Quadratic B-splines in the analog equation method for the nonuniform torsional problem of bars

Abstract

In this paper, the analog equation method, a boundary element-based method, is employed for the nonuniform torsional problem of bars of arbitrary constant cross section, considering a quadratic B-spline approximation for the fictitious loads of a substitute problem. The fictitious loads are established using a boundary element method-based technique, and the solution of the original problem is obtained from the integral representation of the solution of the substitute problem. The bar is subjected to arbitrarily distributed twisting moments along its length, while its edges are subjected to the most general torsional (twisting and warping) boundary conditions. The problem is numerically solved introducing a quadratic B-spline function for the fictitious load in the integral representations of the aforementioned technique. Numerical results are worked out to illustrate the method, designate its efficiency, accuracy and computational effort, as well as verify its integrity comparing with the results of analytical solutions. In addition to this, refinement procedures have been employed in some of the numerical examples in order to investigate their efficiency in increasing accuracy. Knot insertion, which is one of these, is proved to be very beneficial in refining the B-spline curve and increasing the accuracy.