Stiffness Matrices for Axial and Bending Deformations of Non-Prismatic Beams with Linearly Varying Thickness

Abstract

Siffness matrices for axial and bending deformations of a beam having a rectangular cross sectional area of constant width and linearly varying thickness are developed. A consistant load vector for a uniformly distributed lateral load is also calculated, using the principal of potential energy. The matrices are used to obtain numerical results for a variety of beams with non-uniform thickness to show that acceptable degrees of accuracy can be obtained. A comparison of results given by other finite element solutions is made to show the effectiveness of the derived stiffness matrices.