Stability of Thin Web Composite Cantilever Beams of Random Lamination

Abstract

This study addresses the analytical treatment of a closed-form buckling equation for lateral-torsional stability of thin web composite cantilever beams under mid-height tip force. The beam is composed of random ply fiber orientations. Classical lamination theory is embedded into the Vlasov plate formulation to make up the framework of the analytical treatment. A closed-form solution is realized when an innovative dimensional reduction is extended to the 3D constitutive stiffness matrix. This was made possible through a two-step process in which the shear strain, lateral curvature, and twisting curvature are retained first. By condensing the shear strain variable, effective lateral, torsional, and coupling stiffness terms were formulated. Applying the equilibrium conditions in the deformed configuration, two differential equations are obtained in terms of the lateral curvature and twisting angle. Eliminating the lateral curvature, the twisting angle differential equation with nonconstant coefficients is generated. This equation is solved using a hybrid numerical-analytical approach yielding an analytical buckling expression. Finite element results are generated to verify the accuracy of the buckling load predictions indicating very good correlation with the buckling equation results regardless of the random lamination applied.