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 condit...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.展开更多
利用添加多项式项的(Radial Point Interpolation Method,RPIM)形函数,形成了动力学问题的无网格全局弱形式.生成了伴随于域节点的Voronoi图,利用基于应变光滑稳定方案的稳定相容节点积分得到了改进后的总体刚度矩阵离散化形式,并利用...利用添加多项式项的(Radial Point Interpolation Method,RPIM)形函数,形成了动力学问题的无网格全局弱形式.生成了伴随于域节点的Voronoi图,利用基于应变光滑稳定方案的稳定相容节点积分得到了改进后的总体刚度矩阵离散化形式,并利用直接法施加位移边界条件.自由振动分析得到了与有限元参考解吻合良好的数值解,受迫振动分析采用了无条件稳定的Newmark法,从而验证了本方法在求解动力学问题所展现的稳定性、精确性及收敛性.展开更多
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)
文摘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.
文摘利用添加多项式项的(Radial Point Interpolation Method,RPIM)形函数,形成了动力学问题的无网格全局弱形式.生成了伴随于域节点的Voronoi图,利用基于应变光滑稳定方案的稳定相容节点积分得到了改进后的总体刚度矩阵离散化形式,并利用直接法施加位移边界条件.自由振动分析得到了与有限元参考解吻合良好的数值解,受迫振动分析采用了无条件稳定的Newmark法,从而验证了本方法在求解动力学问题所展现的稳定性、精确性及收敛性.
