A perturbation method for dynamic analyses using under-integrated shell elements

Abstract An efficient perturbation method that allows reliable and accurate dynamic analyses of general shell structures using under-integrated elements is proposed. Both the perturbation of the stiffness matrix and the projection of the mass matrix are performed directly in the global coordinate system (thus avoiding local-global transformations of element matrices), and only once for each element instead of at each integration point. The method does not require any factor to be fully integrated over the element. Due to the consistency of the perturbed stiffness, the 9-node element passes several patch tests, including higher order ones. Further, algebraic expression for the projection operator of the mass matrix is derived and contributes significantly to the efficiency of the methodology. Several examples are presented to assess the effectiveness of the proposed method in filtering all spurious modes from the eigenspectrum, and the accuracy of the resulting eigenfrequencies of the genuine mode shapes.