摘要
对于厚度变化比较平缓,而且平分厚度的中面仍然是平面的薄板弯曲分析。首先在板上布置节点,选定支持域半径和适当的权函数,然后利用移动最小二乘法(MLS)得到支持域内节点的形函数,将形函数代入控制微分方程,得到支持域内节点的刚度和作用在节点上的力,将节点刚度和力装配成系统的刚度矩阵和力的列向量,求解方程得到各节点的位移以及内力,并用有限元分析软件(ANSYS)对同一问题进行研究,对两种方法所得结果进行了比较,数值结果表明应用无网格Local Petrov-Galerkin法计算变厚度薄板弯曲具有足够的精度和效率。
The bending of a thin plate with varying gently thickness is analyzed based on the Meshless Local Petrov-Galerkin method. The plate is assumed to be divided equally by its middle plane. The nodal points are firstly distributed on the plate, the radius of the nodal support domain and proper weighted functions are chosen. And then the shape functions of the nodal points within the support domain are obtained by the moving least square approximation. Substituting the shape functions into the governing equations leads to the stiffness and forces of these nodes in a support domain. The stiffness and forces of all the nodes are assembled into the total stiffness matrix and force vector. The displacements and inner forces of all the nodes are solved by the solution of the governing equation. The software ANSYS is used to analyze identical problems. The present numerical results compared to ANSYS illustrate that the Meshless Local Petrov-Galerkin （MLPG） method is easy to use and with high accuracy for solving the bending problem of variable thickness thin plates.
出处
《工程力学》
EI
CSCD
北大核心
2013年第5期19-23,62,共6页
Engineering Mechanics
基金
汽车车身先进设计制造国家重点实验室开放基金项目(31015009)
湖南科技大学研究生创新基金项目(S100107)
关键词
变厚度薄板
无网格LPGM
挠度
内力
移动最小二乘法
variable thickness thin plate
Local Petrov-Galerkin method
deflection
inner force
moving leastsquare method
