Abstract
Taking into account (or leaving out) the transverse shear deformations, we formulate the governing equations of shallow shells of variable thickness and variable initial curvatures as a coupled problem of a constant rigidity Reissner (or Kirchhoff) plate and an uniform thickness plane-stress sheet subjected to the fictitious loads. The sheets and plates are treated as the special cases of the shallow shells. The equivalence relation of these two plate-models for the polygonal simply-supported plate and axisymmetric bending is proved here. For the spline integral equation method we use only the known and simple fundamental solutions of the plate and sheet of consstant thickness. The shapes, loads and supports of the shallow shells can be in any form. The satisfactory results could be given even with coarse division.
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