Higher-order asymptotic model for a heterogeneous beam, including corrections due to end effects.

The study presented here is devoted to the 1D-modeling of a transversely heterogeneous beam with an arbitrary cross-section. The formal asymptotic expansion method is used, so that the initial SD-problem splits in a sequence of 2D-problems, posed on the cross-section, and 1D-problems, which give the governing equations of the overall outer expansion. However, considering the higher-order terms of this expansion will actually improve the approximation of the 3D solution provided that edge effects are taken into account. The latter are treated following a decay analysis technique, which provide the boundary conditions of the 1D-problems in such a way that the edge effects decay rapidly. Moreover, it is shown that accounting for end effects exempts from using a refined model, since the governing equations for the overall full outer expansion correspond to the classical Euler-Bernoulli ones. The example of a cantilevered layered sandwich beam is treated and results obtained prove that the method enables to recover the exact 3D interior solution, with a very good accuracy.