Simplifications under the kirchhoff hypothesis of taber's nonlinear theory for the axisymmetric bending and torsion of elastic shells of revolution

Abstract

We show that, under the Kirchhoff hypothesis, Taber's recent theory for the simultaneous axisymmetric bending and torsion of shells of revolution undergoing large strains can be simplified considerably. In general, his 33 equations can be reduced to four first-order ordinary differential equations and two algebraic equations for six unknowns. For small strains, the equations can be reduced further to two coupled nonlinear equations for the meridional angle of rotation and a stress function, as in Reissner's theory of torsionless, axisymmetric deformation.