Abstract
This study explores the application of concurrent multiscale topology optimization in the design of lightweight hygral-activated porous compliant mechanisms. The proposed approach utilizes two distinct representations of the design problem, namely macro and microscale domains, to achieve an optimized design. By implementing a concurrent multiscale topology optimization framework, the effective properties of the microscale, including elastic and hygral diffusivity tensors and the hygral expansion coefficient, are calculated and used as the hygro-elastic modeling effective properties of the macroscale. Furthermore, this study considers hygral transport in solids and hygral evaporation, thereby enabling simultaneous consideration of hygral transfer physics. A sensitivity analysis of the proposed concurrent optimization scheme was performed to address both macro and microstructure coupling, as well as hygro-elastic physics coupling. Numerical simulations were conducted for various single and multiple microstructure systems to investigate their performance. A study was also carried out to examine the impact of incorporating multiple microstructures into a single macro design domain on the macrostructure's dependency. The results showed that the use of multiple microstructures improved the design freedom and performance-to-weight ratio of the macrostructure.
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References
Akamatsu D, Noguchi Y, Matsushima K et al (2023) Two-phase topology optimization for metamaterials with negative Poisson’s ratio. Compos Struct 311:116800. https://doi.org/10.1016/j.compstruct.2023.116800
Al Ali M, Shimoda M (2022a) Investigation of concurrent multiscale topology optimization for designing lightweight macrostructure with high thermal conductivity. Int J Therm Sci 179:107653. https://doi.org/10.1016/j.ijthermalsci.2022.107653
Al Ali AM, Shimoda M (2022b) Toward multiphysics multiscale concurrent topology optimization for lightweight structures with high heat conductivity and high stiffness using MATLAB. Struct Multidisc Optim 65:207
Al Ali M, Shimoda M (2023) On concurrent multiscale topology optimization for porous structures under hygro-thermo-elastic multiphysics with considering evaporation. Int J Numer Methods Eng 124:3219–3249. https://doi.org/10.1002/nme.7245
Al Ali M, Al Ali M, Sahib AY, Abbas RS (2018) Design micro piezoelectric actuated gripper for medical applications. In: Proceedings of the 6th IIAE international conference on industrial application engineering, Japan, 2018, pp 175–180
Al Ali M, Shimoda M, Benaissa B, Kobayashi M (2023) Concurrent multiscale hybrid topology optimization for light weight porous soft robotic hand with high cellular stiffness. In: Proceedings of the international conference of steel and composite for engineering structures: ICSCES 2022, 2023, pp 265–278
Al-Rubaiai M, Pinto T, Qian C, Tan X (2019) Soft actuators with stiffness and shape modulation using 3D-printed conductive polylactic acid material. Soft Robot 6:318–332
Ansola R, Vegueria E, Canales J (2010) An element addition strategy for thermally actuated compliant mechanism topology optimization. Eng Comput 27:694–711. https://doi.org/10.1108/02644401011062090
Bendsøe MP (1989) Optimal shape design as a material distribution problem. Struct Optim 1:193–202. https://doi.org/10.1007/BF01650949
Bendsøe MP, Kikuchi N (1988) Generating optimal topologies in structural design using a homogenization method. Comput Methods Appl Mech Eng 71:197–224. https://doi.org/10.1016/0045-7825(88)90086-2
Budzyń D, Zare-Behtash H, Cowley A, Cammarano A (2023) Implicit lunar dust mitigation technology: compliant mechanisms. Acta Astronaut 203:146–156. https://doi.org/10.1016/j.actaastro.2022.11.042
Chan ASL (1960) The design of Michell optimum structures. College of Aeronautics Reports, Report No. 142, Cranfield University
