UNIFIED FORMULATION OF BEAM ELEMENTS IN FINITE ELEMENT SOFTWARE¹⁾

Based on the authors' experience in the development of various finite element software, this paper presents the method of forming the stiffness matrix and the corresponding element load vectors for beam elements to meet the different engineering demands, focusing on the unified formation of Euler and Timoshenko beam elements and variable section beam elements based on the flexibility method, and the unified formation of the element stiffness matrix and the load vector under different beam end conditions. This paper provides a reference for developers in the engineering finite element software industry and to help the teaching of the finite element methods.