Unbalanced joints, analysis

When the linear adhesive-beam model based on the Timoshenko beam theory is used, the distributions of adhesive shear and peel stresses are almost the same as those of the nonlinear model and the values of the shear stress is slightly lower than that of the nonlinear analysis. Therefore, the linear adhesive-beam model based on the Timoshenko beam for stress analysis of asymmetric and unbalanced joints may be sufficiently accurate for engineering applications. 

Analytical approaches for adhesively bonded structures are presented in this chapter. Stress analysis for adhesively bonded joints is conducted using the classical adhesive-beam model and the other adhesive-beam models. Closed-form solutions of symmetric joints are presented and analytical procedures of asymmetric and unbalanced joints are discussed. Load update for single lap joints is investigated in detail. Numerical results calculated using the classical and other formulations are illustrated and compared. It is shown that the nonlinear adhesive-beam model based on the Timoshenko beam theory provides enhanced results compared to the linear adhesive-beam model based on the Euler beam theory for adhesively bonded composite structures. Analytical solutions of energy release rates for cohesive failure and delamination are presented, and several failure criteria are reviewed and discussed. 

Analytical analysis of balanced single lap joints gives us insight into the essences of stress analysis for adhesively bonded joints. It has been widely used for adhesive characteri2ation and benchmarking numerical methods and experimental testing. In general, adherends are asymmetric and adhesive joints are unbalanced. 

Fully coupled nonlinear analytical solutions for asymmetric and unbalanced adhesive joints are very complicated. Nevertheless, when the updated loadings are given, linear analysis based on the Timoshenko beam theory can predict sufficiently accurate adhesive stresses except for the case of very large deflection. 

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