Temporal-spatial dispersion and stability analysis of finite element method in explicit elastodynamics

DOI10.1002/nme.5010zbMath1352.74381OpenAlexW2151532419MaRDI QIDQ2952878

M. Okrouhlík, J. Cerv, Petr Pařík, Radek Kolman, Jiří Plešek

Publication date: 30 December 2016

Published in: International Journal for Numerical Methods in Engineering (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1002/nme.5010

zbMATH Keywords

stability analysisfinite element methodwave propagationbilinear and biquadratic serendipity finite elementstemporal and spatial dispersion

Mathematics Subject Classification ID

Finite element methods applied to problems in solid mechanics (74S05) Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs (65M12) Linear waves in solid mechanics (74J05) Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs (65M60)

Related Items (7)

A two-layer elastic strip under transverse impact loading: analytical solution, finite element, and finite volume simulations ⋮ Finite element method based computational time reversal in elastodynamics: refocusing, reconstruction and its numerical sensitivity ⋮ Bi-penalty stabilized technique with predictor-corrector time scheme for contact-impact problems of elastic bars ⋮ Wave motion in a thick cylindrical rod undergoing longitudinal impact ⋮ B-spline based finite element method in one-dimensional discontinuous elastic wave propagation ⋮ Staggered explicit-implicit time-discretization for elastodynamics with dissipative internal variables ⋮ Variationally consistent inertia templates for B-spline- and NURBS-based FEM: inertia scaling and customization

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Mass matrix templates: general description and 1D examples
• Variational methods for selective mass scaling
• Finite element modeling of linear elastodynamics problems with explicit time-integration methods and linear elements with the reduced dispersion error
• Accurate finite element modeling of linear elastodynamics problems with the reduced dispersion error
• The serendipity family of finite elements
• Dispersion analysis of spectral element methods for elastic wave propagation
• Dispersion of elastic waves in the contact-impact problem of a long cylinder
• Finite element methods for the Helmholtz equation in an exterior domain: Model problems
• Complex wavenumber Fourier analysis of the \(p\)-version finite element method
• Stability analysis of an explicit finite element scheme for plane wave motions in elastic solids
• Isogeometric numerical dispersion analysis for two-dimensional elastic wave propagation
• The influence of the mass matrix on the dispersive nature of the semi-discrete, second-order wave equation
• Evaluation of numerical integration methods in elastodynamics
• A method for multidimensional wave propagation analysis via component-wise partition of longitudinal and shear waves
• Grid dispersion analysis of plane square biquadratic serendipity finite elements in transient elastodynamics
• The effects of element shape on the critical time step in explicit time integrators for elasto-dynamics
• Eigenvalues and Stable Time Steps for the Uniform Strain Hexahedron and Quadrilateral
• A survey of direct time-integration methods in computational structural dynamics—I. Explicit methods
• Dispersion analysis of finite element semidiscretizations of the two-dimensional wave equation
• Finite element dispersion analysis for the three‐dimensional second‐order scalar wave equation
• Practical aspects of numerical time integration
• A contribution to the study of dispersive properties of one-dimensional Lagrangian and Hermitian elements
• Rayleigh wave dispersion due to spatial (FEM) discretization of a thin elastic solid having non-curved boundary
• Selective mass scaling for explicit finite element analyses
• Bounds on the extremal eigenvalues of the finite element stiffness and mass matrices and their spectral condition number
• Symmetry preserving algorithm for large displacement frictionless contact by the pre‐discretization penalty method
• Dispersion-corrected explicit integration of the wave equation

This page was built for publication: Temporal-spatial dispersion and stability analysis of finite element method in explicit elastodynamics