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Spectral, hierarchical, and h-type finite elements (FEs) are compared in the context of their application to structural dynamics analysis. The Timoshenko beam, which is the 1-D analog of Mindlin-type shell elements, is used for comparison in eigenvalue and transient-response analyses. A detailed formulation of each method is presented to illustrate clearly their fundamental differences. The principal advantages of spectral FEs over low-order h-type elements are (a) far superior accuracy for a fixed number of model degrees of freedom (DOF) and (b) much higher computational efficiency at a fixed accuracy level. The principal advantages over hierarchical p-type elements are (a) a mass matrix that is inherently diagonal as opposed to full, (b) DOF that pertain directly to nodal displacements and rotations, and (c) more efficient tensor-product factorization. Copyright © 2007 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

In a dynamic unbounded medium–structure interaction analysis in the time domain performed with the substructure method the unit-impulse response function on the structure–medium interface of the unbounded medium is determined. The consistent infinitesimal finite element cell method based solely on the finite element formulation has been developed for compressible elasticity. In this paper the procedure is expanded to the incompressible case. The limit of Poisson's ratio =0·5 is performed analytically. This yields a concentrated mass in the formulation representing the instantaneous response over the entire domain not present in compressible elasticity. The only modification appears in the coefficient matrices of the consistent infinitesimal finite element equation which can be solved with the same numerical algorithm as in the compressible case. Excellent accuracy results also in very complicated inhomogeneous situations. © 1997 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]