Chen L, Ameer A-S, Rea C et al (2020) Preparation of electrospun nanofibers with desired microstructures using a programmed three-dimensional (3D) nanofiber collector. Mater Sci Eng C 106:110188
Cheng KT, Olhoff N (1981) An investigation concerning optimal design of solid elastic plates. Int J Solids Struct 17:305–323. https://doi.org/10.1016/0020-7683(81)90065-2
Chilali A, Assarar M, Zouari W, Kebir H, Ayad R (2018) Analysis of the hydro-mechanical behaviour of flax fibre-reinforced composites: assessment of hygroscopic expansion and its impact on internal stress. Compos Struct 206:177–184. https://doi.org/10.1016/j.compstruct.2018.08.037
Cho S, Choi JY (2005) Efficient topology optimization of thermo-elasticity problems using coupled field adjoint sensitivity analysis method. Finite Elem Anal Des 41:1481–1495. https://doi.org/10.1016/j.finel.2005.05.003
Clements Kemeny D, Howell LL, Magleby SP (2002) Using compliant mechanisms to improve manufacturability in MEMS. In: International design engineering technical conferences and computers and information in engineering conference, 2022, pp 247–254
Cmathew B, Raikwar M, Negi MS et al (2021) Compliant mechanism and Origami usage in aerospace and space application. IOP Conf Ser Earth Environ Sci 775:012008
Cohn D, Marom G (1983) A stress transfer model for the deformation and failure of polymeric matrices under swelling conditions. In: the role of the polymeric matrix in the processing and structural properties composite materials. Springer, Boston, pp 245–259
Culpepper ML, Anderson G (2004) Design of a low-cost nano-manipulator which utilizes a monolithic, spatial compliant mechanism. Precis Eng 28:469–482. https://doi.org/10.1016/j.precisioneng.2004.02.003
Das S, Sutradhar A (2020) Multi-physics topology optimization of functionally graded controllable porous structures: application to heat dissipating problems. Mater Des 193:108775
Djellouli B, Zouari W, Assarar M, Ayad R (2021) Analysis of the hygroscopic and hygroelastic behaviours of water aged flax–epoxy composite. Compos Struct 265:113692. https://doi.org/10.1016/j.compstruct.2021.113692
Do C, Erbes A, Yan J, Seshia AA (2016) Design and implementation of a low-power hybrid capacitive MEMS oscillator. Microelectronics J 56:1–9. https://doi.org/10.1016/j.mejo.2016.07.007
Drucker DC, Shield RT (1956) Design for minimum weight. Appl Math 15:269–281
Fang L, Wang X, Zhou H (2022) Topology optimization of thermoelastic structures using MMV method. Appl Math Model 103:604–618. https://doi.org/10.1016/j.apm.2021.11.008
Fortino S, Sippola M, Andersson T et al (2018) Modelling of hygroexpansion in birch pulp–PLA composites—a numerical approach based on X-ray micro-tomography. In: 6th European conference on computational mechanics, ECCM 6: 7th European conference on computational fluid dynamics, ECFD 7, 2018
Fujioka M, Shimoda M, Al Ali M (2022) Concurrent shape optimization of a multiscale structure for controlling macrostructural stiffness. Struct Multidisc Optim 65:1–27. https://doi.org/10.1007/s00158-022-03304-y
Gosselin L, Bejan A (2004) Constructal thermal optimization of an electromagnet. Int J Therm Sci 43:331–338. https://doi.org/10.1016/j.ijthermalsci.2003.08.004
Haddar H, Riahi MK (2021) Near-field linear sampling method for axisymmetric eddy current tomography. Inverse Probl 37:105002. https://doi.org/10.1088/1361-6420/ac1c50
Hann SY, Cui H, Nowicki M, Zhang LG (2020) 4D printing soft robotics for biomedical applications. Addit Manuf 36:101567. https://doi.org/10.1016/j.addma.2020.101567
Hoang V-N, Tran P, Vu VT, Nguyen Xuan H (2020) Design of lattice structures with direct multiscale topology optimization. Compos Struct 252:112718. https://doi.org/10.1016/j.compstruct.2020.112718
Hollister SJ, Kikuchi N (1992) A comparison of homogenization and standard mechanics analyses for periodic porous composites. Comput Mech 10:73–95. https://doi.org/10.1007/BF00369853
