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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]

Based on energy functional and with the inclusion of high-order incompatible dynamic displacement modes, a formulation for 3-D finite dynamic element method (DEM) is developed and a new 8-node solid element is derived in this paper. Numerical results exhibit that the present method provides the most economical and efficient solution when compared with the usual FEM and DEM. Copyright © 2000 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

Computational costs for detailed Finite Element approximations can be reduced by using reduced-order models instead. In this contribution, four subspace-based reduced-order modeling methods are compared. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim) [ABSTRACT FROM AUTHOR]