Brazier Effect in Multibay Airfoil Sections

Abstract

Although it has long been recognized that all long thin-walled hollow structures exhibit a nonlinear response to bending moments, the majority of analytical research has focused on circular cross sections. A method of predicting the nonlinear behavior of multibay airfoil sections is presented. Although the approach is simple, the algebraic complexity lends itself toward a solution using algebraic manipulation software. Comparison of the analytical models with finite element analysis shows good correlation and demonstrates the ability of the model in predicting the nonlinear bending response of smooth orthotropic two-bay airfoils. Nomenclature [a ]= shell in-plane compliance matrix C = overall curvature [D ]= shell bending stiffness matrix E =Y oung’s modulus G = shear modulus h = height I = second moment of area l = section Y dimension M = longitudinal bending moment m = cross-sectional bending moment p = cross-sectional reaction force S =w all length U = energy w = cross-section displacement z α = cos(β) β = horizontal wall angles to midplane e = strain κ = cross-sectional curvature λ = element length correction factor µ = I correction factor ν = Poisson’s ratio ψ = distributed Brazier crushing force I. Introduction