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

Journal article, 2022

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