Shear deformation effect in nonlinear analysis of spatial beams

In this paper a boundary element method is developed for the nonlinear analysis of beams of arbitrary doubly symmetrical simply or multiply connected constant cross-section, taking into account shear deformation effect. The beam is subjected in an arbitrarily concentrated or distributed variable axial loading, while the shear loading is applied at the shear centre of the cross-section, avoiding in this way the induction of a twisting moment. To account for shear deformations, the concept of shear deformation coefficients is used. Five boundary value problems are formulated with respect to the transverse displacements, the axial displacement and to two stress functions and solved using the analogue equation method, a BEM-based method. Application of the boundary element technique yields a system of nonlinear equations from which the transverse and axial displacements are computed by an iterative process. The evaluation of the shear deformation coefficients is accomplished from the aforementioned stress functions using only boundary integration. Numerical examples are worked out to illustrate the efficiency, the accuracy and the range of applications of the developed method. The influence of both the shear deformation effect and the variability of the axial loading are remarkable.