On the formulation and solution of shell problems by means of computerized algebraic manipulation

Abstract

The basic equations of shell theory are conveniently formulated as tensor equations. However, the compactness and elegance of tensor notation are counteracted by the fact that the writing out of tensor equations for a given coordinate system results in tedious and cumbersome work in all but the simplest of cases. Use of the symbolic and algebraic manipulation language TENSOR FORMAC removes this limitation. It is shown that TENSOR FORMAC makes it possible to generate and handle, say, the equations of equilibrium expressed in the displacements, for a shell described by a non-trivial coordinate system with non-linear geometric effects taken into account. The solution of the system of equations generated manually or by TENSOR FORMAC can only be expressed in a few, exceptionally simple cases by elementary functions. But for axisymmetric deformations of shells of revolution is it possible to obtain the solution of the system of equations as a power series expansion utilizing a symbolic and algebraic manipulation language.