Closed-Form Analysis of Thin-Walled Composite Beams Using Mixed Variational Approach

Abstract

An analytical methodology is developed for thin-walled composite beams with arbitrary geometries and material distributions. The approach uses a mixed variational theorem which sets the shell displacements, and the shear stress resultants and hoop moments as the unknowns to obtain the stiffness constants at the level of Timoshenko–Vlasov beam. All the field equations and the continuity conditions that should be satisfied over the shell wall are derived in closed form as the part of the analysis. Numerical simulations are conducted to show the validity of the proposed analysis. The comparison of the predicted stresses and the stiffness constants indicates close correlation with those of the detailed finite element (FE)-based analysis and up-to-date beam approaches. Symbolically generated stiffness constants and the sectional warping deformation modes of coupled composite beams are presented explicitly to illustrate the strength of the proposed theory.