Manufacturing cost and reliability-based shape optimization of plate structures. (English) Zbl 1537.74298
Summary: A novel methodology is presented for the manufacturing cost and reliability-based optimization of plate structures with the boundary element method (BEM), with the aim of improving the accuracy, robustness, and efficiency of the optimization of aircraft structures. The BEM plate formulations with respect to plate thickness are derived for the first time, and used as part of an implicit differentiation method (IDM), enabling the full shape optimization of plate structures with the BEM. These implicit derivatives are validated against derivatives obtained from the finite difference method (FDM) and from an analytical solution. Results indicate that the IDM is more robust than the FDM and in excellent agreement with the analytical solution, and more accurate than the FDM for most of the step-sizes investigated. To demonstrate the full shape optimization of plates with the newly developed IDM, a numerical example involving reliability-based design optimization and manufacturing cost optimization is presented for a plate structure. Results show that the newly developed IDM is more efficient than the FDM when performing this optimization.
© 2022 The Authors. International Journal for Numerical Methods in Engineering
© 2022 The Authors. International Journal for Numerical Methods in Engineering
MSC:
| 74P10 | Optimization of other properties in solid mechanics |
| 74S15 | Boundary element methods applied to problems in solid mechanics |
| 74K20 | Plates |
| 74S60 | Stochastic and other probabilistic methods applied to problems in solid mechanics |
Keywords:
boundary element method; implicit differentiation method; integral equation; first-order reliability methodSoftware:
MatWebReferences:
| [1] | TafreshiA. Shape optimization of two‐dimensional anisotropic structures using the boundary element method. J Strain Anal Eng Des. 2003;38(3):219‐232. |
| [2] | AbeK, KazamaS, KoroK. A boundary element approach for topology optimization problem using the level set method. Commun Numer Methods Eng. 2006;23(5):405‐416. · Zbl 1111.74045 |
| [3] | SfantosGK, AliabadiMH. A boundary element sensitivity formulation for contact problems using the implicit differentiation method. Eng Anal Bound Elem. 2006;30(1):22‐30. · Zbl 1195.74257 |
| [4] | CanelasA, HerskovitsJ, TellesJCF. Shape optimization using the boundary element method and a sand interior point algorithm for constrained optimization. Comput Struct. 2008;86(13‐14):1517‐1526. |
| [5] | UllahB, TrevelyanJ. Correlation between hole insertion criteria in a boundary element and level set based topology optimisation method. Eng Anal Bound Elem. 2013;37(11):1457‐1470. · Zbl 1287.74032 |
| [6] | ChangY, ChengH, ChiuM, ChienY. Shape optimisation of multi‐chamber acoustical plenums using BEM, neural networks, and GA method. Arch Acoust. 2016;41(1):43‐53. |
| [7] | UllahB, TrevelyanJ. A boundary element and level set based topology optimisation using sensitivity analysis. Eng Anal Bound Elem. 2016;70:80‐98. · Zbl 1403.74073 |
| [8] | LiuC, ChenL, ZhaoW, ChenH. Shape optimization of sound barrier using an isogeometric fast multipole boundary element method in two dimensions. Eng Anal Bound Elem. 2017;85:142‐157. · Zbl 1403.76092 |
| [9] | UllahB, TrevelyanJ, IslamS. A boundary element and level set based bi‐directional evolutionary structural optimisation with a volume constraint. Eng Anal Bound Elem. 2017;80:152‐161. · Zbl 1403.74245 |
| [10] | TakahashiT, YamamotoT, ShimbaY, IsakariH, MatsumotoT. A framework of shape optimisation based on the isogeometric boundary element method toward designing thin‐silicon photovoltaic devices. Eng Comput. 2018;35(2):423‐449. |
| [11] | MatsushimaK, IsakariH, TakahashiT, MatsumotoT. A topology optimisation of composite elastic metamaterial slabs based on the manipulation of far‐field behaviours. Struct Multidiscip Optim. 2020;63(1):231‐243. |
| [12] | MaduramuthuP, FennerRT. Three‐dimensional shape design optimization of holes and cavities using the boundary element method. J Strain Anal Eng Des. 2004;39(1):87‐98. |
| [13] | BrancatiA, AliabadiMH, MallardoV. A bem sensitivity formulation for three‐dimensional active noise control. Int J Numer Methods Eng. 2012;90(9):1183‐1206. · Zbl 1242.76191 |
