A state space formalism for anisotropic elasticity.: Part II: Cylindrical anisotropy

A state space formalism for thermoelastic analysis of a cylindrically anisotropic elastic body is developed. By proper grouping of the stress and taking rrij instead of rij as the stress variables, the three-dimensional equations of elasticity in the cylindrical coordinates are concisely formulated into a state equation and an output equation using matrix notations. The general solution for the generalized plane problems is derived in a simple manner. Effects of extension, torsion, bending, temperature change and body force are accounted for systematically. The eigen relation arising from the solution process and the degenerate cases of repeated eigenvalues are examined. To demonstrate the power of the formalism, exact solutions to extension, torsion, bending and thermo-mechanical loading of a general cylindrically anisotropic circular tube or bar are obtained. The surface tractions and temperature field may vary in h but not in z. Displacement as well as traction boundary conditions are considered. It appears that many problems of anisotropic elasticity are best viewed and treated in the state space framework