Obliqueness effects in asymptotic cross-sectional analysis of composite beams

Cross-sectional stiffness properties for general composite beams, along wit h the interior solution for warping, are derived in such a way as to provid e the extra freedom to choose a cross-sectional plane that is not perpendic ular to the local beam reference line. The present development treats prism atic as well as initially twisted and curved beams. The main purpose of all owing such a choice of coordinate systems is for the convenience of the ana lyst; one, of course, should not expect the final 3D results to change. The 3D strain field is derived for the corresponding nonorthogonal curvilinear set of coordinates which describe the undeformed and the deformed geometry of the beam. The analysis is carried out based on the variational-asymptot ic method which is used to determine the warping field. For the development of the solution, it is shown that there is a fundamental difference betwee n the solutions for a prismatic beam and a beam with initial twist and curv ature, which in turn produces a limitation of the angle of obliqueness: the effect of obliqueness is treated exactly for a prismatic beam, while for t he initially twisted and curved beam the obliqueness is regarded as a small parameter. The ultimate goal of the analysis is the determination of the c ross-sectional stiffness matrix, which can then be used as input for the 1D problem. Then, using the recovering relations, one can recover the strain field over the entire cross section, once the previous problem has been sol ved. The validity of the method is demonstrated by recovery of accurate cro ss-sectional stiffnesses associated with a normal cross-sectional plane fro m those associated with an oblique cross-sectional plane, using a simple ro tation-of-axes transformation. (C) 2000 Elsevier Science Ltd. All rights re served.