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Analytic solution of rectangular plate buckling with rotationally restrained and free edges
Abstract In this research a new analytical solution is used for finding the buckling loads of rectangular plates with rotationally restrained edges. Until now, analytical solution were available only for a small number of specific combinations of boundary conditions. The solution method in this study is based on the development of a static solution for a plate. The solution is obtained in series form, and the coefficients are solved to match the edge conditions. The solution fits all the combinations of possible boundary conditions, of the deflection, slope, shear force and bending moment along the edges of the plate. The problem of buckling of part of an open cross section with a free edge is solved analytically. Any number of edges, from one to four, with rotational stiffening springs can be solved. Using this new method, the exact buckling loads and modes are found. The results are verified with published data, and many new cases are presented for uni-axially and bi-axially loaded plates.
Graphical abstract Display Omitted
Highlights Static analysis is used to find the exact buckling loads of plates. Exact buckling loads for plates with many combinations of boundary conditions and - rotational restraints are presented. Increase of the rotational stiffness results in higher buckling loads and higher number of waves in the mode shape.
Analytic solution of rectangular plate buckling with rotationally restrained and free edges
Abstract In this research a new analytical solution is used for finding the buckling loads of rectangular plates with rotationally restrained edges. Until now, analytical solution were available only for a small number of specific combinations of boundary conditions. The solution method in this study is based on the development of a static solution for a plate. The solution is obtained in series form, and the coefficients are solved to match the edge conditions. The solution fits all the combinations of possible boundary conditions, of the deflection, slope, shear force and bending moment along the edges of the plate. The problem of buckling of part of an open cross section with a free edge is solved analytically. Any number of edges, from one to four, with rotational stiffening springs can be solved. Using this new method, the exact buckling loads and modes are found. The results are verified with published data, and many new cases are presented for uni-axially and bi-axially loaded plates.
Graphical abstract Display Omitted
Highlights Static analysis is used to find the exact buckling loads of plates. Exact buckling loads for plates with many combinations of boundary conditions and - rotational restraints are presented. Increase of the rotational stiffness results in higher buckling loads and higher number of waves in the mode shape.
Analytic solution of rectangular plate buckling with rotationally restrained and free edges
Tenenbaum, J. (author) / Eisenberger, M. (author)
Thin-Walled Structures ; 157
2020-07-14
Article (Journal)
Electronic Resource
English
Buckling of Orthotropic Plates with Free and Rotationally Restrained Unloaded Edges
| Online Contents | 1996
| British Library Online Contents | 2018