Mathematical Identification of Influential Parameters on the Elastic Buckling of Variable Geometry Plate

Abstract

The problem of elastic stability of plates with square, rectangular, and circular holes as well as slotted holes was discussed. The existence of the hole reduces the deformation energy of the plate and it affects the redistribution of stress flow in comparison to a uniform plate which causes a change of the external operation of compressive forces. The distribution of compressive force is defined as the approximate model of plane state of stress. The significant parameters of elastic stability compared to the uniform plate, including the dominant role of the shape, size, and orientation of the hole were identified. Comparative analysis of the shape of the hole was carried out on the data from the literature, which are based on different approaches and methods. Qualitative and quantitative accordance of the results has been found out and it verifies exposed methodology as applicable in the study of the phenomenon of elastic stability. Sensitivity factor is defined that is proportional to the reciprocal value of the buckling coefficient and it is a measure of sensitivity of plate to the existence of the hole. Mechanism of loss of stability is interpreted through the absorption of the external operation, induced by the shape of the hole.