Differential evolution algorithm and artificial neural network surrogate model for functionally graded material homogenization and design
In this paper, the differential evolution (DE) algorithm is employed to design functionally graded materials (FGMs). The design problem is formulated as a constrained optimization, where the objective function represents the global requirements of the macroscopic boundary value problem (BVPm), and t...
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| Published in | Composite structures Vol. 362; p. 119041 |
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| Main Authors | , , |
| Format | Journal Article |
| Language | English |
| Published |
Elsevier Ltd
15.06.2025
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| Online Access | Get full text |
| ISSN | 0263-8223 |
| DOI | 10.1016/j.compstruct.2025.119041 |
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| Abstract | In this paper, the differential evolution (DE) algorithm is employed to design functionally graded materials (FGMs). The design problem is formulated as a constrained optimization, where the objective function represents the global requirements of the macroscopic boundary value problem (BVPm), and the constraints account for the feasibility (or manufacturability) of the generic microstructure. During optimization, the local constitutive behavior of the material, such as the components of the anisotropic effective stiffness tensor, is derived using homogenization theory, which involves solving the microscopic boundary value problem (BVPµ). Both the macro and micro problems are solved using the finite element method. To accelerate computations, artificial neural networks (ANNs), trained with pre-computed homogenization data, are used as a surrogate homogenization model for the FGM optimization process. The examples presented demonstrate that using ANNs can reduce the optimization effort by several orders of magnitude, even when accounting for the computational cost of database preparation and ANN training. The proposed approach for designing FGMs has proven to be both efficient and reliable for the considered generic microstructure and example global problems. Moreover, the method is general enough to be applied to more complex microstructures and diverse global requirements. |
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| AbstractList | In this paper, the differential evolution (DE) algorithm is employed to design functionally graded materials (FGMs). The design problem is formulated as a constrained optimization, where the objective function represents the global requirements of the macroscopic boundary value problem (BVPm), and the constraints account for the feasibility (or manufacturability) of the generic microstructure. During optimization, the local constitutive behavior of the material, such as the components of the anisotropic effective stiffness tensor, is derived using homogenization theory, which involves solving the microscopic boundary value problem (BVPµ). Both the macro and micro problems are solved using the finite element method. To accelerate computations, artificial neural networks (ANNs), trained with pre-computed homogenization data, are used as a surrogate homogenization model for the FGM optimization process. The examples presented demonstrate that using ANNs can reduce the optimization effort by several orders of magnitude, even when accounting for the computational cost of database preparation and ANN training. The proposed approach for designing FGMs has proven to be both efficient and reliable for the considered generic microstructure and example global problems. Moreover, the method is general enough to be applied to more complex microstructures and diverse global requirements. |
| ArticleNumber | 119041 |
| Author | Lefik, Marek Wojciechowski, Marek Boso, Daniela P. |
| Author_xml | – sequence: 1 givenname: Marek surname: Wojciechowski fullname: Wojciechowski, Marek organization: Department of Concrete Structures, Division of Geotechnics and Engineering Structures, Lodz University of Technology, Al. Politechniki 6, 90-924 Łódź, Poland – sequence: 2 givenname: Marek surname: Lefik fullname: Lefik, Marek organization: Department of Concrete Structures, Division of Geotechnics and Engineering Structures, Lodz University of Technology, Al. Politechniki 6, 90-924 Łódź, Poland – sequence: 3 givenname: Daniela P. surname: Boso fullname: Boso, Daniela P. email: daniela.boso@unipd.it organization: Department of Civil, Environmental and Architectural Engineering, University of Padova, Via Marzolo 9, 35131 Padova, Italy |
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| Cites_doi | 10.1016/j.matpr.2015.07.239 10.1007/978-3-662-05086-6 10.1016/S0045-7825(03)00348-7 10.1016/j.cma.2008.12.036 10.1038/srep11551 10.1016/j.jcp.2020.110010 10.1016/j.compstruct.2019.111517 10.1016/j.ijsolstr.2022.111702 10.4012/dmj.2013-264 10.1109/CEC.2002.1004459 10.36956/sms.v4i1.490 10.1016/j.compstruct.2015.08.041 10.1007/978-3-642-29347-4_22 10.1016/j.compstruct.2022.115718 10.1002/admt.201900981 10.1007/s11665-014-0958-z 10.1023/A:1008202821328 10.1016/j.ijmecsci.2019.07.005 10.1002/ange.201900530 10.1016/j.cma.2018.11.029 10.1615/IntJMultCompEng.2022040213 10.1061/(ASCE)0733-9399(1991)117:1(132) 10.1016/j.euromechsol.2012.03.002 10.1016/j.compstruct.2004.08.003 10.1016/S0377-0427(00)00426-X 10.1038/s41592-019-0686-2 10.1016/j.cma.2023.116282 10.1007/s11831-023-10009-y 10.1007/s10659-006-9076-y 10.1080/0952813X.2013.782346 10.1137/0523084 10.1142/9505 10.1080/0952813X.2013.813978 10.1016/j.cma.2024.116913 10.5019/j.ijcir.2005.32 10.1016/j.compositesb.2021.109152 10.1007/978-94-007-4722-7_27 10.1016/j.ijsolstr.2010.02.004 10.1016/j.compstruct.2016.03.052 10.3390/ma12172735 10.1016/j.compstruct.2021.114862 10.1108/EC-07-2013-0188 10.1007/978-3-540-70928-2_22 10.1016/j.compstruct.2016.10.047 10.1016/S0266-352X(00)00016-1 10.1007/978-3-319-53756-6 10.1007/978-0-387-30877-7_32 10.1007/s11012-011-9532-z 10.1016/j.jmps.2023.105294 10.1007/s41939-020-00087-x 10.1016/j.engappai.2023.106008 10.1007/s004660000212 10.1002/(SICI)1097-0207(19960315)39:5<867::AID-NME886>3.0.CO;2-Q 10.1002/nme.1620361310 10.1016/j.compstruct.2019.01.105 10.1016/j.tws.2010.09.005 10.1016/j.compstruct.2015.11.017 |
