Dynamic equations for a spherical shell

Artikel i vetenskaplig tidskrift, 2012

Using a series expansion technique together with recursion relations the dynamic equations for an elastic spherical shell are derived. The starting point is an expansion of the displacement components into power series in the thickness direction relative the mid-surface of the shell. The three-dimensional elastodynamic equations yield recursion relations among these that can be used to eliminate all but the six of lowest order. The boundary conditions on the surfaces of the shell then give the shell equations as a power series in the thickness that can in principle be truncated to any order. The method is believed to asymptotically exact to any order. Comparisons are made with correct three-dimensional theory and other shell theories.