FINDING CRITICAL BUCKLING LOAD OF RECTANGULAR PLATE USING INTEGRATED FORCE METHOD

A method which couples equilibrium equations and compatibility conditions that are developed based on equilibrium equations by using a systematic concatenation procedure is proposed here for the plate buckling analysis. A RECT_9F_12D plate bending element having 9 force unknowns and 12 displacement degrees of freedom is used with the necessary matrix formulation based on the Integrated Force Method (IFM). The geometric stiffness matrix required for buckling analysis is explicitly derived. Matlab software is used to develop compatibility conditions whereas other calculations are carried out in a program developed in VB.NET. A rectangular plate under uniaxial loading is analysed under 7 different boundary conditions. A case of biaxial loading of simply supported plate with loading ratio equals to one is also attempted using the proposed formulation. Results are obtained by considering either 2 x 2 discretization of quarter plate or 4 x 2 discretization of half plate depending upon the type of symmetry available based on support conditions. Results are compared with the available classical solutions to demonstrate the effectiveness of the proposed method; a good agreement is indicated.