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| Keywords | Computational Homogenization Functionally Graded Material Artificial Neural Network Constrained Optimization Differential Evolution Micro-Macro Approach |
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| References | A. K. Singh, Siddhartha, and S. Hussain, ‘Wear Peculiarity of TiO2 Filled Polyester-Based Homogeneous Composites and their Functionally Graded Materials Using Taguchi Methodology and ANN’ A. Bensoussan, J.-L. Lions, and G. Papanicolaou Dornheim, Morand, Nallani, Helm (b0190) Mar. 2024; 31 P. Virtanen Bouhamed, Jrad, Mars, Wali, Gamaoun, Dammak (b0110) Sep. 2019; 160 Dos Reis, Karathanasopoulos (b0305) Aug. 2022; 250 Storn, Price (b0345) Dec. 1997; 11 Ituarte, Boddeti, Hassani, Dunn, Rosen (b0030) Dec. 2019; 30 Taczała, Buczkowski, Kleiber (b0100) Mar. 2016; 137 Liu, Kumar, Chen, Agrawal, Sundararaghavan, Choudhary (b0160) Jun. 2015; 5 Nika, Constantinescu (b0260) Apr. 2019; 346 SciPy 1.0: fundamental algorithms for scientific computing in Python Liu, Tian, Tao, Yu (b0185) Nov. 2021; 224 , . vol. 53, no. 4, Jun. 2017, Accessed: Jul. 04, 2024. [Online]. Available Shin, Pande (b0145) 2000; 27 N. J. Reynolds, Ed. Khisaeva, Ostoja-Starzewski (b0285) Aug. 2006; 85 Silesian University Press, 2010, pp. 145–166. S. Chandrasekaran and H. S, ‘Functionally graded material and its application to marine structures’ Berlin, Heidelberg: Springer, 2004. doi: 10.1007/978-3-662-05086-6. Oktem, Mantari, Soares (b0090) Nov. 2012; 36 Kouznetsova, Brekelmans, Baaijens (b0280) Jan. 2001; 27 Maleki Jebeli, Shariat Panahi (b0205) 2015; 32 Bhuwal, Pang, Ashcroft, Sun, Liu (b0310) Jun. 2023; 175 Yamanaka, Matsubara, Hirayama, Moriguchi, Terada (b0180) Oct. 2023; 415 in Lecture Notes in Computer Science, vol. 7267. Berlin, Heidelberg: Springer, 2012, pp. 187–195. doi: 10.1007/978-3-642-29347-4_22. Allaire (b0295) Nov. 1992; 23 Roque, Martins (b0200) Dec. 2015; 133 Yas, Kamarian, Pourasghar (b0225) Jan. 2014; 26 Wojciechowski, Lefik, Boso (b0175) 2022; 20 UK ed. edition. New York, NY: Nova Science Pub Inc, 2011. Michalak, Wirowski (b0095) Aug. 2012; 47 Lefik, Boso, Schrefler (b0300) 2009; 198 Feyel (b0250) Jul. 2003; 192 Jędrysiak, Michalak (b0080) May 2011; 49 Vuillod, Zani, Hallo, Montemurro (b0325) May 2024; 425 Wojciechowski (b0365) 2025; V2 L. V. Santana-Quintero and C. A. Coello Coello, ‘An Algorithm Based on Differential Evolution for Multi-Objective Problems’ in Topics in Mining, Metallurgy and Materials Engineering. Cham: Springer International Publishing, 2017. doi: 10.1007/978-3-319-53756-6. arXiv:2003.11372. doi: 10.48550/arXiv.2003.11372. Wojciechowski (b0155) 2011; 18 vol. 4, no. 1, pp. 1–24, Mar. 2021, doi: 10.1007/s41939-020-00087-x. W. N. Sharpe, Ed., in Springer Handbooks, Boston, MA: Springer US, 2008, pp. 891–928. doi: 10.1007/978-0-387-30877-7_32. Springer, 2005. (2007). Python. Accessed: Sep. 27, 2023. [Online]. Available Nikbakht, Kamarian, Shakeri (b0265) Apr. 2019; 214 Springer Berlin Heidelberg, 1980. New Jersey: WSPC, 2015. Ostrowski, Michalak (b0085) 2011; 49 K. Price, R. M. Storn, and J. A. Lampinen M. P. Bendsøe and O. Sigmund Swaminathan, Sangeetha (b0105) Jan. 2017; 160 Kortesis, Panagiotopoulos (b0135) 1993; 36 Kamarian, Yas, Pourasghar, Daghagh (b0220) Apr. 2014; 26 Nash (b0335) 2000; 124 Loh, Pei, Harrison, Monzón (b0025) Oct. 2018; 23 Panesar, Abdi, Hickman, Ashcroft (b0125) Jan. 2018; 19 Linka, Hillgärtner, Abdolazizi, Aydin, Itskov, Cyron (b0165) Mar. 2021; 429 Frazier (b0040) Jun. 2014; 23 Li (b0035) 2020; 5 K. Raju, T.-E. Tay, and V. B. C. Tan, ‘A review of the FE2 method for composites’ T. Tušar and B. Filipič, ‘Differential Evolution versus Genetic Algorithms in Multiobjective Optimization’, in M. Wojciechowski Mirzaali, de la Nava, Gunashekar, Nouri-Goushki, Doubrovski, Zadpoor (b0060) Aug. 2019; 12 H. Bruck, ‘Implantable Biomedical Devices and Biologically Inspired Materials’, in vol. 1, no. 2, 2005, doi: 10.5019/j.ijcir.2005.32. S. Dana and M. F. Wheeler, ‘A machine learning accelerated FE$^2$ homogenization algorithm for elastic solids’, Jul. 30, 2021 T. A. N. Silva and M. A. R. Loja, ‘Differential Evolution on the Minimization of Thermal Residual Stresses in Functionally Graded Structures’, in North-Holland Publishing Company, 1978. E. Sanchez-Palencia R. Enneti, R. Morgan, T. Wolfe, A. Harooni, and S. Volk, ‘Direct metal laser sintering/selective laser melting of tungsten powders’ S. Obayashi, K. Deb, C. Poloni, T. Hiroyasu, and T. Murata, Eds., Berlin, Heidelberg: Springer, 2007, pp. 257–271. doi: 10.1007/978-3-540-70928-2_22. (2013). Python. Accessed: Sep. 27, 2023. [Online]. Available: https://fempy.org vol. 17, no. 3, Art. no. 3, Mar. 2020, doi: 10.1038/s41592-019-0686-2. Anthoine (b0075) Jun. 2010; 47 Roque, Martins, Ferreira, Jorge (b0210) Nov. 2016; 156 Truong, Lee, Lee (b0215) Feb. 2020; 233 Wojciechowski (b0290) Aug. 2022; 294 Costantini (b0065) 2019; 131 Lefik, Wojciechowski (b0150) 2005; 12 R. M. Mahamood and E. T. Akinlabi Cui, Sun (b0055) 2014; 33 Montemurro, Refai, Catapano (b0120) Jan. 2022; 280 M. Wojciechowski, ‘Solving Differential Equations by Means of Feed-Forward Artificial Neural Networks’, in I. Elishakoff, D. Pentaras, and