A direct approach for three-dimensional elasto-static and elasto-dynamic solutions in curvilinear cylindrical coordinates with application to classical cylinder problems

This paper deals with introducing a unique representation of the three-dimensional Navier's equations motion in cylindrical coordinate system an exact simplified form without any approximation, aiming at facilitating solution procedure for different 3-D elasto-static and elasto-dynamic problems future. A novel elasticity including body forces is derived uncoupled terms longitudinal (axial) displacement component ‘r-θ’ in-plane anti-symmetric rotation function instead additional auxiliary unknown potential function. The other components (i.e., circumferential radial components) are shown to be obtained from two independent determined axial aforementioned component. correctness, validity easy implementation introduced approach obtaining solutions various demonstrated through solving number known problems. Three-dimensional static free vibrations finite-length solid cylinders as well thick-walled hollow shells analytically solved. Numerical comparative results discussion conducted. Excellent agreement between those reported literature observed all cases, confirming proposed new approach. • curvilinear coordinates. General scheme Exact analytical solutions. Non-axisymmetric vibration behavior shells.