基于三变量伽辽金无单元法的杆系模型动力计算与参数分析  

Vibration analysis and parameter analysis of beam-column models based on three-variable EFG

作　　者：吴琛 杜喜朋 项洪 邓智元 

机构地区：[1]福建工程学院土木工程学院,福州350108 [2]福建省土木工程新技术与信息化重点实验室,福州350108

出　　处：《应用力学学报》2018年第2期234-240,共7页Chinese Journal of Applied Mechanics

基　　金：国家自然科学基金(51108083);福建省自然科学基金(2015J01631);福建省高等学校新世纪优秀人才支持计划(GYZ-160144);福建工程学院科研发展基金(GYZ-160126)

摘　　要：将移动最小二乘法与广义移动最小二乘法相结合,提出同时考虑节点轴向变形、切向变形和转角的三变量无单元插值形函数,应用于框架结构杆系模型的动力计算。运用伽辽金弱形式推导离散动力方程,采用罚函数法引入边界条件,建立三变量无单元法动力计算公式,采用Newmark-β法进行动力时程分析。讨论了节点数量、影响半径以及基函数阶次对计算结果的影响。研究结果表明,当节点的间距≤10%杆件长度,影响半径scale乘子界于2.5~4.0,采用三阶多项式基函数时,无单元的动力计算可获得较好的精度。Frame is processed as beam-column model and a three-variable element-free Galerkin(EFG) method is presented to compute the natural frequencies and dynamic responses. The moving least square method in combination with the generalized moving least square method is used to construct shape functions and then the horizontal displacement, vertical displacement and rotational angle of every node are approximated. The Galerkin weak form is employed to derive the discretized system equations, and the Newmark-β time integration method is applied for the time history analyses. In the modelling process, the penalty method is used to impose the essential boundary conditions to obtain the corresponding formulae of the three-variable EFG for elastodynamics.Applicability of the method is demonstrated by solving numerical examples for different values of number of nodes, scaling factor and order of basis functions. It is indicated that when the nodal spacing is less than 10% of the length of a member bar, the scaling factor is 2.5≤s≤4.0, and the order of the basis function is large enough and not greater than the scaling factor, the dynamic solutions are accurate.

关 键 词：伽辽金无单元法 三变量 杆系模型 离散方程 动力计算 参数分析 

分 类 号：O039[理学]