Axisymmetric Deformation of a Transversely Isotropic Cylindrical Body: A Hamiltonian State-Space Approach

Abstract

A state-space approach for exact analysis of axisymmetric deformation and stress distribution in a circular cylindrical body of transversely isotropic material is developed. By means of Hamiltonian variational formulation via Legendre’s transformation, the basic equations in cylindrical coordinates are formulated into a state-space framework in which the unknown state vector comprises the displacements and associated stress components as the dual variables and the system matrix possesses the symplectic characteristics of a Hamiltonian system. Upon delineating the symplecticity of the formulation, a viable solution approach using eigenfunction expansion is developed. For illustration, an exact analysis of a finite thick-walled circular cylinder under internal and external pressures is presented, with emphasis on the end effects.