Refined theory of bi-layer beams for a transversely isotropic body

Based on elastic theory, the refined theory of bi-layer beams for a transversely isotropic body is studied. Using the Elliott–Lodge (E–L) solution and Luré method, the refined theory of beams is derived from continuity conditions without ad hoc assumptions. It is shown that the displacements and stresses of the beam can be represented by displacements and stresses of the interface of two layers of different materials. The governing equations about the transverse displacement of the interface can be obtained directly from the refined theory under transverse surface loading. Approximate solutions are derived for beams by dropping terms of high order. In addition, one example is examined to illustrate the application of the theory proposed in this paper.