The refined analysis of bi-layer beams without ad hoc assumption

Cheng's refined theory is extended to investigate bi-layer beams, and an extension of recent analyses for bi-layer beams is given. Expressions are obtained for all the displacements and stress components in terms of displacement and stress of the interface of upper layer and lower layer. Using Lur'e operator functions, the refined analysis of the bi-layer beams is given from continuity conditions. On the basis of the refined analysis developed in the present paper, solutions are obtained for bi-layer beams under transverse surface loading. The refined analysis provides exact solutions which satisfy all of the governing equations.