Legendre spectral finite elements for structural dynamics analysis

• Published in: Communications in numerical methods in engineering Vol. 24; no. 12; pp. 1953 - 1965
• Main Authors: Sprague, M. A., Geers, T. L.
• Format: Journal Article
• Language: English
• Published: Chichester, UK John Wiley & Sons, Ltd 01-12-2008; Wiley
• Subjects: Computational techniques; Exact sciences and technology; finite-element method; Fundamental areas of phenomenology (including applications); hierarchical; high order; Mathematical methods in physics; p-type; Physics; Solid mechanics; Structural and continuum mechanics; Timoshenko beam; Vibration, mechanical wave, dynamic stability (aeroelasticity, vibration control...); Transient response; Spectral method; Vibration; high order; Timoshenko beam; finite-element method; Factorization; Modeling; Legendre polynomial; Finite element method; Diagonal matrix; p type semiconductor; hierarchical; p-type; Mindlin model; Mass matrix; Eigenvalue problem; Structural analysis
• ISSN: 1069-8299; 1099-0887
• DOI: 10.1002/cnm.1086

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.