Thick Plates on Elastic Foundations by Finite Elements

The plate is subdivided into an assemblage of triangular elements. The triangular plate bending element developed earlier for contact problems is here enriched by shear degrees-of-freedom to include the plate thickness effect. The vertical displacement field of the plate element is approximated by a seventh-degree polynomial, resulting in 33 degrees-of-freedom, while shear is represented by independent linear or cubic polynomials. The total number of degrees-of-freedom for these two types of elements is 39 and 53. The analysis is performed for two different foundation models: (1) A homogeneous isotropic elastic half space; and (2) a Winkler spring model. The contact between the plate and its support is assumed to be frictionless. The contact pressure is approximated by cubic polynomials under each triangular element. A parametric study is performed by varying plate thickness and elastic moduli of the plate and foundation. Results, deformations, and contact stress are presented and analyzed.