On a New Method of Quasi-static and Dynamic Analysis of Viscoelastic Plate on Elastic Foundation

Abstract

An alternative solution technique based on mixed finite element (MFE) formulation in the Laplace-Carson domain is proposed for quasi-static and dynamic analyses of viscoelastic plate (VEP) resting on an elastic foundation (EF). This work contributes a numerical solution to the problem of a viscoelastic Kirchhoff plate supported on a Winkler foundation. VEP-EF interaction problems are taken into account under different wave-type loadings. The viscoelastic material behavior of the plate is modeled by the Zener rheological solid model. A four-nodded linear isoparametric element with sixteen degrees of freedom is used to model the VEP. The functional developed in the Laplace-Carson domain based on the Gateaux differential method is transformed to the real time domain by utilizing the Dubner and Abate (D&A) inverse Laplace transform technique (ILTT). To evaluate the applicability of the results, five numerical samples are considered. Further analyzes are performed on different wave type loadings to offer a new perspective on the time-dependent behavior of VEP on EF.