A 3D shell-like approach using element-free Galerkin method for analysis of thin and thick plate structures  

作　　者：Yu Yin Lin-Quan Yao Yang Cao 

机构地区：[1]School of Mathematical Science, Soochow University [2]School of Urban Rail Transportation, Soochow University [3]School of Transportation, Nantong University

出　　处：《Acta Mechanica Sinica》2013年第1期85-98,共14页力学学报（英文版）

基　　金：supported by the National Natural Science Foundation of China (11172192);the College Postgraduate Research and Innovation Project of Jiangsu province (CXZZ12 0803)

摘　　要：A new efficient meshless method based on the element-free Galerkin method is proposed to analyze the static deformation of thin and thick plate structures in this paper. Using the new 3D shell-like kinematics in analogy to the solid-shell concept of the finite element method, discretization is carried out by the nodes located on the upper and lower surfaces of the structures. The approximation of all unknown field variables is carried out by using the moving least squares （MLS） approximation scheme in the in-plane directions, while the linear interpolation is applied through the thickness direction. Thus, different boundary conditions are defined only using displacements and penalty method is used to enforce the essential boundary conditions. The constrained Galerkin weak form, which incorporates only dis- placement degrees of freedom （d.o.f.s）, is derived. A modified 3D constitutive relationship is adopted in order to avoid or eliminate some self-locking effects. The numeric efficiency of the proposed meshless formulation is illustrated by the numeric examples.A new efficient meshless method based on the element-free Galerkin method is proposed to analyze the static deformation of thin and thick plate structures in this paper. Using the new 3D shell-like kinematics in analogy to the solid-shell concept of the finite element method, discretization is carried out by the nodes located on the upper and lower surfaces of the structures. The approximation of all unknown field variables is carried out by using the moving least squares （MLS） approximation scheme in the in-plane directions, while the linear interpolation is applied through the thickness direction. Thus, different boundary conditions are defined only using displacements and penalty method is used to enforce the essential boundary conditions. The constrained Galerkin weak form, which incorporates only dis- placement degrees of freedom （d.o.f.s）, is derived. A modified 3D constitutive relationship is adopted in order to avoid or eliminate some self-locking effects. The numeric efficiency of the proposed meshless formulation is illustrated by the numeric examples.

关 键 词：Meshless methods 3D shell-like Moving least squares approximation SELF-LOCKING Thin plate 

分 类 号：O241.82[理学—计算数学]