A Topology Optimization Formulation Applied to Highly Flexible Structures

A Topology Optimization Formulation Applied to Highly Flexible Structures

Lima, Cícero Ribeiro de; Teves, André da Costa; Silva, Emílio Carlos Nelli

Full Article:

Highly flexible structures (springs) can be found in many precise devices, such as small actuators of optical disc drive and mobile cameras. A good configuration design is crucial for correct operation of these devices. In this case, optimization techniques can be applied to design of these flexible structures, aiming to reduce development time and costs. Remarkably, the design of these structures turns out to be a challenge in topology optimization. Thus, in this work, a formulation for designing highly flexible structures by using topology optimization is investigated. The topology optimization problem is defined as minimization of the mean compliance subjected to material volume and perimeter constraints, combined with a projection technique. The material model is based on the traditional SIMP approach and the optimization problem is implemented by using COMSOL software and solved by using MMA algorithm. A well-known plane string case has been carried out to evaluate the potential of the proposed topology optimization formulation.

Highly flexible structures (springs) can be found in many precise devices, such as small actuators of optical disc drive and mobile cameras. A good configuration design is crucial for correct operation of these devices. In this case, optimization techniques can be applied to design of these flexible structures, aiming to reduce development time and costs. Remarkably, the design of these structures turns out to be a challenge in topology optimization. Thus, in this work, a formulation for designing highly flexible structures by using topology optimization is investigated. The topology optimization problem is defined as minimization of the mean compliance subjected to material volume and perimeter constraints, combined with a projection technique. The material model is based on the traditional SIMP approach and the optimization problem is implemented by using COMSOL software and solved by using MMA algorithm. A well-known plane string case has been carried out to evaluate the potential of the proposed topology optimization formulation.

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DOI: 10.5151/matsci-mmfgm-170-f

Referências bibliográficas

• [1] D. Qiao, G. Pang, M-K. Mui, and D. Lam, A single-axis low-cost accelerometer fabricated using printed-circuit-board techniques. Electron Device Letters, IEEE, 30 (2009), 1293-1295.
• [2] S. Desrochers, D. Pasini, and J. Angeles, Optimum design of a compliant uniaxial accelerometer. Journal of Mechanical Design, 132 (2010).
• [3] S. Nishiwaki, M.I. Frecker, S. Min, and N. Kikuchi, Topology optimization of compliant mechanisms using the homogenization method. International Journal for Numerical Methods in Engineering, 42 (1998), 535-559.
• [4] M-G. Song, N-C. Park, K-S. Park, and Y-P. Park, Design of a leaf spring using a genetic algorithm. IEEE Trans. on Magnetics, 47 (2011), 590-593.
• [5] M.P. Bendsøe, Optimal shape design as a material distribution problem. Structural and Multidisciplinary Optimization, 1 (1989), 193-202.
• [6] M.P. Bendsøe and O. Sigmund, (2003) Topology Optimization: Theory, Methods and Applications. Springer Verlag.
• [7] B. Bourdin, Filters in topology optimization. International Journal for Numerical Methods In Engineering, 50 (2001), 2143-2158.
• [8] K. Suzuki and N. Kikuchi, A homogenization method for shape and topology optimization. Computer Methods in Applied Mechanics and Engineering, 93 (1991), 291-318.
• [9] T.E. Bruns and D.A. Tortorelli, Topology optimization of non-linear elastic structures and compliant mechanisms. Computer Methods in Applied Mechanics and Engineering. 190 (2001) 3443-3459.
• [10] R.B. Haber, C.S. Jog, and M.P. Bendsøe, A new approach to variable-topology shape design using a constraint on perimeter. Structural and Multidisciplinary Optimization, 11 (1996), 1-12.
• [11] W. Zhang and P. Duysinx, Dual approach using a variant perimeter constraint and efficient sub-iteration scheme for topology optimization. Computers Andamp; Structures, 81 (2003), 2173-2181.
• [12] L. Ambrosio and G. Buttazzo, An optimal design problem with perimeter penalization. Calculus of Variations and Partial Differential Equations, 1 (1993), 55–69.
• [13] D. Chapelle and K. J. Bathe, (2003) The Finite Element Analysis of Shells: Fundamentals. Springer.
• [14] K. Svanberg, The method of moving asymptotes: a new method for structural optimization. International Journal for Numerical Methods in Engineering, 24 (1987), 359-373.

Como citar:

Lima, Cícero Ribeiro de; Teves, André da Costa; Silva, Emílio Carlos Nelli; "A Topology Optimization Formulation Applied to Highly Flexible Structures", p-78-81. In: Proceedings of the 13th International Symposium on Multiscale, Multifunctional and Functionally Graded Materials [=Blucher Material Science Proceedings, v.1, n.1]. São Paulo: Blucher, 2014.
ISSN 23589337, DOI 10.5151/matsci-mmfgm-170-f