C. Gentilini Ghaboussi, Garret, Wu (b0130) 1991; 117 A. Madureira, C. Reis, and V. Marques, Eds., Dordrecht: Springer Netherlands, 2013, pp. 289–299. doi: 10.1007/978-94-007-4722-7_27. vol. 2, pp. 1468–1473, https://www.researchgate.net/publication/3949425, 2002, doi: 10.1109/CEC.2002.1004459. J. Lampinen, ‘A constraint handling approach for the differential evolution algorithm’ Piotrowski, Napiorkowski, Piotrowska (b0355) May 2023; 121 vol. 4, no. 1, Art. no. 1, Feb. 2022, doi: 10.36956/sms.v4i1.490. Ferreira, Batra, Roque, Qian, Martins (b0235) Aug. 2005; 69 M. Lefik, ‘Combined approach to the FGM - modeling’, in Yagawa, Okuda (b0140) 1996; 39 vol. 2, no. 4, pp. 2718–2727, Jan. 2015, doi: 10.1016/j.matpr.2015.07.239. Li (10.1016/j.compstruct.2025.119041_b0035) 2020; 5 Cui (10.1016/j.compstruct.2025.119041_b0055) 2014; 33 Swaminathan (10.1016/j.compstruct.2025.119041_b0105) 2017; 160 Kamarian (10.1016/j.compstruct.2025.119041_b0220) 2014; 26 Jędrysiak (10.1016/j.compstruct.2025.119041_b0080) 2011; 49 Yas (10.1016/j.compstruct.2025.119041_b0225) 2014; 26 Khisaeva (10.1016/j.compstruct.2025.119041_b0285) 2006; 85 Liu (10.1016/j.compstruct.2025.119041_b0160) 2015; 5 Bhuwal (10.1016/j.compstruct.2025.119041_b0310) 2023; 175 Roque (10.1016/j.compstruct.2025.119041_b0210) 2016; 156 Bouhamed (10.1016/j.compstruct.2025.119041_b0110) 2019; 160 Shin (10.1016/j.compstruct.2025.119041_b0145) 2000; 27 Costantini (10.1016/j.compstruct.2025.119041_b0065) 2019; 131 10.1016/j.compstruct.2025.119041_b0340 10.1016/j.compstruct.2025.119041_b0020 Michalak (10.1016/j.compstruct.2025.119041_b0095) 2012; 47 Wojciechowski (10.1016/j.compstruct.2025.119041_b0175) 2022; 20 Wojciechowski (10.1016/j.compstruct.2025.119041_b0365) 2025; V2 Taczała (10.1016/j.compstruct.2025.119041_b0100) 2016; 137 Nika (10.1016/j.compstruct.2025.119041_b0260) 2019; 346 Roque (10.1016/j.compstruct.2025.119041_b0200) 2015; 133 Ituarte (10.1016/j.compstruct.2025.119041_b0030) 2019; 30 Dornheim (10.1016/j.compstruct.2025.119041_b0190) 2024; 31 Mirzaali (10.1016/j.compstruct.2025.119041_b0060) 2019; 12 Kortesis (10.1016/j.compstruct.2025.119041_b0135) 1993; 36 Lefik (10.1016/j.compstruct.2025.119041_b0300) 2009; 198 10.1016/j.compstruct.2025.119041_b0050 Linka (10.1016/j.compstruct.2025.119041_b0165) 2021; 429 10.1016/j.compstruct.2025.119041_b0170 10.1016/j.compstruct.2025.119041_b0010 Maleki Jebeli (10.1016/j.compstruct.2025.119041_b0205) 2015; 32 Oktem (10.1016/j.compstruct.2025.119041_b0090) 2012; 36 10.1016/j.compstruct.2025.119041_b0330 Truong (10.1016/j.compstruct.2025.119041_b0215) 2020; 233 10.1016/j.compstruct.2025.119041_b0255 10.1016/j.compstruct.2025.119041_b0015 Wojciechowski (10.1016/j.compstruct.2025.119041_b0155) 2011; 18 10.1016/j.compstruct.2025.119041_b0315 Ferreira (10.1016/j.compstruct.2025.119041_b0235) 2005; 69 Loh (10.1016/j.compstruct.2025.119041_b0025) 2018; 23 Montemurro (10.1016/j.compstruct.2025.119041_b0120) 2022; 280 Liu (10.1016/j.compstruct.2025.119041_b0185) 2021; 224 Kouznetsova (10.1016/j.compstruct.2025.119041_b0280) 2001; 27 Dos Reis (10.1016/j.compstruct.2025.119041_b0305) 2022; 250 Anthoine (10.1016/j.compstruct.2025.119041_b0075) 2010; 47 Storn (10.1016/j.compstruct.2025.119041_b0345) 1997; 11 10.1016/j.compstruct.2025.119041_b0360 Yagawa (10.1016/j.compstruct.2025.119041_b0140) 1996; 39 10.1016/j.compstruct.2025.119041_b0240 10.1016/j.compstruct.2025.119041_b0045 10.1016/j.compstruct.2025.119041_b0320 10.1016/j.compstruct.2025.119041_b0245 10.1016/j.compstruct.2025.119041_b0005 Vuillod (10.1016/j.compstruct.2025.119041_b0325) 2024; 425 Nash (10.1016/j.compstruct.2025.119041_b0335) 2000; 124 Ostrowski (10.1016/j.compstruct.2025.119041_b0085) 2011; 49 Panesar (10.1016/j.compstruct.2025.119041_b0125) 2018; 19 Nikbakht (10.1016/j.compstruct.2025.119041_b0265) 2019; 214 Wojciechowski (10.1016/j.compstruct.2025.119041_b0290) 2022; 294 10.1016/j.compstruct.2025.119041_b0070 10.1016/j.compstruct.2025.119041_b0270 Frazier (10.1016/j.compstruct.2025.119041_b0040) 2014; 23 Ghaboussi (10.1016/j.compstruct.2025.119041_b0130) 1991; 117 Yamanaka (10.1016/j.compstruct.2025.119041_b0180) 2023; 415 10.1016/j.compstruct.2025.119041_b0195 10.1016/j.compstruct.2025.119041_b0230 10.1016/j.compstruct.2025.119041_b0350 10.1016/j.compstruct.2025.119041_b0275 Piotrowski (10.1016/j.compstruct.2025.119041_b0355) 2023; 121 10.1016/j.compstruct.2025.119041_b0115 Lefik (10.1016/j.compstruct.2025.119041_b0150) 2005; 12 Feyel (10.1016/j.compstruct.2025.119041_b0250) 2003; 192 Allaire (10.1016/j.compstruct.2025.119041_b0295) 1992; 23 |
| References_xml | – reference: M. Lefik, ‘Combined approach to the FGM - modeling’, in – volume: 33 start-page: 173 year: 2014 end-page: 178 ident: b0055 article-title: Optimizing the design of bio-inspired functionally graded material (FGM) layer in all-ceramic dental restorations publication-title: Dent Mater J – reference: K. Raju, T.-E. Tay, and V. B. C. Tan, ‘A review of the FE2 method for composites’, – volume: 160 start-page: 43 year: Jan. 2017 end-page: 60 ident: b0105 article-title: Thermal analysis of FGM plates – a critical review of various modeling techniques and solution methods publication-title: Compos Struct – volume: 36 start-page: 163 year: Nov. 2012 end-page: 172 ident: b0090 article-title: Static response of functionally graded plates and doubly-curved shells based on a higher order shear deformation theory publication-title: Eur J Mech A Solids – reference: , vol. 2, no. 4, pp. 2718–2727, Jan. 2015, doi: 10.1016/j.matpr.2015.07.239. – reference: P. Virtanen – volume: 23 start-page: 1917 year: Jun. 2014 end-page: 1928 ident: b0040 article-title: Metal additive manufacturing: a review publication-title: J Materi Eng Perform – reference: A. Bensoussan, J.