Bending Analysis of Circular Thin Plates Resting on Elastic Foundations Using Two Modified Vlasov Models

Abstract

<jats:p>The influence of soil heterogeneity is studied on the bending of circular thin plates using two modified Vlasov foundation models. The model parameters are determined reasonably using an iterative technique. According to the principle of minimum potential energy and considering transversely isotropic soils and Gibson soils, the governing differential equations and boundary conditions for circular thin plates on two modified Vlasov foundations are derived using a variational approach, respectively. The determination of attenuation parameters is a difficult problem, which has hindered the further application of the Vlasov foundation model. The equation that must be satisfied by the attenuation parameter is determined, and an iterative method is used to solve the problem. A comparative analysis is conducted between two modified Vlasov models and the traditional Vlasov model. The results show that the governing equations and boundary conditions for circular thin plates resting on two modified foundations are consistent with those for a circular thin plate on traditional two-parameter foundation after degradation. The accuracy and reliability of the proposed solutions are demonstrated by comparing the obtained results with those reported in the literature. The heterogeneity of soils, including the transversely isotropic soils and Gibson soils, has a certain effect on characteristic parameters of the foundation models as well as the deformations and internal forces of circular thin plates. The present study could be employed as a reference for future engineering designs.</jats:p>

Numerical Analysis of Thick Isotropic and Transversely Isotropic Plates in Bending using FE Based New Inverse Shear Deformation Theory

“…Shape functions and derivatives are requisites in strain calculations. Equation (12) shows the shape functions for the element illustrated in Figure 3 that are derived based on local coordinates " & " at a given node.…”

“…For the static flexure and free vibration study of isotropic plates, two variable refined plate theories were developed [11], and this theory produces frequencies similar to those of the theory of FSDT. Employing two modified Vlasov foundation models [12], the effect of soil variability on the bending of circular thin plates is investigated. Several refined shell methods [13] were used to assess the static and free vibrations of composite laminates and sandwiched geometrical shapes.…”

Bending Analysis of Stepped Rectangular Plates Resting on an Elastic Half-Space Foundation

“…Investigations of the Kirchhoff plate on foundations are also reported in the literature. Yue et al [19] analyzed the influence of soil heterogeneity on the bending of a circular thin plate using two modified Vlasov foundation models. Mohammadimehr et al [20] obtained the buckling and free vibration response of functionally graded materials resting on a Pasternak foundation.…”