Analytical model for adhesively bonded composite panel-flange joints based on the Timoshenko beam theory

An analytical model for adhesively bonded composite panel-flange joints is developed using the kinematic relations of the Timoshenko beam theory and the constitutive equations in linear elasticity. The governing equations are derived for the normal and shear stresses in the adhesive layer of a composite joint containing two symmetric or unsymmetric laminates (as adherends) with equal- or unequal-thickness. For a composite joint with two equal-thickness symmetric adherends, closed-form solutions are obtained for the normal and shear stresses in the adhesive layer. Due to the consideration of the transverse shear effect in the current model, the solution for the normal (peel) stress derived here is different from that provided in an existing model using the Bernoulli-Euler beam theory-based classical laminate theory, even though the solution for the shear stress obtained here is the same as that given in the latter. The new model is quantitatively illustrated and compared with the existing model for two sample cases of composite panel-flange joints. The numerical results reveal that the peel stress for the joint under pure bending is tensile over the entire length of the adhesive and its values near the two ends of the adhesive are significantly larger than those predicted by the existing Bernoulli-Euler beam theory-based model.