Jabbar HH, Naguib AM (2019) A computational study of vortex rings interacting with a constant-temperature heated wall. Int J Heat Fluid Flow 76:197–214
Jiang L, Gu XD, Chen S (2021) Generative design of bionic structures via concurrent multiscale topology optimization and conformal geometry method. J Mech Des 143:11701. https://doi.org/10.1115/1.4047345
Kameyama K, Shimoda M, Morimoto T (2014) Shape identification for controlling the static deformation of frame structures. In: International design engineering technical conferences and computers and information in engineering conference, 2014, p V01AT02A024
Kato J, Yachi D, Kyoya T, Terada K (2018) Micro–macro concurrent topology optimization for nonlinear solids with a decoupling multiscale analysis. Int J Numer Methods Eng 113:1189–1213. https://doi.org/10.1002/nme.5571
Kucíková L, Šejnoha M, Vorel J (2018) Determination of hygroexpansion coefficients of wood using analytical and numerical homogenization. In: Acta Polytechnica CTU proceedings, 2018, pp 51–56
Lai M, Botsis J, Cugnoni J (2014) Studies of hygrothermal degradation of a single fiber composite: an iterative approach with embedded optical sensors and numerical analysis. Composites B 60:577–585. https://doi.org/10.1016/j.compositesb.2013.08.091
Li Y, Luo ZX (2000) Physical mechanisms of moisture diffusion into hygroscopic fabrics during humidity transients. J Text Inst 91:302–316. https://doi.org/10.1080/00405000008659508
Li Y, Saitou K, Kikuchi N (2002) Design of heat-activated compliant mechanisms and its application to product-embedded disassembly
Liu L, Yan J, Cheng G (2008) Optimum structure with homogeneous optimum truss-like material. Comput Struct 86:1417–1425. https://doi.org/10.1016/j.compstruc.2007.04.030
Luo Z, Chen LP, Yang J, Zhang YQ (2006) Multiple stiffness topology optimizations of continuum structures. Int J Adv Manuf Technol 30:203–214. https://doi.org/10.1007/s00170-005-0084-z
Mantovani S, Barbieri SG, Giacopini M et al (2021) Synergy between topology optimization and additive manufacturing in the automotive field. Proc Inst Mech Eng B 235:555–567. https://doi.org/10.1177/0954405420949209
Marom G (1977) Swelling and hygroelasticity of polymeric composites. Polym Eng Sci 17:799–802. https://doi.org/10.1002/pen.760171107
Marom G (1985) The role of water transport in composite materials. In: Polymer permeability. Springer, Berlin, pp 341–374
Michell AGM (1904) LVIII. The limits of economy of material in frame-structures. Lond Edinb Dublin Philos Mag J Sci 8:589–597. https://doi.org/10.1080/14786440409463229
Misra RN, Young JH (1980) Numerical solution of simultaneous moisture diffusion and shrinkage during soybean drying. Trans ASAE 23:1277–1282. https://doi.org/10.13031/2013.34760
Mukhopadhyay D, Dong J, Pengwang E, Ferreira P (2008) A SOI-MEMS-based 3-DOF planar parallel-kinematics nanopositioning stage. Sens Actuators A 147:340–351. https://doi.org/10.1016/j.sna.2008.04.018
Newns AD (1950) The methods of determining the water vapour permeability of laminae, a review of the literature. J Text Inst 41:267–307
Rao MA, Rizvi SH, Datta AK, Ahmed J (2014) Engineering properties of foods. CRC Press, Boca Raton
Rosen HN (1974) Penetration of water into hardwoods. Wood Fiber Sci 5:275–287
Sadouki H, Wittmann FH (2001) Damage in a composite material under combined mechanical and hygral load. In: Continuous and discontinuous modelling of cohesive-frictional materials. Springer, Berlin, pp 293–307
Seltmann S, Hasse A (2023) Topology optimization of compliant mechanisms with distributed compliance (hinge-free compliant mechanisms) by using stiffness and adaptive volume constraints instead of stress constraints. Mech Mach Theory 180:105133. https://doi.org/10.1016/j.mechmachtheory.2022.105133
Sha W, Hu R, Xiao M et al (2022) Topology-optimized thermal metamaterials traversing full-parameter anisotropic space. NPJ Comput Mater 8:1–10
