How to cite this paper
Dang, H & Pham, Q. (2026). Hybrid computational approach for nonlinear bending of bio-inspired helicoid composite plates using MITC3i and AN.Engineering Solid Mechanics, 14(1), 35-52.
References
Amara, R., Riadh, B., Hassen, A. A., Mokhtar, N., & Hadji, L. (2024). Hygrothermal effect of bio-inspired helicoid laminate plate for strengthening damaged RC beam. Mechanics of Advanced Materials and Structures, 1-18. doi:10.1080/15376494.2024.2392623
Barbero, E. J. (2011). Introduction to Composite Materials Design. Boca Raton: CRC Press.
Benyus, J. (1997). Innovation inspired by nature: Biomimicry: New York: William Morrow & Co.
Bischoff, M., & Bletzinger, K.-U. (2004). Improving stability and accuracy of Reissner–Mindlin plate finite elements via algebraic subgrid scale stabilization. Computer Methods in Applied Mechanics and Engineering, 193(15-16), 1517-1528. doi:10.1016/j.cma.2003.12.036
Cui, X. Y., & Tian, L. (2017). A Central Point-Based Discrete Shear Gap Method for Plates and Shells Analysis Using Triangular Elements. International Journal of Applied Mechanics, 09(04). doi:10.1142/s1758825117500557
Do, N.-T., Nguyen, T. T., Tran, T. T., Le, P. B., & Pham, Q.-H. (2023). Free vibration analysis of bio-inspired helicoid laminated composite plates resting on elastic foundation using isogeometric analysis and artificial neural network. Mechanics of Time-Dependent Materials, 28(4), 2487-2510. doi:10.1007/s11043-023-09649-1
Fadlallah, S. O., Anderson, T. N., & Nates, R. J. (2021). Artificial Neural Network–Particle Swarm Optimization (ANN-PSO) Approach for Behaviour Prediction and Structural Optimization of Lightweight Sandwich Composite Heliostats. Arabian Journal for Science and Engineering, 46(12), 12721-12742. doi:10.1007/s13369-021-06126-0
Garg, A., Belarbi, M.-O., Li, L., Sharma, N., Gupta, A., & Chalak, H. D. (2023). Free vibration analysis of bio-inspired helicoid laminated composite plates. The Journal of Strain Analysis for Engineering Design, 58(7), 538-548. doi:10.1177/03093247231160414
Hagan, M. T., & Menhaj, M. B. (1994). Training feedforward networks with the Marquardt algorithm. IEEE Trans Neural Netw, 5(6), 989-993. doi:10.1109/72.329697
Kant, T., & Kommineni, J. R. (1992). C0 Finite element geometrically non-linear analysis of fibre reinforced composite and sandwich laminates based on a higher-order theory. Computers & Structures, 45(3), 511-520. doi:10.1016/0045-7949(92)90436-4
Karamanli, A., Vo, T. P., & Eltaher, M. A. (2024). Comprehensive analysis of bio-inspired laminated composites plates using a quasi-3D theory and higher order FE models. Thin-Walled Structures, 198. doi:10.1016/j.tws.2024.111735
Khatir, S., Tiachacht, S., Le Thanh, C., Ghandourah, E., Mirjalili, S., & Abdel Wahab, M. (2021). An improved Artificial Neural Network using Arithmetic Optimization Algorithm for damage assessment in FGM composite plates. Composite Structures, 273. doi:10.1016/j.compstruct.2021.114287
Lee, P.-S., & Bathe, K.-J. (2004). Development of MITC isotropic triangular shell finite elements. Computers & Structures, 82(11-12), 945-962. doi:10.1016/j.compstruc.2004.02.004
Lee, P.-S., & Bathe, K.-J. (2010). The quadratic MITC plate and MITC shell elements in plate bending. Advances in Engineering Software, 41(5), 712-728. doi:10.1016/j.advengsoft.2009.12.011
Lee, Y., Jeon, H.-M., Lee, P.-S., & Bathe, K.-J. (2015). The modal behavior of the MITC3+ triangular shell element. Computers & Structures, 153, 148-164. doi:10.1016/j.compstruc.2015.02.033
Lee, Y., Lee, P.-S., & Bathe, K.-J. (2014). The MITC3+ shell element and its performance. Computers & Structures, 138, 12-23. doi:10.1016/j.compstruc.2014.02.005
Mahesh, V. (2023). Artificial neural network (ANN) based investigation on the static behaviour of piezo-magneto-thermo-elastic nanocomposite sandwich plate with CNT agglomeration and porosity. International Journal of Non-Linear Mechanics, 153. doi:10.1016/j.ijnonlinmec.2023.104406
Mohamed, S. A., Mohamed, N., & Eltaher, M. A. (2022a). Bending, buckling and linear vibration of bio-inspired composite plates. Ocean Engineering, 259. doi:10.1016/j.oceaneng.2022.111851
