The DOI matches its Crossref record; 105 of the 105 references it cites were found in a registry or an index.
Eighty Years of the Finite Element Method: Birth, Evolution, and Future
Open accessAbstract
This document presents comprehensive historical accounts on the developments of finite element methods (FEM) since 1941, with a specific emphasis on developments related to solid mechanics. We present a historical overview beginning with the theoretical formulations and origins of the FEM, while discussing important developments that have enabled the FEM to become the numerical method of choice for so many problems rooted in solid mechanics.
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Cites
Multilayer feedforward networks are universal approximators
Hornik, K., Stinchcombe, M., & White, H. (1989) · Neural Networks · doi:10.1016/0893-6080(89)90020-8 · Cited by 21,728
Raissi, M., Perdikaris, P., & Karniadakis, G. E. (2019) · Journal of Computational Physics · doi:10.1016/j.jcp.2018.10.045 · Cited by 20,384
Approximation by superpositions of a sigmoidal function
Cybenko, G. (1989) · Mathematics of Control, Signals, and Systems · doi:10.1007/bf02551274 · Cited by 13,883
Bathe, K. (1995) · CERN Document Server (European Organization for Nuclear Research) · Cited by 10,651
Multilayer feedforward networks are universal approximators
HornikK., StinchcombeM., & WhiteH. (1989) · Neural Networks · doi:10.5555/70405.70408 · Cited by 9,081
Physics-informed machine learning
Karniadakis, G. E., Kevrekidis, I. G., Lu, L., Perdikaris, P., Wang, S., & Yang, L. (2021) · Nature Reviews Physics · doi:10.1038/s42254-021-00314-5 · Cited by 8,718
Generating optimal topologies in structural design using a homogenization method
Bendsøe, M. P., & Kikuchi, N. (1988) · Computer Methods in Applied Mechanics and Engineering · doi:10.1016/0045-7825(88)90086-2 · Cited by 7,467
Hillerborg, A., Modéer, M., & Petersson, P.-E. (1976) · Cement and Concrete Research · doi:10.1016/0008-8846(76)90007-7 · Cited by 6,874
A finite element method for crack growth without remeshing
Mo�s, N., Dolbow, J., & Belytschko, T. (1999) · International Journal for Numerical Methods in Engineering · doi:10.1002/(sici)1097-0207(19990910)46:1<131::aid-nme726>3.0.co;2-j · Cited by 6,446
Isogeometric analysis: CAD, finite elements, NURBS, exact geometry and mesh refinement
Hughes, T. J. R., Cottrell, J. A., & Bazilevs, Y. (2005) · Computer Methods in Applied Mechanics and Engineering · doi:10.1016/j.cma.2004.10.008 · Cited by 6,335
Metadata
- Authors
- Liu, W. K., Li, S., & Park, H. S.
- Venue
- Archives of Computational Methods in Engineering
- Published
- 2022-06-13
- Volume
- 29
- Issue
- 6
- Pages
- 4431-4453
- ISSN
- 1134-3060 (ISSN-L)
- 1886-1784
- OpenAlex
- W3181577275
- Cited by
- 322
- References
- 105
- FWCI
- 31.11
- Type
- journal article
- Language
- en
- Open access
- hybrid
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