Assessing the impact of different foundations on the thermodynamic response of bidirectional FG porous beams

In this work, analytical solutions are presented for the thermodynamic behavior of bidirectional functionally graded (BDFG) porous beam lying on different supports by the mean of a quasi-3D shear deformation theory. The beams are composed of two distinct materials, and the material properties are expected to be smooth varying in both length and thickness direction according to a simple power law. The beams are supposed to be simply supported and lying on various types of foundations such Winkler, Pasternak, Variable, Kerr, and viscoelastic. The governing equations are found analytically by the mean of the presented quasi-3D model, and then, Navier’s method is used to obtain the different solutions. The impact of the characteristics of various factors like the grading indexes and type of foundation, porosity on the displacements, and stresses of the BDFG beam lying on elastic foundation is discussed in detail.