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

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 C0 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.

► Multi-node quadrilateral spectral finite element is elaborated.
► Its applicability to problems with irregularities of FEM mesh is evaluated.
► Locking, spurious zero-energy modes, influence of mesh distortion on dispersion are studied.
► Temporal integration takes an advantage of the diagonal structure of element matrices.
► Propagation of elastic wave in L-shaped structure is analyzed.