Convolution finite element method: an alternative approach for time integration and time-marching algorithms

A. Amiri-Hezaveh, A. Masud, M. Ostoja-Starzewski

Research output: Contribution to journalArticlepeer-review

Abstract

A finite element procedure is proposed for wave propagation in elastic media. The method is based on an alternative formulation for the equations of motion that can systematically be constructed for linear evolutionary partial differential equations. A weak formulation—corresponding to convolutional variational principles—is then defined, which paves the way for introducing a particular type of time-wise shape functions. Next, some mathematical characteristics of the method are investigated, and upon those properties, a new solution procedure for elastodynamics problems is proposed. Subsequently, several numerical examples are considered, including a single degree of freedom mass-spring-damper system as the prototype of structural dynamics along with 1d and 2d elastodynamics problems for the case of the wave motion in elastic solids. The present method can be considered as an alternative approach for time integration and time-marching algorithms, e.g., Newmark’s algorithm, to solve time-domain problems in elastic media.

Original languageEnglish (US)
Pages (from-to)667-696
Number of pages30
JournalComputational Mechanics
Volume68
Issue number3
DOIs
StatePublished - Sep 2021

Keywords

  • Convolutional variational principles
  • Elastodynamics
  • Finite element method
  • Initial boundary value problems
  • Structural dynamics

ASJC Scopus subject areas

  • Computational Mechanics
  • Ocean Engineering
  • Mechanical Engineering
  • Computational Theory and Mathematics
  • Computational Mathematics
  • Applied Mathematics

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