Large deflection bending analysis of elliptic plates on orthotropic elastic foundation with mixed finite element method

This study mainly deals with the large deflection bending of moderately thick elliptic plates resting on arbitrarily orthotropic elastic foundation. Field equations of isotropic plate were based on the Mindlin plate assumptions with von Kármán strains. Elastic foundation was defined with three parameters (one spring constant, two shear parameters referring to the orthotropy directions) as an extension of Pasternak model. A non-linear mixed finite element formulation was developed by means of Hellinger–Reissner principle and it is linearized using the incremental method. During the numerical solution procedure the Newton–Raphson iteration scheme was adopted. Mixed formulation is not only shear lock free in thin plate solutions, but also gives force and moment components at the element nodes directly. A convergence with a comparison study was performed to verify the formulation. Parametric studies were carried out to investigate the large deflection behavior of clamped elliptic plates on orthotropic Pasternak foundation for various foundation parameters and ellipticity of the plate. The influences of foundation parameters and thickness to with ratio were examined as well. It is observed that, the large deflection responses of elliptic plates is highly influenced from the foundation parameters, principle directions of the orthotropy, order of the non-linearity due to the load intensity and ellipticity of the plate.

Highlight
► Mindlin plate with von Kármán strains resting on orthotropic Pasternak foundation.
► Hellinger–Reissner functional, incremental formulation and Newton–Raphson algorithm.
► Shear locking free mixed formulation and direct calculation of stress resultants.
► Factors in direction of minor axis influence the behavior of the elliptical plate.