Analytical Solutions for Dynamic Behavior of Thin-Walled Open-Section Composite Beams

Abstract

In this paper, we demonstrate the application of the proposed iterative “marching method” from 1 to model thin walled open-section beams. We discuss closed-form iterative analytical solutions describing both quasi-static and dynamic behavior of thin walled open-section beams. The method has been shown to be applicable during application of both conservative and non-conservative system of forces and moments. I. Introduction I.A. Modeling of Thin Walled Open-Section Beams Thin walled composite beams have become an integral part of many engineering structures today. The technology which mainly evolved for aerospace industry (E.g., rocket motor casings, space booms, rotor blades) finds its application in fields as diverse as sports (E.g., skis, tennis racket, golf clubs), sea hulls, off shore rigs, automobile industry (E.g., filament wound power transmission shafts), and architecture (E.g., I-beams, channel-section beams). Despite their superior engineering properties and enhanced manufacturing technology, their production is not up to their potential due to cost considerations. One of the sure ways to reduce the development cost is to establish accurate analysis tools to aid in composite tailoring. In particular, analytical tools which can be used in preliminary design and efficient numerical tools which can be used in detailed design are of prime importance. Thin walled composite beams are widely favored in aerospace structures and examples of sections which can be analyzed using the present work are I-section, T-section, X-section, Z-section, cruciform and any custom section. Though 3-D finite element modeling of such beams is possible, it is computationally inefficient. Existing classical analytical tools suffice for a majority of simple structures. However many important practical phenomenon have been observed in thin-walled composite as well as isotropic beams to which classical tools are blind. Many existing 1-D models make ad hoc assumptions for thin walled beams and neglect the non-classical effects. Physical nonlinearities are basically nonlinearities in the stress-strain relationship becoming important by virtue of strain being large. Geometrical nonlinearities, on the other hand, are nonlinearities in the straindisplacement relationship becoming important by virtue of displacement being large. A non-linear beam theory could arise either due to 1-D physical nonlinearities or 1-D geometric nonlinearities or both. But there are certain 1-D physical nonlinearities occurring due to 3-D geometric nonlinearities (large 3-D warping) and these are called non-classical nonlinearities. Composite open section beams have low torsional rigidity and hence allow fairly large twist rates, not only in torsion but also other types of loading which thus brings to importance the nonlinearities involving twist. These effects are important in the case of thin walled beams and not so important in the case of solid and thick walled beams. The current work is motivated by a need and the absence in the literature of a general purpose tool to capture, in closed form solutions, all the non-classical effects, in an asymptotic manner in thin walled open section composite beams. It is focused at developing analytical solutions incorporating non-linear strain fields which are the