An Investigation of the Out-of Plane Deflection Behavior of Thin Sheets with Cut-Outs in a Tensile Field.
GEORGIA INST OF TECH ATLANTA SCHOOL OF AEROSPACE ENGINEERING
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The problem of a tensioned thin plate containing a centrally located hole is considered. The Karman plate formulation for moderately large deflection is extended to include multiply connected plates by deriving the set of auxiliary conditions which must be satisfied by a solution on each internal boundary. The coupled, nonlinear Karman equations may be linearized and uncoupled under specified conditions and then the equations describe a plane stress elasticity problem and a buckling problem with a nonuniform prebuckle stress state. The stress distribution for a tensioned infinite sheet with a slot hole is determined by a complex variable analysis. Results of a photoelastic stress analysis for finite width plates are also presented and compared with the complex variable solution for the same hole geometries. By an examination of the stability problem, it is shown that a Southwell form load-displacement relation can be derived. The limit of applicability of the Southwell technique is found to depend on the extent to which stiffening due to middle surface stretching influences the load-deflection response. A method of experimentally detecting this effect is described and used as a basis for an experimental study of the local buckling behavior of tensioned sheets with slots. The buckling data obtained are analyzed and a relation for the tensile buckling stress as a function of slot geometry is developed. Author