Generalized warping analysis of curved beams by BEM

• Formulation for the generalized warping analysis of curved beams.
• Curved beams under general loading and boundary conditions.
• BEM approach with quadratic discretization elements.
• Flexural–torsional shear lag and secondary torsional shear deformation effects.
• Comparison with FEM solid models for the accuracy of the method.

In this paper, the analysis of homogenous curved beams of arbitrary cross section (thin- or thick-walled) taking into account the coupling of extension, flexure and torsion, nonuniform warping as well as shear deformation effects (shear lag due to both flexure and torsion) has been studied. The curved 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. 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 and solved employing the Analog Equation Method (AEM), a boundary element based method, using either constant or quadratic elements for the representation of the adopted fictitious loads. Results are compared with FEM solutions employing curved beam, shell or 3-d solid elements.