B-splines in the Analog Equation Method for the generalized beam analysis including warping effects

Abstract

In this paper, the Analog Equation Method (AEM), a boundary element based method, is employed for the analysis of homogenous beams of arbitrary cross section (thin- or thick-walled) taking into account nonuniform warping and shear deformation effects (shear lag due to both flexure and torsion), considering a B-spline approximation for the fictitious loads of a substitute problem. The fictitious loads are established using a BEM-based technique and the solution of the original problem is obtained from the integral representation of the solution of the substitute problem. The beam is subjected to the combined action of arbitrarily distributed or concentrated axial and transverse loading, as well as to bending, twisting and warping moments. Its edges are subjected to the most general boundary conditions, including also elastic support. Nonuniform warping distributions are taken into account by employing four independent warping parameters multiplying a shear warping function in each direction and two torsional warping functions, which are obtained by solving corresponding boundary value problems, formulated exploiting the longitudinal local equilibrium equation. Ten one-dimensional boundary value problems are described by second-order differential equations. Integrating B-splines in the AEM technique, the computational cost is efficiently reduced while the results are highly accurate.