Treffer: Layer wise finite element for mechanical buckling of FGM plates under non-uniform edge loading

In many engineering handbooks and texts, the dependence of buckling loads on in-plane loads are given for uniform type of in-plane loading. However, plates are usually part of complex structural systems and in-plane load may not be always linear. These are the cases of structures like I-beams or wide flange beam subjected to bending moments at the end or lateral loads on the flange, while the web of the beam is under non-uniform in-plane loads. Over the last decades, due to the advance properties of functionally graded materials (FGM), when compared to the laminated composites, the demand for buckling analysis of FGM plates subjected to in‐plane loads is increased. Therefore, in this paper, the elastic stability analysis of functionally graded material (FGM) plate under non-uniform mechanical in–plane load is analysed. The displacement model based on Generalized Laminate Plate Theory (GLPT) assumes piece–wise linear variation of in–plane displacements, constant transverse displacement, non–linear strain–displacement relations (in von Karman sense) and linear material properties. The properties of FGMs are assumed to be constant in xy–plane and vary through thickness by a power law function in terms of volume fraction of the constituents. The mathematical model includes the quadratic variation of transverse shear stresses within each layer of the plate. The principle of virtual displacements (PVD) is used to derive the weak form of linearized buckling problem. Linearized buckling problem is solved using Finite element method (FEM). In-plane plate is discretized using nine node Lagrangian isoparametric finite element or 2D quadratic in-plane interpolation, while 1D Lagrangian interpolation is used for discretization through the thickness. The original MATLAB computer program is coded for the FEM numerical solution. The solutions are verified by comparison with the results from the literature. The results are shown that the effects of in-plane load distribution, side–to–thickness ratio b/h and power–low index had ...