-L. Lions, and G. Papanicolaou, – reference: N. J. Reynolds, Ed., – reference: , Silesian University Press, 2010, pp. 145–166. – volume: 23 start-page: 34 year: Oct. 2018 end-page: 44 ident: b0025 article-title: An overview of functionally graded additive manufacturing publication-title: Addit Manuf – reference: , W. N. Sharpe, Ed., in Springer Handbooks, Boston, MA: Springer US, 2008, pp. 891–928. doi: 10.1007/978-0-387-30877-7_32. – volume: 425 year: May 2024 ident: b0325 article-title: Handling noise and overfitting in surrogate models based on non-uniform rational basis spline entities publication-title: Comput Methods Appl Mech Eng – reference: A. K. Singh, Siddhartha, and S. Hussain, ‘Wear Peculiarity of TiO2 Filled Polyester-Based Homogeneous Composites and their Functionally Graded Materials Using Taguchi Methodology and ANN’, – reference: . New Jersey: WSPC, 2015. – reference: , UK ed. edition. New York, NY: Nova Science Pub Inc, 2011. – volume: 39 start-page: 867 year: 1996 end-page: 883 ident: b0140 article-title: Finite element solutions with feedback network mechanism through direct minimization of energy functionals publication-title: Int J Numer Meth Eng – reference: S. Dana and M. F. Wheeler, ‘A machine learning accelerated FE$^2$ homogenization algorithm for elastic solids’, Jul. 30, 2021, – reference: , – reference: , A. Madureira, C. Reis, and V. Marques, Eds., Dordrecht: Springer Netherlands, 2013, pp. 289–299. doi: 10.1007/978-94-007-4722-7_27. – reference: . (2013). Python. Accessed: Sep. 27, 2023. [Online]. Available: https://fempy.org, – volume: 23 start-page: 1482 year: Nov. 1992 end-page: 1518 ident: b0295 article-title: Homogenization and two-scale convergence publication-title: SIAM J Math Anal, – reference: , vol. 2, pp. 1468–1473, https://www.researchgate.net/publication/3949425, 2002, doi: 10.1109/CEC.2002.1004459. – reference: S. Chandrasekaran and H. S, ‘Functionally graded material and its application to marine structures’, – reference: L. V. Santana-Quintero and C. A. Coello Coello, ‘An Algorithm Based on Differential Evolution for Multi-Objective Problems’, – volume: 280 year: Jan. 2022 ident: b0120 article-title: Thermal design of graded architected cellular materials through a CAD-compatible topology optimisation method publication-title: Compos Struct – volume: 85 start-page: 153 year: Aug. 2006 ident: b0285 article-title: On the size of RVE in finite elasticity of random composites publication-title: J Elasticity – volume: 12 start-page: E2735 year: Aug. 2019 ident: b0060 article-title: Fracture behavior of bio-inspired functionally graded soft-hard composites made by multi-material 3D printing: the case of colinear cracks publication-title: Materials (Basel) – reference: H. Bruck, ‘Implantable Biomedical Devices and Biologically Inspired Materials’, in – reference: , in Lecture Notes in Computer Science, vol. 7267. Berlin, Heidelberg: Springer, 2012, pp. 187–195. doi: 10.1007/978-3-642-29347-4_22. – volume: 117 start-page: 132 year: 1991 end-page: 153 ident: b0130 article-title: Knowledge-based modeling of material behavior with neural networks publication-title: J Eng Mech – reference: M. Wojciechowski, ‘Solving Differential Equations by Means of Feed-Forward Artificial Neural Networks’, in – volume: 250 year: Aug. 2022 ident: b0305 article-title: Inverse metamaterial design combining genetic algorithms with asymptotic homogenization schemes publication-title: Int J Solids Struct – volume: 160 start-page: 412 year: Sep. 2019 end-page: 420 ident: b0110 article-title: Homogenization of elasto-plastic functionally graded material based on representative volume element: application to incremental forming process publication-title: Int J Mech Sci – reference: , vol. 4, no. 1, pp. 1–24, Mar. 2021, doi: 10.1007/s41939-020-00087-x. – reference: . (2007). Python. Accessed: Sep. 27, 2023. [Online]. Available: – volume: 47 start-page: 1477 year: Jun. 2010 end-page: 1489 ident: b0075 article-title: Second-order homogenisation of functionally graded materials publication-title: Int J Solids Struct – volume: 5 year: 2020 ident: b0035 article-title: A review on functionally graded materials and structures via additive manufacturing: from multi-scale design to versatile functional properties publication-title: Adv Mater Technol – reference: R. M. Mahamood and E. T. Akinlabi, – reference: R. Enneti, R. Morgan, T. Wolfe, A. Harooni, and S. Volk, ‘Direct metal laser sintering/selective laser melting of tungsten powders’, – reference: M. Wojciechowski, – reference: T. Tušar and B. Filipič, ‘Differential Evolution versus Genetic Algorithms in Multiobjective Optimization’, in – volume: 137 start-page: 85 year: Mar. 2016 end-page: 92 ident: b0100 article-title: Nonlinear free vibration of pre- and post-buckled FGM plates on two-parameter foundation in the thermal environment publication-title: Compos Struct – volume: 18 start-page: 303 year: 2011 end-page: 311 ident: b0155 article-title: Application of artificial neural network in soil parameter identification for deep excavation numerical model publication-title: CAMES – volume: 133 start-page: 1191 year: Dec. 2015 end-page: 1197 ident: b0200 article-title: Differential evolution for optimization of functionally graded beams publication-title: Compos Struct – volume: 346 start-page: 388 year: Apr. 2019 end-page: 409 ident: b0260 article-title: Design of multi-layer materials using inverse homogenization and a level set method publication-title: Comput Methods Appl Mech Eng – volume: 36 start-page: 2305 year: 1993 end-page: 2318 ident: b0135 article-title: Neural networks for computing in structural analysis: methods and prospects of applications publication-title: Int J Numer Meth Eng – volume: 192 