Contact interaction of the plate with supporting deformable bases under the conditions of bending

Abstract

© Published under licence by IOP Publishing Ltd. We consider a one-dimensional linear problem on the transverse bending of a plate, which is cantilevered in an absolutely rigid and fixed support through elastic and resting support elements of finite length, which are transversally soft bases for the plate. The research is based on the previously proposed equations constructed using the known Kirchhoff-Love and S.P. Timoshenko models for the plate, and for bases using the equations of elasticity theory simplified in accordance with the model of a transversally soft layer and integrated over the transverse coordinate with satisfaction of the kinematic conditions of the interface between the plate and the bases. Numerical solutions of the problem were found by the finite element method on the basis of using the application package ANSYS and by integrating the one-dimensional equations used by the finite sum method. On the basis of a comparison of the solutions found, the quality of the previously proposed equations is analyzed in relation to static problems on the deformation of plates elastically fixed at one end in the support element.