Mohamed, S. A., Mohamed, N., & Eltaher, M. A. (2022b). Bending, buckling and linear vibration of bio-inspired composite plates. Ocean Engineering, 259, 111851. doi:10.1016/j.oceaneng.2022.111851
Mohammad Malekzadeh, S. H.-J., Saeed Shojaee (2021). Improvement of Numerical Manifold Method using Nine-node Quadrilateral and Ten-node Triangular Elements along with Complex Fourier RBFs in Modeling Free and Forced Vibrations. Journal of Applied and Computational Mechanics, 7(4), 2049-2063. doi:10.22055/jacm.2020.32423.2027
Nath, Y., Prithviraju, M., & Mufti, A. A. (2006). Nonlinear statics and dynamics of antisymmetric composite laminated square plates supported on nonlinear elastic subgrade. Communications in Nonlinear Science and Numerical Simulation, 11(3), 340-354. doi:10.1016/j.cnsns.2004.11.003
Nguyen-Van, H., Nguyen-Hoai, N., Chau-Dinh, T., & Nguyen-Thoi, T. (2014). Geometrically nonlinear analysis of composite plates and shells via a quadrilateral element with good coarse-mesh accuracy. Composite Structures, 112, 327-338. doi:10.1016/j.compstruct.2014.02.024
Nguyen, T.-K., Nguyen, V.-H., Chau-Dinh, T., Vo, T. P., & Nguyen-Xuan, H. (2016). Static and vibration analysis of isotropic and functionally graded sandwich plates using an edge-based MITC3 finite elements. Composites Part B: Engineering, 107, 162-173. doi:10.1016/j.compositesb.2016.09.058
Pawlyn, M. (2019). Biomimicry in Architecture. London: RIBA Publishing.
Pham, Q.-H., Nguyen, P.-C., & Tran, T. T. (2022a). Free vibration response of auxetic honeycomb sandwich plates using an improved higher-order ES-MITC3 element and artificial neural network. Thin-Walled Structures, 175. doi:10.1016/j.tws.2022.109203
Pham, Q.-H., Pham, T.-D., Trinh, Q. V., & Phan, D.-H. (2019). Geometrically nonlinear analysis of functionally graded shells using an edge-based smoothed MITC3 (ES-MITC3) finite elements. Engineering with Computers, 36(3), 1069-1082. doi:10.1007/s00366-019-00750-z
Pham, Q.-H., Thanh Tran, T., Ke Tran, V., Nguyen, P.-C., & Nguyen-Thoi, T. (2022b). Free vibration of functionally graded porous non-uniform thickness annular-nanoplates resting on elastic foundation using ES-MITC3 element. Alexandria Engineering Journal, 61(3), 1788-1802. doi:10.1016/j.aej.2021.06.082
Pham, Q.-H., Tran, V. K., & Tran, T. T. (2023). Vibration characteristics of sandwich plates with an auxetic honeycomb core and laminated three-phase skin layers under blast load. Defence Technology, 24, 148-163. doi:10.1016/j.dt.2022.10.002
Pica, A., Wood, R. D., & Hinton, E. (1980). Finite element analysis of geometrically nonlinear plate behaviour using a mindlin formulation. Computers & Structures, 11(3), 203-215. doi:10.1016/0045-7949(80)90160-1
Reddy, J. N. ((2003)). Mechanics of laminated composite plates and shells: theory and analysis: CRC press.
Ribeiro Junior, R. F., & Gomes, G. F. (2023). On the Use of Machine Learning for Damage Assessment in Composite Structures: A Review. Applied Composite Materials, 31(1), 1-37. doi:10.1007/s10443-023-10161-5
Setoodeh, A. R., & Karami, G. (2004). Static, free vibration and buckling analysis of anisotropic thick laminated composite plates on distributed and point elastic supports using a 3-D layer-wise FEM. Engineering Structures, 26(2), 211-220. doi:10.1016/j.engstruct.2003.09.009
Sharma, A., Belarbi, M. O., Garg, A., & Li, L. (2023). Bending analysis of bio-inspired helicoidal/Bouligand laminated composite plates. Mechanics of Advanced Materials and Structures, 31(21), 5326-5340. doi:10.1080/15376494.2023.2214934
Weil, N. A., & Newmark, N. M. (1956). Large Deflections of Elliptical Plates. Journal of Applied Mechanics, 23(1), 21-26. doi:10.1115/1.4011202
Zhang, Y. X., & Cheung, Y. K. (2003). Geometric nonlinear analysis of thin plates by a refined nonlinear non-conforming triangular plate element. Thin-Walled Structures, 41(5), 403-418. doi:10.1016/s0263-8231(02)00114-3
Zhang, Y. X., & Kim, K. S. (2006). Geometrically nonlinear analysis of laminated composite plates by two new displacement-based quadrilateral plate elements. Composite Structures, 72(3), 301-310. doi:10.1016/j.compstruct.2005.01.001
Barbero, E. J. (2011). Introduction to Composite Materials Design. Boca Raton: CRC Press.
