Buckling of cracked functionally graded plates supported by Pasternak foundation

•Buckling of cracked FGM plates resting on elastic foundation was studied.•Classical plate theory with special elements around crack tips was used.•As crack grows the effect of foundation stiffness on buckling load decreases.•In bi-axial loading the effect of foundation stiffness on buckling is smaller.•Effect of Poisson׳s ratio on buckling is different in high and low stiffnesses.

Buckling of cracked functionally graded plates resting on Pasternak foundation under tension has been studied. Classical plate theory in framework of the finite element method has been used. Shape functions for elements surrounding crack tips have been derived using previous solutions of displacement fields around crack tips. In-plane loads have been obtained by a pre-buckling solution using quarter-point elements around crack tips. Results show that an increase of foundation stiffness, leads to greater values of buckling loads. For longer cracks the effect of foundation stiffness on buckling load diminishes. For bi-axial loading such stiffness has less effect on buckling compared to uni-axial case.

Graphical abstractThis figure shows the first mode of buckling of a cracked FGM plate under uni-axial tension along with the graph of critical load versus crack length to plate width ratio for different foundation stiffnesses.Figure optionsDownload full-size imageDownload as PowerPoint slide