| [14] | BandaraK, CirakF, OfG, SteinbachO, ZapletalJ. Boundary element based multiresolution shape optimisation in electrostatics. J Comput Phys. 2015;297:584‐598. · Zbl 1349.78081 |
| [15] | UllahB, TrevelyanJ, IvrissimtzisI. A three‐dimensional implementation of the boundary element and level set based structural optimisation. Eng Anal Bound Elem. 2015;58:176‐194. · Zbl 1403.74244 |
| [16] | ChenLL, LianH, LiuZ, ChenHB, AtroshchenkoE, BordasSPA. Structural shape optimization of three dimensional acoustic problems with isogeometric boundary element methods. Comput Methods Appl Mech Eng. 2019;355:926‐951. · Zbl 1441.74290 |
| [17] | GaggeroS, VernengoG, VillaD, BonfiglioL. A reduced order approach for optimal design of efficient marine propellers. Ships Offshore Struct. 2019;15(2):200‐214. |
| [18] | LiS, TrevelyanJ, WuZ, LianH, WangD, ZhangW. An adaptive SVD-Krylov reduced order model for surrogate based structural shape optimization through isogeometric boundary element method. Comput Methods Appl Mech Eng. 2019;349:312‐338. · Zbl 1441.74187 |
| [19] | BabouskosNG, KatsikadelisJT. Optimum design of thin plates via frequency optimization using bem. Arch Appl Mech. 2014;85(9‐10):1175‐1190. · Zbl 1341.74138 |
| [20] | MorseL, Sharif KhodaeiZ, AliabadiMH. A dual boundary element based implicit differentiation method for determining stress intensity factor sensitivities for plate bending problems. Eng Anal Bound Elem. 2019;106:412‐426. · Zbl 1464.74301 |
| [21] | MellingsS, AliabadiMH. Dual boundary element formulation for inverse potential problems in crack identification. Eng Anal Bound Elem. 1993;12(4):275‐281. |
| [22] | MellingsS, AliabadiMH. Flaw identification using the boundary element method. Int J Numer Methods Eng. 1995;38(3):399‐419. · Zbl 0846.73075 |
| [23] | MallardoV, AliabadiMH. A BEM sensitivity and shape identification analysis for acoustic scattering in fluid-solid problems. Int J Numer Methods Eng. 1998;41(8):1527‐1541. · Zbl 0907.73074 |
| [24] | AlessandriC, MallardoV. Crack identification in two‐dimensional unilateral contact mechanics with the boundary element method. Comput Mech. 1999;24:100‐109. · Zbl 0964.74074 |
| [25] | MallardoV, AlessandriC. Inverse problems in the presence of inclusions and unilateral constraints a boundary element approach. Comput Mech. 2000;26:571‐581. · Zbl 1010.74076 |
| [26] | HuangX, AliabadiMH. Probabilistic fracture mechanics by the boundary element method. Int J Fract. 2011;171(1):51‐64. · Zbl 1283.74061 |
| [27] | HuangX, AliabadiMH. A Boundary Element Method for Structural Reliability. Key Engineering Materials. Vol 627. Trans Tech Publications Ltd; 2015. |
| [28] | MorseL, Sharif KhodaeiZ, AliabadiMH. A multi‐fidelity boundary element method for structural reliability analysis with higher‐order sensitivities. Eng Anal Bound Elem. 2019;104:183‐196. · Zbl 1464.74300 |
| [29] | MellingsS, AliabadiMH. Three‐dimensional flaw identification using inverse analysis. Int J Eng Sci. 1996;34(4):453‐469. · Zbl 0900.73913 |
| [30] | NASA. Nasa cost estimating handbook version 4.0 ‐ appendix C: cost estimating methodologies report; 2015. |
| [31] | YounBD, ChoiKK, ParkYH. Hybrid analysis method for reliability‐based design optimization. J Mech Des. 2003;125(2):221‐232. |
| [32] | AliabadiMH. The Boundary Element Method: Applications in Solids and Structures. Vol 2. John Wiley and Sons; 2002. · Zbl 0994.74003 |
| [33] | Di PisaC, AliabadiMH. Boundary Element Analysis for Multi‐Layered Panels and Structures. Report. Queen Mary University of London; 2005. |
| [34] | DirgantaraT, AliabadiMH. Crack growth analysis of plates loaded by bending and tension using dual boundary element method. Int J Fract. 1999;105(1):27‐47. |
| [35] | TellesJCF. A self adaptive coordinate transformation for efficient numerical evaluation of general boundary element integrals. Int J Numer Methods Eng. 1987;24(5):959‐973. · Zbl 0622.65014 |
| [36] | TimoshenkoS. Theory of Plates and Shells. McGraw Hill; 1959. |
| [37] | MatWeb. Aluminum 6061‐T6; 2021 [Online]. Accessed May 25, 2021. http://www.matweb.com/search/datasheet_print.aspx?matguid=1b8c06d0ca7c456694c7777d9e10be5b |
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