Benyus, J. (1997). Innovation inspired by nature: Biomimicry: New York: William Morrow & Co.
Bischoff, M., & Bletzinger, K.-U. (2004). Improving stability and accuracy of Reissner–Mindlin plate finite elements via algebraic subgrid scale stabilization. Computer Methods in Applied Mechanics and Engineering, 193(15-16), 1517-1528. doi:10.1016/j.cma.2003.12.036
Cui, X. Y., & Tian, L. (2017). A Central Point-Based Discrete Shear Gap Method for Plates and Shells Analysis Using Triangular Elements. International Journal of Applied Mechanics, 09(04). doi:10.1142/s1758825117500557
Do, N.-T., Nguyen, T. T., Tran, T. T., Le, P. B., & Pham, Q.-H. (2023). Free vibration analysis of bio-inspired helicoid laminated composite plates resting on elastic foundation using isogeometric analysis and artificial neural network. Mechanics of Time-Dependent Materials, 28(4), 2487-2510. doi:10.1007/s11043-023-09649-1
Fadlallah, S. O., Anderson, T. N., & Nates, R. J. (2021). Artificial Neural Network–Particle Swarm Optimization (ANN-PSO) Approach for Behaviour Prediction and Structural Optimization of Lightweight Sandwich Composite Heliostats. Arabian Journal for Science and Engineering, 46(12), 12721-12742. doi:10.1007/s13369-021-06126-0
Garg, A., Belarbi, M.-O., Li, L., Sharma, N., Gupta, A., & Chalak, H. D. (2023). Free vibration analysis of bio-inspired helicoid laminated composite plates. The Journal of Strain Analysis for Engineering Design, 58(7), 538-548. doi:10.1177/03093247231160414
Hagan, M. T., & Menhaj, M. B. (1994). Training feedforward networks with the Marquardt algorithm. IEEE Trans Neural Netw, 5(6), 989-993. doi:10.1109/72.329697
Kant, T., & Kommineni, J. R. (1992). C0 Finite element geometrically non-linear analysis of fibre reinforced composite and sandwich laminates based on a higher-order theory. Computers & Structures, 45(3), 511-520. doi:10.1016/0045-7949(92)90436-4
Karamanli, A., Vo, T. P., & Eltaher, M. A. (2024). Comprehensive analysis of bio-inspired laminated composites plates using a quasi-3D theory and higher order FE models. Thin-Walled Structures, 198. doi:10.1016/j.tws.2024.111735
Khatir, S., Tiachacht, S., Le Thanh, C., Ghandourah, E., Mirjalili, S., & Abdel Wahab, M. (2021). An improved Artificial Neural Network using Arithmetic Optimization Algorithm for damage assessment in FGM composite plates. Composite Structures, 273. doi:10.1016/j.compstruct.2021.114287
Lee, P.-S., & Bathe, K.-J. (2004). Development of MITC isotropic triangular shell finite elements. Computers & Structures, 82(11-12), 945-962. doi:10.1016/j.compstruc.2004.02.004
Lee, P.-S., & Bathe, K.-J. (2010). The quadratic MITC plate and MITC shell elements in plate bending. Advances in Engineering Software, 41(5), 712-728. doi:10.1016/j.advengsoft.2009.12.011
Lee, Y., Jeon, H.-M., Lee, P.-S., & Bathe, K.-J. (2015). The modal behavior of the MITC3+ triangular shell element. Computers & Structures, 153, 148-164. doi:10.1016/j.compstruc.2015.02.033
Lee, Y., Lee, P.-S., & Bathe, K.-J. (2014). The MITC3+ shell element and its performance. Computers & Structures, 138, 12-23. doi:10.1016/j.compstruc.2014.02.005
Mahesh, V. (2023). Artificial neural network (ANN) based investigation on the static behaviour of piezo-magneto-thermo-elastic nanocomposite sandwich plate with CNT agglomeration and porosity. International Journal of Non-Linear Mechanics, 153. doi:10.1016/j.ijnonlinmec.2023.104406
Mohamed, S. A., Mohamed, N., & Eltaher, M. A. (2022a). Bending, buckling and linear vibration of bio-inspired composite plates. Ocean Engineering, 259. doi:10.1016/j.oceaneng.2022.111851
Mohamed, S. A., Mohamed, N., & Eltaher, M. A. (2022b). Bending, buckling and linear vibration of bio-inspired composite plates. Ocean Engineering, 259, 111851. doi:10.1016/j.oceaneng.2022.111851
