## Canonical Duality Theory for Topology Optimization

*Gao, David Yang*;

- Subject: Mathematics - Optimization and Control | Computer Science - Discrete Mathematics

- References (19) 19 references, page 1 of 2
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1. Ali, E.J. and Gao, D.Y. (2016). Improved Canonical Dual Finite Element Method and Algorithm for Post Buckling Analysis of Nonlinear Gao Beam, Canonical Duality-Triality: Unified Theory and Methodology for Multidisciplinary Study, D.Y. Gao, N. Ruan and V. Latorre (eds). Springer.

2. Bendsoe MP. Optimal shape design as a material distribution problem. Structural Optimization, 1:193C202, 1989.

3. Bendsoe MP and Kikuchi N. Generating optimal topologies in structural design using a homogenization method. Computer Methods in Applied Mechanics and Engineering, 72(2):197-224, 1988.

4. Cai, K., Gao, D.Y., Qin, Q.H. (2014). Post-buckling solutions of hyper-elastic beam by canonical dual finite element method. Mathematics and Mechanics of Solids 19(6), 659-671 (2014)

5. Gao, D.Y.: Panpenalty finite element programming for limit analysis, Computers & Structures 28, 749-755 (1988)

6. Gao, D.Y.: Complementary finite element method for finite deformation nonsmooth mechanics. J. Eng. Math., 30, 339-353 (1996)

7. Gao, D.Y.: Canonical duality theory: unified understanding and generalized solutions for global optimization. Comput. & Chem. Eng. 33, 1964-1972 (2009)

8. Gao, D.Y. Duality Principles in Nonconvex Systems: Theory, Methods and Applications, Kluwer Academic Publishers, Dordrecht /Boston /London, xviii + 454pp (2000)

9. Gao, D.Y.: Solutions and optimality to box constrained nonconvex minimization problems. J. Indust. Manage. Optim. 3(2), 293-304 (2007)

10. Gao, D.Y., Ruan, N.: Solutions to quadratic minimization problems with box and integer constraints. J. Glob. Optim. 47, 463-484 (2010)

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