Development of a higher order finite element on a Winkler foundation

Analyzing thick plates as a construction component has been of interest to structural engineering research for several decades. In particular, thick plates resting on elastic foundations are more specific. Mindlinʹs plate theory for thick plate analysis and the Winkler theory for elastic foundation analyses have wide applications. The current research considers analysis of isotropic plates on a Winkler foundation according to Mindlinʹs plate theory. The analysis uses a higher order plate element to avoid shear locking phenomena in the plate. The main features of this element are representation of real displacement functions of the plate perfect and shear locking do not occur at the plates modeled with this element. Derivation of the equations for finite element formulation for thick plate theory uses fourth-order displacement shape functions. A computer program using the finite element method, coded in C++, analyzes the plates resting on an elastic foundation. The analysis involves a 17-noded finite element. The studyʹs graphs and tables assist engineersʹ designs of thick plates resting on elastic foundations. The study concludes with the computer-coded program, which allows effective use for the shear locking-free analysis of thick Mindlin plates resting on elastic foundations.