基于三变量无单元法的杆系模型动力计算  

Dynamic calculation of beam-column model based on three-variable element free Galerkin method

作　　者：吴琛[1,2] 周瑞忠[3] 项洪 

机构地区：[1]福建工程学院土木工程学院,福建福州350118 [2]福建省土木工程新技术与信息化重点实验室,福建福州350118 [3]福州大学土木工程学院,福建福州350116

出　　处：《地震工程与工程振动》2016年第2期198-206,共9页Earthquake Engineering and Engineering Dynamics

基　　金：国家自然科学基金项目(51108083);福建省自然科学基金项目(2015J01631)~~

摘　　要：无单元法无需网格划分,可避免结构震动开裂或产生大变形而不断更新网格所导致的计算复杂。本文基于移动最小二乘法建立考虑水平位移、竖向位移和转角的三变量无单元插值函数。局部坐标系下利用三变量插值函数形成节点质量矩阵和刚度矩阵,并经坐标转换集成整体坐标系下的质量和刚度矩阵,进而进行杆系模型动力特性的计算和无单元法离散动力方程的求解,获得地震响应。分析了影响半径scale乘子对权函数、插值函数及二者导数的影响。研究表明,当scale发生变化时,虽然对权函数影响不大,但权函数导数的绝对值随着scale的增大而逐渐减小,这种改变进而影响了插值函数的数值。当scale发生微小变化时,对轴向变形分量的插值函数及导数影响较小,但将使横向变形及转角产生较大变化。经试算,建议三变量无单元法动力计算中scale乘子取3.0~4.0。最后,将本文方法应用于框架杆系模型简谐荷载、地震动作用下的位移响应计算,经与理论解和有限元解比较,验证了三变量无单元法应用于杆系模型的正确性,表明了参数设置的合理性。Element Free Galerkin Method（ EFM） does not require the design of meshes,which is an extremely tedious and time-consuming process. Furthermore,when a construction is subjected to seismic motion,large deformations of the mesh may encounter re-meshing. Interpolation functions for three-variable is set up in this paper based on Moving Least Squares Method. In which,horizontal displacement,vertical displacement and rotation angle are included. Mass matrix and stiffness matrix in local coordinate are calculated and assembled into global coordinate after coordination transformation,and then structural dynamic characteristics can be calculated and the earthquake response can be gained through solving discrete dynamic equation. The influence of scaling factor to weight function,interpolation function and their derivatives are analyzed. It is indicated that with the increase of the scaling factor,the weight function has not remarkable change,but the absolute values of its derivative decrease obviously,and the change will affect the interpolation function. When the small changes in scaling factor,it has little effect on the axial component of the interpolation function and its derivative,but the transverse component and the rotationangle have great changes. After the trial,it is recommended that the scaling factor of three-variable EFG in dynamic calculation can be set as 3. 0 to 4. 0. Three-variable EFG is applied to displacement calculation of beam-column model under harmonic load and ground motion. With comparison of analytical solution and finite element solution,it＇s indicated that three-variable EFM can be applied in beam-column model and the parameter is reasonable.

关 键 词：三变量 无单元 杆系模型 动力计算 影响半径 

分 类 号：TU323.5[建筑科学—结构工程] O241.5[理学—计算数学]