Analytical solution for bi-material beam with graded intermediate layer

Using the Airy stress function, an analytical solution is obtained for a bi-material beam with a graded intermediate layer, which is subjected to a uniform load on the upper surface and has different boundary conditions at the two ends. Young’s modulus of the graded intermediate layer is assumed to be an arbitrary function of the thickness coordinate and its Poisson’s ratio is kept a constant. The solution can easily degenerate into the ones of the tri-material beam, the bi-material beam, the homogeneous beam, and the graded beam, and some of them coincide with the available solutions. The analytical and numerical (finite-element-based) results are in agreement with each other for several examples. The influence on the stress distribution for the cantilever beam is discussed when Young’s modulus of the graded intermediate layer takes different functions.