Solution of stability problem of infinite plate strips

The aim of the paper is to solve a stability problem of infinite plate strips using the finite strip method (FSM). Contrary to well-known solutions for 2D continuous systems the authors present an idea for solving a stability problem of infinite discrete plates.

A continuous plate strip simply supported on its opposite edges is divided into a regular mesh of identical finite strips. According to the finite strip procedure the field of loading and displacement functions are expressed in the form of harmonic series [

1

]. Stiffness and geometrical matrices for a four-degree-of-freedom finite strip are determined.

The unknowns are deflections and transverse slope amplitudes along the nodal lines. Equilibrium conditions are derived from the FSM formulation. An infinite set of linear equations being the equilibrium conditions for each nodal line is expressed in the form of two second-order difference equations [

2

]. For a regular discrete system these equations written in the recurrent form are equivalent to the FSM matrix formulation.

The exact solution of these difference equations is found in an analytical form. The displacement function fulfils the boundary conditions of the analysed plate strip and is given as a discrete expression for an arbitrary nodal load [

3

].

The solution of eigenvalue problem of the difference equations enables one to determine the critical forces of the structure. The main advantage of the presented approach is the analytical form of the solution obtained in the discrete domain. This enables a detailed parametrical analysis and investigations of the influence of geometrical and physical properties on the critical force value.