Asymptotic treatment of the trapeze effect in finite element cross-sectional analysis of composite beams

Early analyses for numerical cross-sectional analysis of anisotropic beams were based on linear elasticity theory. For more general treatment of non-l inear phenomena, asymptotic formulations can serve as the basis for the num erical method, say a finite element method. When based on geometrically non -linear elasticity theory, an intermediate result of such analyses is frequ ently the splitting of the non-linear 3-D problem into a linear 2-D analysi s of the cross section and a non-linear 1-D analysis along the beam. Thus, the published work to date cannot treat the so-called "trapeze effect", bec ause it stems from non-linearity of the cross-sectional analysis. Herein, a non-linear numerical cross-sectional analysis is presented, based on the v ariational-asymptotic method and capable of treating cross sections of arbi trary geometry and generally anisotropic material. This type of analysis is particularly important in rotating structures, such as helicopter rotor bl ades. Results from this model are compared with those available in the lite rature, both theoretical and experimental. (C) 1999 Elsevier Science Ltd. A ll rights reserved.