Abstract
Many discrete design variables in broadband dynamic optimization cause intensive computational and storage burdens in both frequency response and sensitivity analysis. One solution is to adopt the continuous angle design model. However, a local optimum solution is more likely to be obtained due to its high non-convex character. Consequently, this paper develops an integrated optimization model for minimizing composite plate’s local response in a given frequency band by the discrete–continuous parameterization model (DCP). The DCP is adopted to optimize fiber angles where it divides the total angle range into several subranges and combines the discrete and continuous variables. Thus, it offers a wide and flexible design space for selecting the fiber angle and is useful to find better-optimized results. In addition, the solid isotropic material with penalty scheme (SIMP) is used to optimize the layout of the dam** material. Additionally, due to the dominant role of the low-order resonant peak on the structural vibration, the low-order resonant peak constraint is also considered. The mode acceleration method (MAM) and the decoupled sensitivity analysis method are incorporated for frequency and sensitivity analysis. Several numerical examples are employed to investigate the validity of the developed model.
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References
Bendsøe, M.P., Sigmund, O.: Material interpolation schemes in topology optimization. Arch. Appl. Mech. 69(9–10), 635–654 (1999)
Bendsøe, M.P., Sigmund, O.: Topology Optimization: Theory. Springer, Verlag, Methods and Applications (2003)
Delissen, A., Keulen, F.V., Langelaar, M.: Efficient limitation of resonant peaks by topology optimization including modal truncation augmentation. Struct. Multidiscip. Optim. 61, 19 (2020)
Diaz, A.R., Kikuchi, N.: Solutions to shape and topology eigenvalue optimization problems using a homogenization method. Int. J. Numer. Methods Eng. 35(7), 1487–1502 (1992)
Du, J., Olhoff, N.: Topological design of freely vibrating continuum structures for maximum values of simple and multiple eigen-frequencies and frequency gaps. Struct. Multidiscip. Optim. 34(2), 91–110 (2007a)
Du, J., Olhoff, N.: Topological design of freely vibrating continuum structures for maximum values of simple and multiple eigenfrequencies and frequency gaps. Struct Multidiscip Optim. 34(2), 91–11 (2007b)
Duan, Z., Yan, J., Zhao, G.: Integrated optimization of the material and structure of composites based on the Heaviside penalization of discrete material model. Struct. Multidiscip. Optim. 51(3), 721–732 (2015)
Fang Z., Zheng L.: Topology Optimization for Minimizing the Resonant Response of Plates with Constrained Layer Dam** Treatment. Shock and Vibration. (PT.2):1–11 (2015)
Ghiasi, H., Pasini, D., Lessard, L.: Optimum stacking sequence design of composite materials part i: constant stiffness design. Compos. Struct. 90, 1–11 (2009)
Ghiasi, H., Fayazbakhsh, K., Pasini, D., Lessard, L.: Optimum stacking sequence design of composite materials part ii: variable stiffness design. Compos. Struct. 93, 1–13 (2010)
Huang, X., Zhou, S., Sun, G., Li, G., **e, Y.M.: Topology optimization for microstructures of viscoelastic composite materials. Comput. Methods Appl. Mech. Eng. 283, 503–516 (2015)
Kang, Z., Wang, R., Tong, L.: Combined optimization of bi-material structural layout and voltage distribution for in-plane piezoelectric actuation. Comput. Methods Appl. Mech. Eng. 200, 1467–1478 (2011)
Kiyono, C.Y., Silva, E.C.N., Reddy, J.N.: Design of laminated piezocomposite shell transducers with arbitrary fiber orientation using topology optimization approach. Int. J. Numer. Methods Eng. 90(12), 1452–1484 (2012)
Liu, H., Zhang, W., Gao, T.: A comparative study of dynamic analysis methods for structural topology optimization under harmonic force excitations. Struct. Multidiscip. Optim. 51(6), 1321–1333 (2015)
