On shallow shell equations
The author presents explicit formulas for the shallow shell model consisting of a coupled system of a wave equation and a plate equation, where the middle surface is viewed as a natural manifold with the induced metric from the classical Euclidean space of three dimensions. The Green formula for the shallow shell is given by the displacement field which expresses the relationship between the interior and the boundary. Next, the ellipticity of the strain energy for the shallow shell is studied under some curvature assumptions on the middle surface. Finally, the motion equations for shallow shells are obtained in terms of the displacement field as an unknown. The new ingredients in these formulas are that they take a form which is not described by a coordinate patch to provide the shell theory with the modern geometry.
scientific article; zbMATH DE number 5613328