Influence of the Order Exchange of the Node Connection in the Force Analysis of Steel Structures

Abstract

In the mechanical analysis of steel structures, whether it is static analysis or dynamic analysis, it is necessary to establish the structural stiffness matrix first. In the process of building the structural stiffness matrix, the same element usually has different node code connection orders, and it has never been argued whether the different connection orders of the same element will have an effect on the building of the stiffness matrix. In this study, the influence of the difference in the node connection order on the construction of the element stiffness matrix is studied. First, the structural element stiffness matrix in the global coordinate system is established when the node connection order is different. It is found that the element stiffness matrix in the global coordinate system is indeed inconsistent for the same element with different connection orders. In this study, the elements of the established element stiffness matrix are extracted into the global stiffness matrix of the structural system based on the law of energy conservation; it is found that the global stiffness matrix finally established by using two different connection relationships is the same. The research results of the example show that in the stress analysis of steel structures, selecting different node connection sequences to establish the structural stiffness matrix will obtain the element stiffness matrix under different global coordinate systems. However, through the aggregation process of the global stiffness matrix of the structural system, the global stiffness matrix obtained is consistent, so the different connection sequences of nodes will not affect the stress analysis of steel structures. The example further analyzes the static stress and dynamic responses of the steel structure. The conclusions of this study provide a reliable theoretical basis for the situation that the order of node connections need not be consistent in the finite element modeling of steel structures and are of reference value for the finite element modeling of steel structures.