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CANONICAL DUAL FINITE ELEMENT METHOD FOR SOLVING NONCONVEX MECHANICS AND TOPOLOGY OPTIMISATION PROBLEMS

Published online by Cambridge University Press:  25 November 2019

ELAF J. ALI Open the ORCID record for ELAF J. ALI [Opens in a new window]
ELAF J. ALI*
Affiliation:
Faculty of Science and Technology, Centre for Informatics and Applied Optimisation, Federation University Australia, Mt Helen, Victoria 3353, Australia Mathematics Department, College of Science, University of Basrah, Basra, Iraq email elaf.j.ali@gmail.com
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Abstract

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Keywords

canonical duality theorycanonical penalty-duality3D topology optimisation problemlarge deformationpostbuckling problemsnonconvex functionalfinite element method

MSC classification

Primary: 90C46: Optimality conditions, duality
Secondary: 90C26: Nonconvex programming, global optimization
Type
Abstracts of Australasian PhD Theses
Information
Bulletin of the Australian Mathematical Society , Volume 101 , Issue 1 , February 2020 , pp. 172 - 173
Copyright
© 2019 Australian Mathematical Publishing Association Inc. 

Footnotes

Thesis submitted to Federation University in February 2018; degree approved on 25 September 2018; principal supervisor David Gao.

References

Ali, E. J. and Gao, D. Y., ‘Canonical finite element method for solving nonconvex variational problems to post buckling beam problem’, AIP Conf. Proc. 1776(1) (2016), Article ID 090045.Google Scholar
Ali, E. J. and Gao, D. Y., ‘Improved canonical dual finite element method and algorithm for post buckling analysis of nonlinear Gao beam’, in: Canonical Duality Theory: Unified Methodology for Multidisciplinary Study (Springer, Cham, 2017), 277–289.Google Scholar
Ali, E. J. and Gao, D. Y., ‘On SDP method for solving canonical dual problem in post buckling of large deformed elastic beam’, Commun. Math. Sci. 16(5) (2018), 1225–1240.Google Scholar
Gao, D. Y., ‘Canonical duality theory for topology optimization’, in: Canonical Duality-Triality: Unified Theory and Methodology for Multidisciplinary Study (eds. Gao, D. Y., Ruan, N. and Latorre, V.) (Springer, New York, 2019), 263–276.Google Scholar
Gao, D. and Ali, E. J., ‘A novel canonical duality theory for solving 3-D topology optimization problems’, in: Emerging Trends in Applied Mathematics and High-Performance Computing (eds. Singh, V. K., Gao, D. Y. and Fisher, A.) (Springer, New York, 2019), 209–246.Google Scholar