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

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...

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Bibliographic Details
Published in:Computational mechanics 2021-09, Vol.68 (3), p.667-696
Main Authors: Amiri-Hezaveh, A., Masud, A., Ostoja-Starzewski, M.
Format: Article
Language:English
Subjects:
Algorithms
Analysis
Classical and Continuum Physics
Computational Science and Engineering
Convolution
Differential equations
Elastic media
Elastodynamics
Engineering
Equations of motion
Finite element method
Mass-spring-damper systems
Mathematical analysis
Methods
Original Paper
Partial differential equations
Shape functions
Theoretical and Applied Mechanics
Time integration
Variational principles
Wave propagation
Waves
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Summary: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.
ISSN:0178-7675
1432-0924
DOI:10.1007/s00466-021-02046-w