start-page: 3233 year: Jul. 2003 end-page: 3244 ident: b0250 article-title: A multilevel finite element method (FE2) to describe the response of highly non-linear structures using generalized continua publication-title: Comput Methods Appl Mech Eng – volume: 26 start-page: 197 year: Apr. 2014 end-page: 209 ident: b0220 article-title: Application of firefly algorithm and ANFIS for optimisation of functionally graded beams publication-title: J Exp Theor Artif Intell – volume: 30 year: Dec. 2019 ident: b0030 article-title: Design and additive manufacture of functionally graded structures based on digital materials publication-title: Addit Manuf – volume: 69 start-page: 449 year: Aug. 2005 end-page: 457 ident: b0235 article-title: Static analysis of functionally graded plates using third-order shear deformation theory and a meshless method publication-title: Compos Struct – volume: 11 start-page: 341 year: Dec. 1997 end-page: 359 ident: b0345 article-title: Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces publication-title: J Glob Optim – volume: 49 year: 2011 ident: b0085 article-title: Non-stationary heat transfer in a hollow cylinder with functionally graded material properties publication-title: J Theor Appl Mech – volume: 294 year: Aug. 2022 ident: b0290 article-title: On generalized boundary conditions for mesoscopic volumes in computational homogenization publication-title: Compos Struct – reference: T. A. N. Silva and M. A. R. Loja, ‘Differential Evolution on the Minimization of Thermal Residual Stresses in Functionally Graded Structures’, in – reference: , vol. 1, no. 2, 2005, doi: 10.5019/j.ijcir.2005.32. – volume: 429 year: Mar. 2021 ident: b0165 article-title: Constitutive artificial neural networks: A fast and general approach to predictive data-driven constitutive modeling by deep learning publication-title: J Comput Phys – volume: 27 start-page: 161 year: 2000 end-page: 178 ident: b0145 article-title: On self-learning finite element codes based on monitored response of structures publication-title: Comput Geotech – volume: 224 year: Nov. 2021 ident: b0185 article-title: A review of artificial neural networks in the constitutive modeling of composite materials publication-title: Compos B Eng – volume: 198 start-page: 1785 year: 2009 end-page: 1804 ident: b0300 article-title: Artificial Neural Networks in numerical modelling of composites publication-title: Comput Methods Appl Mech Eng – volume: 5 start-page: 11551 year: Jun. 2015 ident: b0160 article-title: A predictive machine learning approach for microstructure optimization and materials design publication-title: Sci Rep – volume: 415 year: Oct. 2023 ident: b0180 article-title: Surrogate modeling for the homogenization of elastoplastic composites based on RBF interpolation publication-title: Comput Methods Appl Mech Eng – volume: 27 start-page: 37 year: Jan. 2001 end-page: 48 ident: b0280 article-title: An approach to micro-macro modeling of heterogeneous materials publication-title: Comput Mech – reference: J. Lampinen, ‘A constraint handling approach for the differential evolution algorithm’, – reference: I. Elishakoff, D. Pentaras, and C. Gentilini, – volume: 47 start-page: 1487 year: Aug. 2012 end-page: 1498 ident: b0095 article-title: Dynamic modelling of thin plate made of certain functionally graded materials publication-title: Meccanica – reference: . Berlin, Heidelberg: Springer, 2004. doi: 10.1007/978-3-662-05086-6. – volume: 32 start-page: 234 year: 2015 end-page: 257 ident: b0205 article-title: An evolutionary approach for simultaneous optimization of material property distribution and topology of FG structures publication-title: Eng Comput – volume: 12 start-page: 183 year: 2005 end-page: 194 ident: b0150 article-title: Artificial Neural Network as a numerical form of effective constitutive law for composites with parametrized and hierarchical microstructure publication-title: CAMES – reference: M. P. Bendsøe and O. Sigmund, – volume: 156 start-page: 29 year: Nov. 2016 end-page: 34 ident: b0210 article-title: Differential evolution for free vibration optimization of functionally graded nano beams publication-title: Compos Struct – reference: , vol. 53, no. 4, Jun. 2017, Accessed: Jul. 04, 2024. [Online]. Available: – reference: . Springer, 2005. – volume: 19 start-page: 81 year: Jan. 2018 end-page: 94 ident: b0125 article-title: Strategies for functionally graded lattice structures derived using topology optimisation for Additive Manufacturing publication-title: Addit Manuf – reference: E. Sanchez-Palencia, – reference: . North-Holland Publishing Company, 1978. – volume: 214 start-page: 83 year: Apr. 2019 end-page: 102 ident: b0265 article-title: A review on optimization of composite structures part II: functionally graded materials publication-title: Compos Struct – volume: V2 year: 2025 ident: b0365 article-title: Homogenization results for the X-shaped microstructure publication-title: Mendeley Data – reference: , vol. 4, no. 1, Art. no. 1, Feb. 2022, doi: 10.36956/sms.v4i1.490. – volume: 26 start-page: 1 year: Jan. 2014 end-page: 12 ident: b0225 article-title: Application of imperialist competitive algorithm and neural networks to optimise the volume fraction of three-parameter functionally graded beams publication-title: J Exp Theor Artif Intell – reference: . Springer Berlin Heidelberg, 1980. – volume: 31 start-page: 1097 year: Mar. 2024 end-page: 1127 ident: b0190 article-title: Neural networks for constitutive modeling: from universal function approximators to advanced models and the integration of physics publication-title: Arch Computat Methods Eng – reference: , vol. 17, no. 3, Art. no. 3, Mar. 2020, doi: 10.1038/s41592-019-0686-2. – volume: 233 year: Feb. 2020 ident: b0215 article-title: