摘要
基于一阶剪切理论,提出一种求解平行四边形加肋板自由振动问题的无网格法,通过用一系列点来离散平板及肋条,得到加肋板的无网格模型。基于一阶剪切理论及移动最小二乘近似求出位移场,以梁模拟肋条,求出平行四边形加肋板总动能及总势能。再由Hamilton原理导出加肋板自由振动的控制方程,采用完全转换法引入边界条件,求解方程得出结构自振频率。以不同参数的加肋板为例,将该文解与ABAQUS有限元解进行比较分析。研究表明,该方法能有效地分析平行四边形加肋板自由振动问题,在肋条位置改变时,又避免了网格重构。
Based on the first-order shear deformation theory(FSDT), a meshfree method for solving the free vibration problem of ribbed skew plates is proposed. The plates and ribs are discretized with a series of points to obtain a meshfree model of the stiffened plate. The FSDT and the moving least-squares approximation are used to establish the displacement field. The total dynamic energy and total potential energy of the stiffened plate are obtained by simulating the ribs as beams. The governing equation for the free vibration of the stiffened plate is derived by the Hamilton principle. The boundary condition is introduced by the full transformation method, and the free vibration frequencies are solved. Several examples are calculated, and the results given by the proposed method are compared with those from other researches or ABAQUS. The results show that the method can effectively analyze the free vibration problem of ribbed skew plates and can avoid the redistribution of plate nodes when the rib position changes.
作者
覃霞
刘珊珊
吴宇
彭林欣
QIN Xia;LIU Shan-shan;WU Yu;PENG Lin-xin(Civil Engineering and Architecture School, Guangxi University, Nanning 530004, China;Key Laboratory of Disaster Prevention and Structural Safety of China Ministry of Education, Guangxi Key Laboratory of Disaster Prevention andEngineering Safety of Guangxi University, Guangxi University, Nanning 530004, China)
出处
《工程力学》
EI
CSCD
北大核心
2019年第3期24-32,39,共10页
Engineering Mechanics
基金
国家自然科学基金项目(11562001
11102044)
关键词
无网格法
平行四边形加肋板
一阶剪切理论
自由振动
完全转换法
meshfree method
ribbed skew plate
first-order shear deformation theory
free vibration
full transformation method
