Abstract
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.
Highlights
Plates supported directly by the soil continuum are widely used in structural engineering. ey are the basic components of highways, bridges, high-rise building foundations, and other structures. e behaviour of the plate when it carries external loads is influenced by the foundation, and the behaviour of the foundation is in turn influenced by the action of the plate under load
It is very important to calculate and analyse these models accurately. e existing elastic foundation models include the Winkler foundation model [1], two-parameter elastic model [2], and elastic continuous medium foundation model [3], each of which has its own characteristics in accordance with the corresponding hypotheses. e two-parameter foundation model has the advantages of a simple mathematical process and a perfect theory
A sound mathematical model is developed for determining the displacements, bending moments, and shear forces in circular thin plates resting on two modified Vlasov foundations. e influence of heterogeneous soils on the bending of the circular thin plates and the characteristic parameters of two modified Vlasov foundation models is analysed. e presented method can be expanded to consider layered soils, solve the problem of free vibration, and so forth
Summary
Plates supported directly by the soil continuum are widely used in structural engineering. ey are the basic components of highways, bridges, high-rise building foundations, and other structures. e behaviour of the plate when it carries external loads is influenced by the foundation, and the behaviour of the foundation is in turn influenced by the action of the plate under load. In terms of the Vlasov foundation model, Vallabhan et al [4,5,6] analysed the governing equations and boundary conditions for the bending of rectangular plates and beams resting on a refined Vlasov foundation, using variational principles. Us, Gibson foundation is more in line with the actual situation As another example, even though the traditional two-parameter model for plates resting on elastic foundations represents the interaction between the plates and the foundation better than the Winkler model, it requires the estimation of a third parameter c, which represents the distribution of displacements within the foundation. Erefore, in the present study, circular thin plates resting on two modified Vlasov foundations are analysed based on heterogeneous soils with transverse isotropy and Gibson characteristics, respectively. The governing equations and boundary conditions for a circular thin plate resting on two modified Vlasov foundations are established, according to the principle of energy variation. The relatively accurate deflections and internal forces of circular thin plate are obtained
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