Derivation of the higher-order stiffness matrix of a space frame element

Abstract

A physical concept, the rigid body rule, is applied for the derivation of the higher-order stiffness matrix of a space frame element. The derivation has a physical meaning that is the higher-order stiffness matrix can be derived by regarding that there is a set of incremental nodal forces existing on the element, then the element undergoes a small rigid body rotation. The incremental forces should keep their magnitude and follow the rigid body motions. Then taking advantage of the established geometric stiffness matrix derived by former researchers, the higher-order stiffness matrix can be analogy derived in explicit forms without any difficulty. It can be used at the forces recovery stage in the geometric nonlinear analysis of frame structures. Meanwhile an effective numerical method, the generalized displacement control method, was adopted to trace the load–deflection curves of structures. Some famous numerical examples were tested by the element which included the proposed higher-order stiffness matrix in tangential stiffness matrix.