Time finite element methods for structural dynamics
TLDR
In this paper, the time-discontinuous Galerkin and least-squares methods for structural dynamics were used to prove a general convergence theorem in a norm stronger than the energy norm.Abstract:
SUMMARY Time finite element methods are developed for the equations of structural dynamics. The approach employs the time-discontinuous Galerkin method and incorporates stabilizing terms having least-squares form. These enable a general convergence theorem to be proved in a norm stronger than the energy norm. Results are presented from finite difference analyses of the time-discontinuous Galerkin and least-squares methods with various temporal interpolations and commonly used finite difference methods for structural dynamics. These results show that, for particular interpolations, the time finite element method exhibits improved accuracy and stability.read more
Citations
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A monolithic approach to fluid–structure interaction using space–time finite elements
TL;DR: In this article, the authors present a simultaneous solution procedure for fluid-structure interaction problems, where the structural motion is described by geometrically nonlinear elastodynamics, and the fluid is modeled by the incompressible Navier-Stokes equations.
Journal ArticleDOI
Numerical solutions of partial differential equations by the finite element method, by C. Johnson. Pp 278. £40 (hardback), £15 (paperback). 1988. ISBN 0-521-34514-6, 34758-0 (Cambridge University Press)
Journal ArticleDOI
Variationally consistent discretization schemes and numerical algorithms for contact problems
TL;DR: The starting point is to weakly incorporate the constraint into the setting and to reformulate the inequality in the displacement in terms of a saddle-point problem, and to establish optimal low-order a priori convergence rates for the discretization error in the primal and dual variables.
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Implementation and adaptivity of a space-time finite element method for structural dynamics
Xiangdong Li,Nils-Erik Wiberg +1 more
TL;DR: Numerical examples are presented, showing that the considered DG method is of second- order accuracy in space and third-order accuracy in time, and the adaptive procedure is capable of updating the spatial meshes and the time steps when necessary, making the solutions reliable and the computation efficient.
Journal ArticleDOI
Structural dynamic analysis by a time-discontinuous galerkin finite element method
Xiangdong Li,Nils-Erik Wiberg +1 more
TL;DR: In this article, a time-discontinuous Galerkin finite element method for structural dynamic problems is proposed, by which both displacements and velocities are approximated as piecewise linear functions in the time domain and may be discontinuous at the discrete time levels.
References
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Book
The finite element method
TL;DR: In this article, the methodes are numeriques and the fonction de forme reference record created on 2005-11-18, modified on 2016-08-08.
Journal ArticleDOI
Improved numerical dissipation for time integration algorithms in structural dynamics
TL;DR: In this article, a new family of unconditionally stable one-step methods for the direct integration of the equations of structural dynamics is introduced and is shown to possess improved algorithmic damping properties which can be continuously controlled.
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Numerical Solution of Partial Differential Equations by the Finite Element Method
TL;DR: In this article, the authors present an easily accessible introduction to one of the most important methods used to solve partial differential equations, which they call finite element methods for integral equations (FEME).