Session: 01-01-01: General Topics of Aerospace Structures

Paper Number: 110409

110409 - Fully Analytic Solution Framework for General Thin-Walled Composite Beams Based on Mixed Variational Approach 

Thin-walled beams made of advanced composites exhibit complex mechanical behavior that cannot be observed for the isotropic counterpart structures. Particularly, anisotropic composites induce elastic couplings between various deformation modes such as the extension, bending, torsion, and shear, which make the theory quite involved. To address the effects adequately, there is a need to model the local behavior of the shell wall in response to the global deformation modes of the beam. It is conceived that three-dimensional (3D) solid or shell finite element (FE) approaches lead to solutions of high resolution, however, these numerical methods essentially demand heavy computational costs with large modeling effort. In this regard, a closed-form analysis methodology that takes into account all nonclassical structural effects of the composite beam in correct and rigorous manner has clear benefits for many engineering applications (e.g., optimum structural design of wind turbine blades).

In the present work, a variationally consistent, purely analytical formulation that represents the beam in a Timoshenko-Vlasov level is developed in the framework of the Reissner-Tsai mixed variational theorem. Given the shell theory as the starting point, all the field governing equations (equilibrium and continuity) as well as the boundary conditions of the shell wall are derived in closed form, which results in a (7x7) stiffness constants. One clear advantage of applying the mixed variational theorem is that it enables to find the explicit form of the reactive stresses which lead to recover the out-of-plane warping functions for each of the seven sectional stress resultants. The reactive stresses and out-of-plane warping functions are systematically evaluated through several progressive steps, dependent upon the level of the beam theory required for the analysis. It is emphasized that the out-of-plane warping functions and the section stress resultants are obtained in closed form as the part of the analysis. The stress recovery part is incorporated in the post-stage of the analysis to compute the layerwise distribution of stresses (and strains) over the cross-sectional wall of the beam. The current analysis is validated against a number of benchmark test cases available in the literature. These include beams with highly heterogeneous section, multi-layered rectangular strip section with elastic couplings, thin-walled anisotropic box section, and elastically coupled two-cell airfoil section. The comparison of the predicted stresses and the stiffness constants shows excellent correlations with those of detailed 3D FE-based analysis and other up-to-date beam approaches. Symbolically generated stiffness coefficients as well as the sectional warping modes of coupled composite beams are presented explicitly to illustrate the validity and the strength of the proposed beam theory. The hierarchical representation of the beam stiffness constants is attempted also to demonstrate the fundamental differences of the various beam approximations (e.g., Euler-Bernoulli, Timoshenko, and Vlasov level) for thin-walled anisotropic box section beams.

Presenting Author: Jae Seong Bae Konkuk University

Presenting Author Biography: Jaeseong Bae is a graduate research assistant at Department of Aerospace Information Engineering in Konkuk University, Seoul, Korea. He earned his MS and BS degrees from Konkuk University, Seoul, Korea, in 2017 and 2014, respectively. His research interests include structural dynamics, rotorcraft dynamics and aeroelasticity.

Authors:

SUNG JUNG Konkuk University
Jae Seong Bae Konkuk University