Elastsete plaatide painde ülesanded

Abstract

The aim of this work is to introduce the Basic equations of the Kirchhoff’s bending theory. The current study consists on two parts. In the first part we derive the governing differential equation for the deflection for thin plate bending. In the second part we study the bending of thin rectangular plates subjected to the transverse pressure. We find the middle surface of the plate in the case of cylindrical bending. It appears that in this case the differential equation of equilibrium can be solved by direct integration. Also we present Navier’s method for rectangular plates with simply supported boundary conditions on all four edges. We look for the solution of the equilibrium equation in the form of double seires. Each term of this series is a product of trigonometrical functions which meet the boundary conditions spontaneously.