Free vibration analysis for shells of revolution based on p-version mixed finite element formulation

• We present a new p-version mixed finite element for free vibration analysis of shells of revolution.
• The introduction of hierarchical high-order displacement functions and field-consistent stress parameters yield locking-free and accurate numerical results.
• The loss of accuracy due to Guyan reduction in formulating the present mixed finite element is not observed.
• The element having the cubic displacement functions and quadratic stress resultant functions shows the most efficient performance.

In this study, an effective p-version two-node mixed finite element is newly presented for predicting the free vibration frequencies and mode shapes of isotropic shells of revolution. The present element considering shear strains is based on Reissner–Mindlin shear deformation shell theory and Hellinger–Reissner variational principle. To improve the accuracy and resolve the numerical difficulties due to the spurious constraints, field-consistent stress parameters are employed corresponding to displacement shape functions with high-order hierarchical shape functions. The elimination of stress parameters and the reduction of the nodeless degrees by the Guyan reduction yield the standard stiffness and mass matrix. Results of the proposed element are compared with analytical, experimental and numerical solutions found in the literature. We can confirm a very satisfactory numerical behavior of the present p-version mixed element.