Abstract
A high precision triangular shallow shell element is proposed and it is applied to free vibration analysis of composite and isotropic shells. The Mindlin's hypothesis is followed to include the effect of shear deformation. The formulation is made in an efficient manner to make the element free from shear locking problem. The element has some internal nodes, which are eliminated through static condensation technique to improve the computational elegance of the element. In the present vibration problem, the implementation of the static condensation became possible with the help of an efficient mass lumping scheme. It is quite interesting that the effect of rotary inertia can be included in the recommended scheme for lumped mass matrix. Numerical examples covering a wide range of problems are solved and the results obtained are compared with the published results in many cases, which show the precision and range of applicability of the proposed element. The performance of the proposed technique for rotary inertia is found to be excellent. Some new results are produced, which may be useful in future research.