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.

A weighted extended B-spline solver for bending and buckling of stiffened plates

“…This case has been solved in several works, for example [47,14,16]. A square plate with a free hole in its center is uniformly loaded in-plane at its left and right boundary, cf.…”

“…Another class of methods are the sometimes called semi-analytic methods based on Navier's sine solution. Among these we find the method by [15] for rectangular plates and stiffener arrangements and the one by [16] for buckling of plates of more complex geometries. As a method, which is more related to the present work, B-splines have been in use for plate deformation, vibration and buckling problems, for example for rectangular domains [17,18,19,20] or in connection with the isoparametric stripe approach for more complicated geometries [21,22].…”

Unconventional Bearing Capacity Analysis and Optimization of Multicell Box Girders

“…Studies of elastic stability of uniform vertical and longitudinally stiffened girder plates subjected to bending moment and live loads are presented in [ 9 – 12 ]. A significant contribution to this field is that of the analytical approach to stability analysis of perforated plates [ 13 ] which is based on a mathematical model, the basic assumptions of which are presented in [ 14 – 16 ]. The systematic analysis of local stresses in a transversely loaded box girder of rectangular cross section is provided in [ 17 ].…”