Dynamic Analysis of Thick Plates Resting on Winkler Foundation Using a New Finite Element

Abstract

The aim of this paper is to study parametric earthquake analysis of thick plates resting on Winkler foundation. The governing equation of the plate is prepared with Mindlin’s thick plate theory. In the dynamic analysis, Newmark method is used for the time integration of the governing dynamic equation. This study investigates the effects of the thickness/span ratio, the aspect ratio, and the boundary conditions on the linear responses of thick plates subjected to earthquake excitations. In the analysis, finite element method is used for spatial integration. For the formulation of the equations of the thick plate theory, a finite element is derived by using higher-order displacement shape functions which is named MT17. This is a fourth-order finite element that shows excellent performance for thick plate analysis. A computer program using finite element method is coded in C++ to analyze the plates clamped or simply supported along all four edges. Graphs are presented that should help engineers in the design of thick plates subjected to earthquake excitations. It is concluded that MT17 element can be effectively used in the earthquake analysis of thick plates. It is also concluded that in general, the changes in the thickness/span ratio are more effective on the maximum responses considered in this study than the changes in the aspect ratio.