Static analysis of a Bickford beam by means of the DQEM

In this paper the recently proposed differential quadrature element method is employed in order to solve the equilibrium equations of a higher-order beam. A simple five-node element is introduced, in which the vertical displacement is approximated by a sixth-order polynomial, whereas the rotation is consistently approximated by a fourth-order polynomial, and the resulting weighting coefficient matrix is given. Moreover, a general procedure is outlined, for an N-node element, in which vertical displacements and rotations are given by polynomials of order N+1 and N-1, respectively. Numerical examples are aimed both at checking the convergence of the results for increasing values of the nodes, and at comparing the used cubic beam theory with the simpler, linear, Timoshenko theory.