An artificial neural network-differential evolution approach for optimization of bidirectional functionally graded beams publication-title: Compos Struct – reference: . in Topics in Mining, Metallurgy and Materials Engineering. Cham: Springer International Publishing, 2017. doi: 10.1007/978-3-319-53756-6. – volume: 121 year: May 2023 ident: b0355 article-title: Particle Swarm optimization or differential evolution—a comparison publication-title: Eng Appl Artif Intel – volume: 49 start-page: 627 year: May 2011 end-page: 635 ident: b0080 article-title: On the modelling of stability problems for thin plates with functionally graded structure publication-title: Thin-Walled Struct – reference: : arXiv:2003.11372. doi: 10.48550/arXiv.2003.11372. – volume: 124 start-page: 45 year: 2000 end-page: 59 ident: b0335 article-title: A survey of truncated-Newton methods publication-title: J Comput Appl Math – reference: K. Price, R. M. Storn, and J. A. Lampinen, – reference: , S. Obayashi, K. Deb, C. Poloni, T. Hiroyasu, and T. Murata, Eds., Berlin, Heidelberg: Springer, 2007, pp. 257–271. doi: 10.1007/978-3-540-70928-2_22. – reference: . – reference: , ‘SciPy 1.0: fundamental algorithms for scientific computing in Python’, – volume: 131 start-page: 7702 year: 2019 end-page: 7707 ident: b0065 article-title: 3D-printing of functionally graded porous materials using on-demand reconfigurable microfluidics publication-title: Angew Chem – volume: 20 start-page: 33 year: 2022 end-page: 51 ident: b0175 article-title: Inverse problems in the light of homogenisation methods: identification of a composite microstructure publication-title: Int J Multiscale Comput Eng – volume: 175 year: Jun. 2023 ident: b0310 article-title: Discovery of quasi-disordered truss metamaterials inspired by natural cellular materials publication-title: J Mech Phys Solids – ident: 10.1016/j.compstruct.2025.119041_b0170 – ident: 10.1016/j.compstruct.2025.119041_b0230 doi: 10.1016/j.matpr.2015.07.239 – volume: 23 start-page: 34 year: 2018 ident: 10.1016/j.compstruct.2025.119041_b0025 article-title: An overview of functionally graded additive manufacturing publication-title: Addit Manuf – ident: 10.1016/j.compstruct.2025.119041_b0005 doi: 10.1007/978-3-662-05086-6 – volume: 192 start-page: 3233 issue: 28 year: 2003 ident: 10.1016/j.compstruct.2025.119041_b0250 article-title: A multilevel finite element method (FE2) to describe the response of highly non-linear structures using generalized continua publication-title: Comput Methods Appl Mech Eng doi: 10.1016/S0045-7825(03)00348-7 – volume: 198 start-page: 1785 issue: 21–26 year: 2009 ident: 10.1016/j.compstruct.2025.119041_b0300 article-title: Artificial Neural Networks in numerical modelling of composites publication-title: Comput Methods Appl Mech Eng doi: 10.1016/j.cma.2008.12.036 – volume: 5 start-page: 11551 issue: 1 year: 2015 ident: 10.1016/j.compstruct.2025.119041_b0160 article-title: A predictive machine learning approach for microstructure optimization and materials design publication-title: Sci Rep doi: 10.1038/srep11551 – volume: 429 year: 2021 ident: 10.1016/j.compstruct.2025.119041_b0165 article-title: Constitutive artificial neural networks: A fast and general approach to predictive data-driven constitutive modeling by deep learning publication-title: J Comput Phys doi: 10.1016/j.jcp.2020.110010 – volume: 233 year: 2020 ident: 10.1016/j.compstruct.2025.119041_b0215 article-title: An artificial neural network-differential evolution approach for optimization of bidirectional functionally graded beams publication-title: Compos Struct doi: 10.1016/j.compstruct.2019.111517 – volume: 250 year: 2022 ident: 10.1016/j.compstruct.2025.119041_b0305 article-title: Inverse metamaterial design combining genetic algorithms with asymptotic homogenization schemes publication-title: Int J Solids Struct doi: 10.1016/j.ijsolstr.2022.111702 – volume: 33 start-page: 173 issue: 2 year: 2014 ident: 10.1016/j.compstruct.2025.119041_b0055 article-title: Optimizing the design of bio-inspired functionally graded material (FGM) layer in all-ceramic dental restorations publication-title: Dent Mater J doi: 10.4012/dmj.2013-264 – ident: 10.1016/j.compstruct.2025.119041_b0360 doi: 10.1109/CEC.2002.1004459 – ident: 10.1016/j.compstruct.2025.119041_b0070 doi: 10.36956/sms.v4i1.490 – volume: 19 start-page: 81 year: 2018 ident: 10.1016/j.compstruct.2025.119041_b0125 article-title: Strategies for functionally graded lattice structures derived using topology optimisation for Additive Manufacturing publication-title: Addit Manuf – volume: 133 start-page: 1191 year: 2015 ident: 10.1016/j.compstruct.2025.119041_b0200 article-title: Differential evolution for optimization of functionally graded beams publication-title: Compos Struct doi: 10.1016/j.compstruct.2015.08.041 – ident: 10.1016/j.compstruct.2025.119041_b0320 doi: 10.1007/978-3-642-29347-4_22 – volume: 294 year: 2022 ident: 10.1016/j.compstruct.2025.119041_b0290 article-title: On generalized boundary conditions for mesoscopic volumes in computational homogenization publication-title: Compos Struct doi: 10.1016/j.compstruct.2022.115718 – ident: 10.1016/j.compstruct.2025.119041_b0315 – ident: 10.1016/j.compstruct.2025.119041_b0330 – volume: 5 issue: 6 year: 2020 ident: 10.1016/j.compstruct.2025.119041_b0035 article-title: A review on functionally graded materials and structures via additive manufacturing: from multi-scale design to versatile functional properties publication-title: Adv Mater Technol doi: 10.1002/admt.201900981 – volume: 23 start-page: 1917 issue: 6 year: 2014 ident: 10.1016/j.compstruct.2025.119041_b0040 article-title: Metal additive manufacturing: a review publication-title: J Materi Eng Perform doi: 10.1007/s11665-014-0958-z – volume: 11 start-page: 341 issue: 4 year: 1997 ident: 10.1016/j.compstruct.2025.119041_b0345 article-title: Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces publication-title: J Glob Optim doi: 10.1023/A:1008202821328 – volume: 160 start-page: 412 year: 2019 ident: 10.1016/j.compstruct.2025.119041_b0110 article-title: Homogenization of elasto-plastic functionally graded material based on representative volume element: application to incremental forming process publication-title: Int J Mech Sci doi: 10.1016/j.ijmecsci.2019.07.005 – ident: 10.1016/j.compstruct.2025.119041_b0115 – volume: 131 start-page: 7702 issue: 23 year: 2019 ident: 10.1016/j.compstruct.2025.119041_b0065 article-title: 3D-printing of functionally graded porous materials using on-demand reconfigurable microfluidics publication-title: Angew Chem doi: 10.1002/ange.201900530 – volume: 346 start-page: 388 year: 2019 ident: 10.1016/j.compstruct.2025.119041_b0260 article-title: Design of multi-layer materials using inverse homogenization and a level set method publication-title: Comput Methods Appl Mech Eng doi: 10.1016/j.cma.2018.11.029 – volume: 20 start-page: 33 issue: 5 year: 2022 ident: 10.1016/j.compstruct.2025.119041_b0175 article-title: Inverse problems in the light of homogenisation methods: identification of a composite microstructure publication-title: Int J Multiscale Comput Eng doi: 10.1615/IntJMultCompEng.2022040213 – volume: 117 start-page: 132 issue: 1 year: 1991 ident: 10.1016/j.compstruct.2025.119041_b0130 article-title: Knowledge-based modeling of material behavior with neural networks publication-title: J Eng Mech doi: 10.1061/(ASCE)0733-9399(1991)117:1(132) – volume: 36 start-page: 163 year: 2012 ident: 10.1016/j.compstruct.2025.119041_b0090 article-title: Static response of functionally graded plates and doubly-curved shells based on a higher order shear deformation theory publication-title: Eur J Mech A Solids doi: 10.1016/j.euromechsol.2012.03.002 – volume: 69 start-page: 449 issue: 4 year: 2005 ident: 10.1016/j.compstruct.2025.119041_b0235 article-title: Static analysis of functionally graded plates using third-order shear deformation theory and a meshless method publication-title: Compos Struct doi: 10.1016/j.compstruct.2004.08.003 – volume: 124 start-page: 45 issue: 1–2 year: 2000 ident: 10.1016/j.compstruct.2025.119041_b0335 article-title: A survey of truncated-Newton methods publication-title: J Comput Appl Math doi: 10.1016/S0377-0427(00)00426-X – ident: 10.1016/j.compstruct.2025.119041_b0340 doi: 10.1038/s41592-019-0686-2 – volume: 415 year: 2023 ident: 10.1016/j.compstruct.2025.119041_b0180 article-title: Surrogate modeling for the homogenization of elastoplastic composites based on RBF interpolation publication-title: Comput Methods Appl Mech Eng doi: 10.1016/j.cma.2023.116282 – ident: 10.1016/j.compstruct.2025.119041_b0350 – volume: 31 start-page: 1097 issue: 2 year: 2024 ident: 10.1016/j.compstruct.2025.119041_b0190 article-title: Neural networks for constitutive modeling: from universal function approximators to advanced models and the integration of physics publication-title: Arch Computat Methods Eng doi: 10.1007/s11831-023-10009-y – volume: 85 start-page: 153 issue: 2 year: 2006 ident: 10.1016/j.compstruct.2025.119041_b0285 article-title: On the size of RVE in finite elasticity of random composites publication-title: J Elasticity doi: 10.1007/s10659-006-9076-y – volume: 30 year: 2019 ident: 10.1016/j.compstruct.2025.119041_b0030 article-title: Design and additive manufacture of functionally graded structures based on digital materials publication-title: Addit Manuf – volume: 26 start-page: 1 issue: 1 year: 2014 ident: 10.1016/j.compstruct.2025.119041_b0225 article-title: Application of imperialist competitive algorithm and neural networks to optimise the volume fraction of three-parameter functionally graded beams publication-title: J Exp Theor Artif Intell doi: 10.1080/0952813X.2013.782346 – ident: 10.1016/j.compstruct.2025.119041_b0275 – volume: 12 start-page: 183 issue: 2–3 year: 2005 ident: 10.1016/j.compstruct.2025.119041_b0150 article-title: Artificial Neural Network as a numerical form of effective constitutive law for composites with parametrized and hierarchical microstructure publication-title: CAMES – volume: 23 start-page: 1482 issue: 6 year: 1992 ident: 10.1016/j.compstruct.2025.119041_b0295 article-title: Homogenization and two-scale convergence publication-title: SIAM J Math Anal, doi: 10.1137/0523084 – ident: 10.1016/j.compstruct.2025.119041_b0015 doi: 10.1142/9505 – volume: 26 start-page: 197 issue: 2 year: 2014 ident: 10.1016/j.compstruct.2025.119041_b0220 article-title: Application of firefly algorithm and ANFIS for optimisation of functionally graded beams publication-title: J Exp Theor Artif Intell doi: 10.1080/0952813X.2013.813978 – volume: 425 year: 2024 ident: 10.1016/j.compstruct.2025.119041_b0325 article-title: Handling noise and overfitting in surrogate models based on non-uniform rational basis spline entities publication-title: Comput Methods Appl Mech Eng doi: 10.1016/j.cma.2024.116913 – volume: V2 year: 2025 ident: 10.1016/j.compstruct.2025.119041_b0365 article-title: Homogenization results for the X-shaped microstructure publication-title: Mendeley Data – ident: 10.1016/j.compstruct.2025.119041_b0245 doi: 10.5019/j.ijcir.2005.32 – volume: 18 start-page: 303 issue: 4 year: 2011 ident: 10.1016/j.compstruct.2025.119041_b0155 article-title: Application of artificial neural network in soil parameter identification for deep excavation numerical model publication-title: CAMES – volume: 224 year: 2021 ident: 10.1016/j.compstruct.2025.119041_b0185 article-title: A review of artificial neural networks in the constitutive modeling of composite materials