Analysis of beam with variable cross-section by using direct element-based equilibrium framework

The element shape functions with fixed shapes cannot rationally approximate the deformation in a deformed beam with variable cross-section, which results in an inaccuracy of traditional beam elements. The paper presents a method to analyze beam with variable cross-section by using direct element-based equilibrium framework. This method avoids the inaccuracy caused by the limitation of element shape functions. The stiffness matrix, equivalent nodal load and consistent mass matrix are derived for the beam element with variable cross-section. A computer program is then developed and a numerical example is provided to verify the presented method. It is shown that the theory is correct and the method has higher accuracy than the traditional beam elements.