Mohammad Malekzadeh, S. H.-J., Saeed Shojaee (2021). Improvement of Numerical Manifold Method using Nine-node Quadrilateral and Ten-node Triangular Elements along with Complex Fourier RBFs in Modeling Free and Forced Vibrations. Journal of Applied and Computational Mechanics, 7(4), 2049-2063. doi:10.22055/jacm.2020.32423.2027
Nath, Y., Prithviraju, M., & Mufti, A. A. (2006). Nonlinear statics and dynamics of antisymmetric composite laminated square plates supported on nonlinear elastic subgrade. Communications in Nonlinear Science and Numerical Simulation, 11(3), 340-354. doi:10.1016/j.cnsns.2004.11.003
Nguyen-Van, H., Nguyen-Hoai, N., Chau-Dinh, T., & Nguyen-Thoi, T. (2014). Geometrically nonlinear analysis of composite plates and shells via a quadrilateral element with good coarse-mesh accuracy. Composite Structures, 112, 327-338. doi:10.1016/j.compstruct.2014.02.024
Nguyen, T.-K., Nguyen, V.-H., Chau-Dinh, T., Vo, T. P., & Nguyen-Xuan, H. (2016). Static and vibration analysis of isotropic and functionally graded sandwich plates using an edge-based MITC3 finite elements. Composites Part B: Engineering, 107, 162-173. doi:10.1016/j.compositesb.2016.09.058
Pawlyn, M. (2019). Biomimicry in Architecture. London: RIBA Publishing.
Pham, Q.-H., Nguyen, P.-C., & Tran, T. T. (2022a). Free vibration response of auxetic honeycomb sandwich plates using an improved higher-order ES-MITC3 element and artificial neural network. Thin-Walled Structures, 175. doi:10.1016/j.tws.2022.109203
Pham, Q.-H., Pham, T.-D., Trinh, Q. V., & Phan, D.-H. (2019). Geometrically nonlinear analysis of functionally graded shells using an edge-based smoothed MITC3 (ES-MITC3) finite elements. Engineering with Computers, 36(3), 1069-1082. doi:10.1007/s00366-019-00750-z
Pham, Q.-H., Thanh Tran, T., Ke Tran, V., Nguyen, P.-C., & Nguyen-Thoi, T. (2022b). Free vibration of functionally graded porous non-uniform thickness annular-nanoplates resting on elastic foundation using ES-MITC3 element. Alexandria Engineering Journal, 61(3), 1788-1802. doi:10.1016/j.aej.2021.06.082
Pham, Q.-H., Tran, V. K., & Tran, T. T. (2023). Vibration characteristics of sandwich plates with an auxetic honeycomb core and laminated three-phase skin layers under blast load. Defence Technology, 24, 148-163. doi:10.1016/j.dt.2022.10.002
Pica, A., Wood, R. D., & Hinton, E. (1980). Finite element analysis of geometrically nonlinear plate behaviour using a mindlin formulation. Computers & Structures, 11(3), 203-215. doi:10.1016/0045-7949(80)90160-1
Reddy, J. N. ((2003)). Mechanics of laminated composite plates and shells: theory and analysis: CRC press.
Ribeiro Junior, R. F., & Gomes, G. F. (2023). On the Use of Machine Learning for Damage Assessment in Composite Structures: A Review. Applied Composite Materials, 31(1), 1-37. doi:10.1007/s10443-023-10161-5
Setoodeh, A. R., & Karami, G. (2004). Static, free vibration and buckling analysis of anisotropic thick laminated composite plates on distributed and point elastic supports using a 3-D layer-wise FEM. Engineering Structures, 26(2), 211-220. doi:10.1016/j.engstruct.2003.09.009
Sharma, A., Belarbi, M. O., Garg, A., & Li, L. (2023). Bending analysis of bio-inspired helicoidal/Bouligand laminated composite plates. Mechanics of Advanced Materials and Structures, 31(21), 5326-5340. doi:10.1080/15376494.2023.2214934
Weil, N. A., & Newmark, N. M. (1956). Large Deflections of Elliptical Plates. Journal of Applied Mechanics, 23(1), 21-26. doi:10.1115/1.4011202
Zhang, Y. X., & Cheung, Y. K. (2003). Geometric nonlinear analysis of thin plates by a refined nonlinear non-conforming triangular plate element. Thin-Walled Structures, 41(5), 403-418. doi:10.1016/s0263-8231(02)00114-3
Zhang, Y. X., & Kim, K. S. (2006). Geometrically nonlinear analysis of laminated composite plates by two new displacement-based quadrilateral plate elements. Composite Structures, 72(3), 301-310. doi:10.1016/j.compstruct.2005.01.001