Modified Mixed Variational Principle and the State-Vector Equation for Elastic Bodies and Shells of Revolution

A modified mixed variational principle is established for a class of problems with one spatial variable as the independent variable. The specific applications are on the three-dimensional deformation of elastic bodies and the nonsymmetric deformation of shells of revolution. The possibly novel feature is the elimination in the variational formulation of the stress components which cannot be prescribed on the boundaries. The result is a form exactly analogous to classical mechanics of a dynamic system, with the equations of state exactly in the form of the canonical equations of Hamilton. With the present approach, the correct scale factors of the field variables to make the system self-adjoint are readily identified, and anisotropic materials including composites can be handled effectively. The analysis for shells of revolution is given with and without the transverse shear deformation considered.