publication-title: Compos B Eng doi: 10.1016/j.compositesb.2021.109152 – ident: 10.1016/j.compstruct.2025.119041_b0195 doi: 10.1007/978-94-007-4722-7_27 – volume: 47 start-page: 1477 issue: 11 year: 2010 ident: 10.1016/j.compstruct.2025.119041_b0075 article-title: Second-order homogenisation of functionally graded materials publication-title: Int J Solids Struct doi: 10.1016/j.ijsolstr.2010.02.004 – volume: 156 start-page: 29 year: 2016 ident: 10.1016/j.compstruct.2025.119041_b0210 article-title: Differential evolution for free vibration optimization of functionally graded nano beams publication-title: Compos Struct doi: 10.1016/j.compstruct.2016.03.052 – volume: 12 start-page: E2735 issue: 17 year: 2019 ident: 10.1016/j.compstruct.2025.119041_b0060 article-title: Fracture behavior of bio-inspired functionally graded soft-hard composites made by multi-material 3D printing: the case of colinear cracks publication-title: Materials (Basel) doi: 10.3390/ma12172735 – volume: 280 year: 2022 ident: 10.1016/j.compstruct.2025.119041_b0120 article-title: Thermal design of graded architected cellular materials through a CAD-compatible topology optimisation method publication-title: Compos Struct doi: 10.1016/j.compstruct.2021.114862 – volume: 32 start-page: 234 issue: 2 year: 2015 ident: 10.1016/j.compstruct.2025.119041_b0205 article-title: An evolutionary approach for simultaneous optimization of material property distribution and topology of FG structures publication-title: Eng Comput doi: 10.1108/EC-07-2013-0188 – ident: 10.1016/j.compstruct.2025.119041_b0240 doi: 10.1007/978-3-540-70928-2_22 – volume: 160 start-page: 43 year: 2017 ident: 10.1016/j.compstruct.2025.119041_b0105 article-title: Thermal analysis of FGM plates – a critical review of various modeling techniques and solution methods publication-title: Compos Struct doi: 10.1016/j.compstruct.2016.10.047 – volume: 27 start-page: 161 issue: 3 year: 2000 ident: 10.1016/j.compstruct.2025.119041_b0145 article-title: On self-learning finite element codes based on monitored response of structures publication-title: Comput Geotech doi: 10.1016/S0266-352X(00)00016-1 – ident: 10.1016/j.compstruct.2025.119041_b0020 doi: 10.1007/978-3-319-53756-6 – ident: 10.1016/j.compstruct.2025.119041_b0050 doi: 10.1007/978-0-387-30877-7_32 – volume: 47 start-page: 1487 issue: 6 year: 2012 ident: 10.1016/j.compstruct.2025.119041_b0095 article-title: Dynamic modelling of thin plate made of certain functionally graded materials publication-title: Meccanica doi: 10.1007/s11012-011-9532-z – ident: 10.1016/j.compstruct.2025.119041_b0010 – ident: 10.1016/j.compstruct.2025.119041_b0270 – volume: 175 year: 2023 ident: 10.1016/j.compstruct.2025.119041_b0310 article-title: Discovery of quasi-disordered truss metamaterials inspired by natural cellular materials publication-title: J Mech Phys Solids doi: 10.1016/j.jmps.2023.105294 – ident: 10.1016/j.compstruct.2025.119041_b0045 – ident: 10.1016/j.compstruct.2025.119041_b0255 doi: 10.1007/s41939-020-00087-x – volume: 121 year: 2023 ident: 10.1016/j.compstruct.2025.119041_b0355 article-title: Particle Swarm optimization or differential evolution—a comparison publication-title: Eng Appl Artif Intel doi: 10.1016/j.engappai.2023.106008 – volume: 27 start-page: 37 issue: 1 year: 2001 ident: 10.1016/j.compstruct.2025.119041_b0280 article-title: An approach to micro-macro modeling of heterogeneous materials publication-title: Comput Mech doi: 10.1007/s004660000212 – volume: 39 start-page: 867 issue: 5 year: 1996 ident: 10.1016/j.compstruct.2025.119041_b0140 article-title: Finite element solutions with feedback network mechanism through direct minimization of energy functionals publication-title: Int J Numer Meth Eng doi: 10.1002/(SICI)1097-0207(19960315)39:5<867::AID-NME886>3.0.CO;2-Q – volume: 36 start-page: 2305 issue: 13 year: 1993 ident: 10.1016/j.compstruct.2025.119041_b0135 article-title: Neural networks for computing in structural analysis: methods and prospects of applications publication-title: Int J Numer Meth Eng doi: 10.1002/nme.1620361310 – volume: 214 start-page: 83 year: 2019 ident: 10.1016/j.compstruct.2025.119041_b0265 article-title: A review on optimization of composite structures part II: functionally graded materials publication-title: Compos Struct doi: 10.1016/j.compstruct.2019.01.105 – volume: 49 start-page: 627 issue: 5 year: 2011 ident: 10.1016/j.compstruct.2025.119041_b0080 article-title: On the modelling of stability problems for thin plates with functionally graded structure publication-title: Thin-Walled Struct doi: 10.1016/j.tws.2010.09.005 – volume: 49 issue: 2 year: 2011 ident: 10.1016/j.compstruct.2025.119041_b0085 article-title: Non-stationary heat transfer in a hollow cylinder with functionally graded material properties publication-title: J Theor Appl Mech – volume: 137 start-page: 85 year: 2016 ident: 10.1016/j.compstruct.2025.119041_b0100 article-title: Nonlinear free vibration of pre- and post-buckled FGM plates on two-parameter foundation in the thermal environment publication-title: Compos Struct doi: 10.1016/j.compstruct.2015.11.017 |
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| Snippet | In this paper, the differential evolution (DE) algorithm is employed to design functionally graded materials (FGMs). The design problem is formulated as a... |
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| SubjectTerms | Artificial Neural Network Computational Homogenization Constrained Optimization Differential Evolution Functionally Graded Material Micro-Macro Approach |
| Title | Differential evolution algorithm and artificial neural network surrogate model for functionally graded material homogenization and design |
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