Lund, E., Stegmann, J.: Eigenfrequency and Buckling Optimization of Laminated Composite Shell Structures Using Discrete Material Optimization. Springer, Netherlands (2006)
Luo, Y., Chen, W., Liu, S., Li, Q., Ma, Y.: A discrete-continuous parameterization (DCP) for concurrent optimization of structural topologies and continuous material orientations. Compos. Struct.236:111900 (2020)
Ma, Z.D., Kikuchi, N., Hagiwara, I.: Structural topology and shape optimization for a frequency response problem. Comput. Mech. 13(3), 157–174 (1993)
Nakasone, P.H., Silva, E.C.N.: Dynamic design of piezoelectric laminated sensors and actuators using topology optimization. J. Intell. Mater. Syst. Struct. 21, 1627–1652 (2010)
Niu, B., Olhoff, N., Lund, E., Cheng, G.: Discrete material optimization of vibrating laminated composite plates for minimum sound radiation. Int. J. Solids Struct. 47(16), 2097–2114 (2010)
Niu, B., He, X., Shan, Y., Yang, R.: On objective functions of minimizing the vibration response of continuum structures subjected to external harmonic excitation. Struct. Multidiscip. Optim. 57(6), 2291–2307 (2018)
Olhoff, N., Du J.: On Topological design optimization of structures against vibration and noise emission, pp. 217–276, Springer, Vienna (2009)
Olhoff, N., Du, J.: Generalized incremental frequency method for topological designof continuum structures for minimum dynamic compliance subject to forced vibration at a prescribed low or high value of the excitation frequency. Struct. Multidiscip. Optim. 54(5), 1143 (2016)
Olhoff, N., Niu, B., Cheng, G.: Optimum design of band-gap beam structures. Int. J. Solid Struct. 49(22), 3158–3169 (2012)
Silva, O.M., Neves, M.M., Lenzi, A.: A critical analysis of using the dynamic compliance as objective function in topology optimization of one-material structures considering steady-state forced vibration problems. J. Sound Vibr. 444, 1–20 (2019)
Silva, O.M., Neves, M.M., Lenzi, A.: On the use of active and reactive input power in topology optimization of one-material structures considering steady-state forced vibration problems. J. Sound Vibr. 464:114989 (2020)
Stegmann, J., Lund, E.: Discrete material optimization of general composite shell structures. Int. J. Numer. Methods Eng. 62(14), 2009–2027 (2005)
Svanberg, K.: A class of globally convergent optimization methods based on conservative convex separable approximations. SIAM J. Optim. 12, 555–573 (2002)
Venini, P., **aro, M.: A new approach to optimization of viscoelastic beams: minimization of the input/output transfer function H∞-norm. Struct. Multidiscip. Optim. 55(5), 1559–1573 (2017)
Xu, B.: Integrated optimization of structural topology and control for piezoelectric smart trusses with interval variables. J. Vib. Control. 20(4), 576–588 (2014)
Xu, Y., Zhu, J., Wu, Z., Cao, Y., Zhao, Y., Zhang, W.: A review on the design of laminated composite structures: constant and variable stiffness design and topology optimization. Adv. Compos. Hybrid Mater. 1, 460–477 (2018)
Yoon, G.H.: Structural topology optimization for frequency response problem using model reduction schemes. Comput. Methods Appl. Mech. Eng. 199(25–28), 1744–1763 (2010)
Zhao, J., Yoon, H., Youn, B.D.: An efficient concurrent topology optimization approach for frequency response problems. Comput. Methods Appl. Mech. Eng. 347, 700–734 (2019)
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This work was supported by the National Natural Science Foundation of China (11872311) and the Natural Science Basic Research Plan in Shaanxi Province of China (2020JM085)
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Ding, H., Xu, B. Optimal design of vibrating composite plate considering discrete–continuous parameterization model and resonant peak constraint. Int J Mech Mater Des 17, 679–705 (2021). https://doi.org/10.1007/s10999-021-09553-x
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DOI: https://doi.org/10.1007/s10999-021-09553-x