Comparison of structural functions method approximations of the solution of a linear elastic layered plate bending problem

This paper comes to compare four different approximations of the solution to a layered linear elastic plate bending problem, obtained by the structural functions method. This method is in representation of a nonhomogeneous body displacement field as a weighted sum of spatial derivatives of the so-called concomitant body displacements, the weighting coefficients are named structural functions of the nonhomogeneous body; the concomitant body is a homogeneous one, subjected to the same loadings and boundary conditions, as the nonhomogeneous body; we come through the basic steps of structural functions method in this paper. For the concomitant plate displacements, we consider two well-known approximations: the classical plate theory and the first-order shear deformation theory. We obtain the first- and the second-order structural functions of a layered plate. We derive direct formulae for the first- and second-order structural functions method approximations of the nonhomogeneous plate displacements, using both concomitant plate displacements approximations. For a set of sample plates, we compute the obtained structural functions method approximations, and compare the computation results with a known Pagano solution to the nonhomogeneous plate bending problem. The approximation, based on the first-order shear deformation theory approach to the concomitant body displacements computation, gives an acceptable result in the considered cases.