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Buckling of Plates and Prismatic Shells
Buckling of rectangular plates and thin-walled beams, modeled as prismatic shells, is analyzed. The Kirchhoff plate linear theory is briefly recalled, by following a variational procedure. Plates subject to membrane prestress are then considered, for which, by taking into account the geometric effects, the equilibrium equations and the boundary conditions, holding in the adjacent configuration, are derived. Buckling of rectangular plates under various compression/tensile loads and constraints is successively studied. A one-dimensional exact finite element is formulated, describing the transverse elastic line of a plate, compressed in one direction and simply supported on the loaded sides. The finite element is also used to analyze a plate stiffened by a longitudinal rib. The buckling problem for a plate subject to in-plane uniform shear stress is addressed. The exact solution is given for infinitely long plates. Plates of finite dimensions are then considered, for which the problem is solved in approximate way by the Ritz method. Finally, buckling of thin-walled members, modeled as prismatic shells, is studied, which suffer three different forms of instability, global, distortional and local. The method of finite strips is illustrated for the analysis of compressed thin-walled members. Limiting the attention to the local critical load (and, in some cases, distortional), an exact one-dimensional finite element is introduced, which describes the transverse deformation of the shell, and therefore said sectional model. Finally, the mechanical behavior of various open thin-walled members is discussed, by numerically investigating the effects of stiffening ribs, capable to qualitatively modify the instability pattern.
Buckling of Plates and Prismatic Shells
Buckling of rectangular plates and thin-walled beams, modeled as prismatic shells, is analyzed. The Kirchhoff plate linear theory is briefly recalled, by following a variational procedure. Plates subject to membrane prestress are then considered, for which, by taking into account the geometric effects, the equilibrium equations and the boundary conditions, holding in the adjacent configuration, are derived. Buckling of rectangular plates under various compression/tensile loads and constraints is successively studied. A one-dimensional exact finite element is formulated, describing the transverse elastic line of a plate, compressed in one direction and simply supported on the loaded sides. The finite element is also used to analyze a plate stiffened by a longitudinal rib. The buckling problem for a plate subject to in-plane uniform shear stress is addressed. The exact solution is given for infinitely long plates. Plates of finite dimensions are then considered, for which the problem is solved in approximate way by the Ritz method. Finally, buckling of thin-walled members, modeled as prismatic shells, is studied, which suffer three different forms of instability, global, distortional and local. The method of finite strips is illustrated for the analysis of compressed thin-walled members. Limiting the attention to the local critical load (and, in some cases, distortional), an exact one-dimensional finite element is introduced, which describes the transverse deformation of the shell, and therefore said sectional model. Finally, the mechanical behavior of various open thin-walled members is discussed, by numerically investigating the effects of stiffening ribs, capable to qualitatively modify the instability pattern.
Buckling of Plates and Prismatic Shells
Luongo, Angelo (author) / Ferretti, Manuel (author) / Di Nino, Simona (author)
Stability and Bifurcation of Structures ; Chapter: 10 ; 331-401
2012-02-24
71 pages
Article/Chapter (Book)
Electronic Resource
English
Buckling of rectangular plates , Geometric bearing capacity of a plate , Transverse elastic line , 1D finite element for separable variable problems , Ritz method for plates , Ribbed plates , Exact and approximate solutions for plates under shear stress , Local instability of thin-walled members , Finite strip method for compressed thin-walled members , Finite element sectional model for local buckling Engineering , Mechanical Statics and Structures , Solid Mechanics , Mechanical Engineering , Structural Materials , Solid Construction , Building Construction and Design
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