On some properties of 2D spectral finite elements in problems of wave propagation

  • Authors:

  • Wojciech Witkowski;Magdalena Rucka;Jacek Chrócielewski;Krzysztof Wilde

  • Affiliations:

  • Department of Structural Mechanics and Bridge Structures, Faculty of Civil and Environmental Engineering, Gdansk University of Technology, Narutowicza 11/12, 80-233 Gdańsk, Poland;Department of Structural Mechanics and Bridge Structures, Faculty of Civil and Environmental Engineering, Gdansk University of Technology, Narutowicza 11/12, 80-233 Gdańsk, Poland;Department of Structural Mechanics and Bridge Structures, Faculty of Civil and Environmental Engineering, Gdansk University of Technology, Narutowicza 11/12, 80-233 Gdańsk, Poland;Department of Structural Mechanics and Bridge Structures, Faculty of Civil and Environmental Engineering, Gdansk University of Technology, Narutowicza 11/12, 80-233 Gdańsk, Poland

  • Venue:
  • Finite Elements in Analysis and Design
  • Year:
  • 2012

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Abstract

A computational analysis of plane progressive wave propagation in plane stress body is presented. The initial-boundary value problem of linear elastodynamics of Cauchy continuum is approximated spatially by specially designed multi-node C^0 displacement-based isoparametric quadrilateral spectral finite elements. To integrate element matrices the Gauss-Lobatto-Legendre quadrature rule is used. The temporal discretization is carried out by Newmark type algorithm reformulated to accommodate the structure of local element matrices. The developed multi-node spectral elements with Gauss-Lobatto-Legendre nodes are validated by running some statics and dynamics tests to investigate the presence of locking effect and of spurious zero-energy modes. Dynamic tests, dedicated to wave propagation in L-shaped structure, are concentrated on energy propagation through right-hand angle of the construction.