Elastic buckling of a porous beam

The work deals with the problem a straight beam of a rectangular cross-section pivoted at both ends and loaded with a lengthwise compressive force. The beam is made of an isotropic porous material. Its properties vary through thickness of the beam. The modulus of elasticity is minimal on the beam axis and assumes maximum values at its top and bottom surfaces. The principle of stationarity of the total potential energy enables one to define a system of differential equations that govern the beam stability. The system is analytically solved, which leads to an explicit expression for the critical load of the compressed beam. Results of the solution are verified on an example beam by means of the Finite Element Method (COSMOS).