Z)
the Nominated Excellent Thesis for PHD Candidates Program of Soochow University (No. 23320957)