Shi JX, Kozono S, Shimoda M et al (2019) Non-parametric shape design optimization of elastic–plastic shear panel dampers under cyclic loading. Eng Struct 189:48–61. https://doi.org/10.1016/j.engstruct.2019.03.049
Shimoda M, Umemura M, Al Ali M, Tsukihara R (2023) Shape and topology optimization method for fiber placement design of CFRP plate and shell structures. Compos Struct 309:116729. https://doi.org/10.1016/j.compstruct.2023.116729
Sigmund O (1994) Materials with prescribed constitutive parameters: an inverse homogenization problem. Int J Solids Struct 31:2313–2329. https://doi.org/10.1016/0020-7683(94)90154-6
Sigmund O (2000) A new class of extremal composites. J Mech Phys Solids 48:397–428. https://doi.org/10.1016/S0022-5096(99)00034-4
Sigmund O (2001) Design of multiphysics actuators using topology optimization-Part I: one-material structures. Comput Methods Appl Mech Eng 190:6577–6604. https://doi.org/10.1016/S0045-7825(01)00251-1
Tao XM, Postle R (1989) A viscoelastic analysis of the keratin composite: Part II: thermal and hygral expansion. Text Res J 59:300–306. https://doi.org/10.1177/004051758905900508
Torisaki M, Shimoda M, Al Ali M (2023) Shape optimization method for strength design problem of microstructures in a multiscale structure. Int J Numer Methods Eng 124:1748–1772. https://doi.org/10.1002/nme.7186
Wang C, Zhao Z, Zhou M et al (2021) A comprehensive review of educational articles on structural and multidisciplinary optimization. Struct Multidisc Optim 64:2827–2880
Wu J, Sigmund O, Groen JP (2021) Topology optimization of multi-scale structures: a review. Struct Multidisc Optim 63:1455–1480. https://doi.org/10.1007/s00158-021-02881-8
Xi X, Clancy T, Wu X et al (2016) A MEMS XY-stage integrating compliant mechanism for nanopositioning at sub-nanometer resolution. J Micromech Microeng 26:25014. https://doi.org/10.1088/0960-1317/26/2/025014
Xu B, Huang X, Zhou SW, Xie YM (2016) Concurrent topological design of composite thermoelastic macrostructure and microstructure with multi-phase material for maximum stiffness. Compos Struct 150:84–102
Xu C, Li S, Zou K (2019) Study of heat and moisture transfer in internal and external wall insulation configurations. J Build Eng 24:100724. https://doi.org/10.1016/j.jobe.2019.02.016
Yan S, Wang F, Sigmund O (2018) On the non-optimality of tree structures for heat conduction. Int J Heat Mass Transf 122:660–680. https://doi.org/10.1016/j.ijheatmasstransfer.2018.01.114m
Yang RJ, Chahande AI (1995) Automotive applications of topology optimization. Struct Optim 9:245–249. https://doi.org/10.1007/BF01743977
Zhang TY, Bakshi AS, Gustafson RJ, Lund DB (1984) Finite element analysis of nonlinear water diffusion during rice soaking. J Food Sci 49:246–250. https://doi.org/10.1111/j.1365-2621.1984.tb13719.x
Zhang W, Yang J, Xu Y, Gao T (2014) Topology optimization of thermoelastic structures: mean compliance minimization or elastic strain energy minimization. Struct Multidisc Optim 49:417–429. https://doi.org/10.1007/s00158-013-0991-9
Zhang Y, Li H, Xiao M et al (2019) Concurrent topology optimization for cellular structures with nonuniform microstructures based on the kriging metamodel. Struct Multidisc Optim 59:1273–1299. https://doi.org/10.1007/s00158-018-2130-0
Zuo W, Saitou K (2017) Multi-material topology optimization using ordered SIMP interpolation. Struct Multidisc Optim 55:477–491
Acknowledgements
A part of this work was supported by a Grant-in-Aid for Scientific Research awarded by the Japan Society for the Promotion of Science (JSPS), KAKEN of Grant Number JP21K03757.
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Al Ali, M., Shimoda, M. Hygrally activated displacement inverter using a multiphysics multiscale topology optimization with considering evaporation. Struct Multidisc Optim 66, 224 (2023). https://doi.org/10.1007/s00158-023-03679-6
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DOI: https://doi.org/10.1007/s00158-023-03679-6