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Parameterized stress analysis of bonded joints plays a crucial role in joint design and relevant life prediction. This paper provides a refined stress-function variational method for stress analysis of single-lap joints subjected to mechanical and thermomechanical loads. In the process, two stress functions are introduced to approach the interfacial shear and normal (peeling) stresses along the bonding line. The axial stresses in the adherends are assumed to be linearly varying (i.e., following that of classic Euler-Bernoulli beam), while the lateral normal stress and shear stresses are determined by the stress equilibrium equations within the framework of elasticity. A set of coupled 4th-order ordinary differential equations (ODEs) of these stress functions are determined via minimizing the complementary strain energy of the joints and further solved by using eigenfunctions. The stress field based on the present model can satisfy all the traction boundary conditions (BCs), and its accuracy is validated by finite element method (FEM). Detailed numerical simulations are made to show the capability of the present semi-analytic method for accurately predicting the interfacial stresses of single-lap joints under combined mechanical loads of tension, shearing, bending, and thermomechanical loads. Detailed scaling analysis is performed to explore the dependencies of interfacial stresses upon the joint geometries and material properties of the joint. The generality of this procedure guarantees the extensibility of the present semi-analytic method to other joint systems and loading cases. 

interfacial stresses, thermal stress, single-lap joints, energy method, elasticity.