3D-beam element with continuous variation of the cross-sectional area

This paper presents the exact stiffness matrix of 3D-beam element with a class of continuously varying cross-sectional properties, which is derived using direct stiffness method and transfer functions of the beam. A nodal load vector for continuously distributed beam loading is also described using transfer functions. All the transfer functions, which occur in the stiffness matrix and nodal load vector, are evaluated numerically. Results of numerical experiments show that this new element satisfies all the relevant equations.