TY - JOUR
T1 - Convolution finite element method
T2 - an alternative approach for time integration and time-marching algorithms
AU - Amiri-Hezaveh, A.
AU - Masud, A.
AU - Ostoja-Starzewski, M.
N1 - Funding Information:
The authors wish to thank anonymous reviewers for their constructive comments that improved the quality of the manuscript.
Publisher Copyright:
© 2021, The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature.
PY - 2021/9
Y1 - 2021/9
N2 - 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.
AB - 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.
KW - Convolutional variational principles
KW - Elastodynamics
KW - Finite element method
KW - Initial boundary value problems
KW - Structural dynamics
UR - http://www.scopus.com/inward/record.url?scp=85110073413&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=85110073413&partnerID=8YFLogxK
U2 - 10.1007/s00466-021-02046-w
DO - 10.1007/s00466-021-02046-w
M3 - Article
AN - SCOPUS:85110073413
VL - 68
SP - 667
EP - 696
JO - Computational Mechanics
JF - Computational Mechanics
SN - 0178-7675
IS - 3
ER -