Bending Analysis of Transversely Isotropic Thick Rectangular Plates on Two-Parameter Elastic Foundation

The analysis of plates on elastic foundation has a wide range of applications in various fields of engineering, such as civil, mechanical, aerospace, nuclear and marine engineering. Due to soil behavior is dependent on numerous factors, providing full and comprehensive model for foundation is very complicated. Therefore, in order to express properties of the substrate are used the simpler models based on the elastic properties. The simplest of those models, which was presented by winkler in 1867, assumes that the soil medium containing a system of independent spring (Liew et al, 1996). To increase the accuracy of modeling two-parameter models arose that the effect of shear stresses in the substrate is also included. In these models a new parameter is proposed to establish a mechanical connection between the independent springs. An approximate solution for the bending of moderately thick rectangular plates using numerical differential quadrature method was proposed by Han and Liew (1997). Teo and Liew (2002), presented a solution for analysis of shear deformable rectangular plates on Pasternak foundations by using differential cubature method. Displacement potential functions (DPF) method is one of the effective and efficient techniques that can be used to solve elasticity problems. The most advantage of DPF method is that the system of differential equations is uncoupled or at least simplified. This method has been used for 3D analysis of plates by a number of researchers such as Nematzadeh et al (2010) and Moslemi et al (2016) for the bending and buckling solution, respectively.