关键词: 平面杆系结构, Python, 有限元分析, 耦合单元, 主从关系

Abstract: 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.

Key words: planar bar system structure, Python, finite element analysis, coupling element, master-slave relation