Triangular ring element with analytic expressions for stiffness and mass matrix (Q1096465)

An analytic approach for the generation of stiffness and consistent mass matrix in the case of ring elements is performed. The pure axisymmetric problem is extended with a tangential Fourier expansion of the load and corresponding displacement field. The element geometry employed is a triangular ring element with linear and quadratic displacement assumptions, respectively. No a priori assumption of the element orientation is required. The stiffness and mass matrices are written as linear combinations of a number of basic element matrices given by a few element parameters. The matrices are tested in a computer program solving nonaxisymmetric vibration of axisymmetric solids. The eigenvalue problem is solved by `subspace iteration'. The matrices are found to be extremely numerically stable.