Elastic stability of all edges clamped stepped and stiffened rectangular plate under uni-axial, bi-axial and shearing fo
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Elastic stability of all edges clamped stepped and stiffened rectangular plate under uni-axial, bi-axial and shearing forces A. John Wilson · S. Rajasekaran
Received: 29 April 2012 / Accepted: 22 April 2013 © Springer Science+Business Media Dordrecht 2013
Abstract The stability of clamped stepped and stiffened rectangular plate subjected to in-plane forces is examined. The plate is divided into 900 rectangular meshes and the partial derivatives are approximated using central difference formula. Altogether 841 equations of equilibrium and 248 equations representing boundary conditions are formed, finally leading to the solution of eigenvalue problem. The buckling coefficients are calculated for various types of stepped plates and the results are presented in tables for ready use by designers. The results are compared with the published results and they are in close agreement. Keywords Critical loads · Stepped plates · Stiffened plate · Eigenvalue · Finite difference method · Buckling coefficient Nomenclature a length of the plate a1 step length
A. John Wilson was retired from Dept. of Mathematics, Coimbatore Institute of Technology. A. John Wilson () Dept. of Mathematics, Coimbatore Institute of Technology, Coimbatore 641014, India e-mail: [email protected] S. Rajasekaran Dept. of Civil Engineering, P.S.G. College of Technology, Coimbatore 641004, India e-mail: [email protected]
b a/b D E K KG k, ke l m M M N nj Nx , Ny , Nxy Pcr t ti w x, y α β, γ , δ λ ν τ σx , σy , σ
width of the plate panel aspect ratio flexural rigidity of the plate Young’s modulus flexural stiffness geometric stiffness buckling coefficients mesh length mesh breadth number of divisions in y direction mass matrix number of divisions in x direction number of joints in-plane forces critical load thickness of the plate step thickness lateral deflection Cartesian coordinates ratio between the breadth and length of a mesh tracers corresponding to Nx , Ny , Nxy eigenvalue Poison’s ratio shear stress compressive stresses
1 Introduction Non uniform plates such as stepped or perforated are used in many modern engineering applications.
Meccanica
Examples of such thin walled members include suspension bridge pylons, bridges, flyovers dock gates as well as I and box sections used in plate girder bridges and power stations. The variable thickness helps us to reduce the weight of the structure, stiffness enhancing and designated strengthening etc. The weight reduction is utmost important in space structures. In designing the metal structures the determination of buckling load forms a key factor. For limited cases such as plates of uniform thickness, exact buckling loads are available. The flexural stiffness and buckling capacity of regular plates may significantly be increased by appropriate geometrical stepping. In particular, buckling of stepped plates has attracted much more attention in the past few decades. This type of plate is used extensively because of its high strength to weight ratio. A variety of theoretical approaches have b
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