基于Python的平面杆系结构有限元分析  

Finite element analysis of plane bar system structure based on python

作　　者：董军[1] 张尧 李国华[1] 刘亚立 王秀芳[1] DONG Jun;ZHANG Yao;LI Guo-hua;LIU Ya-li;WANG Xiu-fang(Beijing Higher Institution Engineering Research Center of Structural Engineering and New Materials,Beijing University of Civil Engineering and Architecture,Beijing,100044,China)

机构地区：[1]北京建筑大学工程结构与新材料北京市高等学校工程研究中心,北京100044

出　　处：《兰州理工大学学报》2024年第2期104-110,共7页Journal of Lanzhou University of Technology

基　　金：国家自然科学基金(51808025);北京市自然科学基金(8202012);长江学者和创新团队发展计划资助(IRT_17R06)。

摘　　要：基于Python程序,将杆单元位移不连续、理想刚杆两种力学对象关联统一,开展平面杆系结构有限元模型分析,并实现一种基于“变量标记”的自由度集中处理的计算模式.基于虚功原理引入并推证刚体荷载传递定理,表明耦合单元、刚杆及忽略某一自由度的有限元内置算法处理过程中,实质是将单元刚度矩阵进行“刚化”处理.算例分析表明,“变量标记”的计算模式与单元刚度矩阵的“刚化”处理,具有力学模型的普适性和统一性、编程的可行性以及结果的可靠性等特点,能解决平面任意杆系结构的建模问题.研究结果表明,“主从结点”、“刚杆”等建模方法,对于进一步开展有限元二次开发、大变形以及非线性等功能性扩展等有重要的参加价值,证明将Python程序应用于结构有限元分析的可行性.Based on the Python program,two mechanical objects,discontinuous displacements of bar element and ideal rigid rods,are associated and unified.Then the finite element model analysis of the planar bar system structure is carried out,and a computational mode of centralized processing of degrees of freedom based on“variable tagging”is realized.Based on the principle of virtual work,the load transfer theorem of the rigid body is introduced and proved,which elucidates that within the finite element built-in algorithm,the process entails an inherent“stiffening”treatment of element stiffness matrices when handling coupled elements,rigid rods,and the omission of specific degrees of freedom.The analysis of a numerical example shows that the computational mode of“variable tagging”and the"stiffening"treatment of the element stiffness matrix have the characteristics of universality and unity of mechanical model,feasibility of programming,and reliability of results,which can solve the modeling problem of arbitrary bar structure in plane.The results show that“master-slave nodes”,“rigid rods”and other modeling methods have important participation value for advancing finite element methodologies,particularly in finite element secondary development,large deformation,and nonlinear functional expansion.Moreover,it is feasible to apply the Python program to structural finite element analysis.

关 键 词：平面杆系结构 PYTHON 有限元分析 耦合单元 主从关系 

分 类 号：U441[建筑科学—桥梁与隧道工程] O343[交通运输工程—道路与铁道工程]