Generalized Warping Analysis of Composite Beams of an Arbitrary Cross Section by BEM. I: Theoretical Considerations and Numerical Implementation

Abstract

In this two-paper contribution, a general formulation for the nonuniform warping analysis of composite beams of arbitrary simply or multiply connected cross sections, under arbitrary external loading and general boundary conditions, is presented. Part I is devoted to the theoretical development and numerical implementation of the solution method, whereas Part II discusses the examined numerical applications illustrating the efficiency, accuracy, and range of applications of the proposed method as well as the effects arising because of nonuniform warping. The nonuniform warping distributions are taken into account by using four independent warping parameters multiplying a shear warping function in each direction and two torsional warping functions, respectively, which are obtained by solving the corresponding boundary value problems, formulated exploiting the longitudinal local equilibrium equation. A shear stress correction is also performed to improve the stress field arising from the kinematical considerations used. Ten boundary value problems are formulated with respect to the displacement and rotation components as well as to the independent warping parameters and solved using the analog equation method, a boundary element method (BEM)-based technique. The warping functions and the geometric constants including the additional ones due to warping are evaluated with a pure BEM approach.