Nonlinear mechanical analysis of aerospace shell structures through the discontinuous Galerkin method
Giuliano Guarino, Alberto Milazzo
download PDFAbstract. The geometrically non-linear mechanical response of multilayer composite shells is addressed via an innovative discontinuous Galerkin formulation. In the framework of the Carrera Unified formulation, equivalent single layer kinematics with different through-the-thickness accuracy is adopted. The variational statement governing the shell nonlinear behavior is derived. The corresponding governing equations are solved via a discontinuous Galerkin approach, which employs the pure penalty method to weakly enforce the connection between the mesh elements. Numerical tests are presented to show the capabilities of the proposed approach.
Keywords
Multilayered Shells, Nonlinear Structural Behavior, Discontinuous Galerkin Method, High-Order Modelling
Published online 11/1/2023, 4 pages
Copyright © 2023 by the author(s)
Published under license by Materials Research Forum LLC., Millersville PA, USA
Citation: Giuliano Guarino, Alberto Milazzo, Nonlinear mechanical analysis of aerospace shell structures through the discontinuous Galerkin method, Materials Research Proceedings, Vol. 37, pp 287-290, 2023
DOI: https://doi.org/10.21741/9781644902813-62
The article was published as article 62 of the book Aeronautics and Astronautics
Content from this work may be used under the terms of the Creative Commons Attribution 3.0 license. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI.
References
[1] B.Wu, A. Pagani, W. Chen, E. Carrera, Geometrically nonlinear refined shell theories by Carrera Unified Formulation, Mechanics of Advanced Materials and Structures. 28 (2021) 1721–1741. https://doi.org/10.1080/15376494.2019.1702237
[2] A. Milazzo, G. Guarino, V. Gulizzi, Buckling and post-buckling of variable stiffness plates with cutouts by a single-domain Ritz method, Thin-Walled Structures. 182 (2023) 110282. https://doi.org/10.1016/j.tws.2022.110282
[3] M. Fouaidi, A. Hamdaoui, M. Jamal, B. Braikat, A high order mesh-free method for buckling and post-buckling analysis of shells, Engineering Analysis with Boundary Elements. 99 (2019) 89–99. https://doi.org/10.1016/j.enganabound.2018.11.014
[4] S. Hosseini, G. Rahimi, D. Shahgholian-Ghahfarokhi, A meshless collocation method on nonlinear analysis of functionally graded hyperelastic plates using radial basis function, ZAMM – Journal of Applied Mathematics and Mechanics. 102 (2022) 202100216. https://doi.org/10.1002/zamm.202100216
[5] Y. Guo, Z. Zou, M. Ruess, Isogeometric multi-patch analyses for mixed thin shells in the framework of non-linear elasticity, Computer Methods in Applied Mechanics and Engineering, 380 (2021) 113771. https://doi.org/10.1016/j.cma.2021.11377.
[6] D. N. Arnold, F. Brezzi, B. Cockburn, L. D. Marini, Unified analysis of discontinuous Galerkin methods for elliptic problems, SIAM Journal on Numerical Analysis. 39 (2002) 1749–1779. https://doi.org/10.1137/S0036142901384162
[7] V. Gulizzi, I. Benedetti, A. Milazzo, Discontinuous Galerkin methods for solids and structures, in: F. M. H. Aliabadi, W. Soboyejo (Eds.), Comprehensive Structural Integrity, 2nd Edition, vol. 3, Elsevier, Oxford, 2023, pp. 348–377. https://doi.org/10.1016/B978-0-12-822944-6.00024-4
[8] G. Guarino, A. Milazzo, V. Gulizzi, Equivalent-single-layer discontinuous Galerkin methods for static analysis of multilayered shells, Applied Mathematical Modelling, 98 (2021) 701–721. https://doi.org/10.1016/j.apm.2021.05.024
[9] G. Guarino, V. Gulizzi, A. Milazzo, High-fidelity analysis of multilayered shells with cut-outs via the discontinuous Galerkin method, Composite Structures, 276 (2021), 114499. https://doi.org/10.1016/j.compstruct.2021.114499
[10] G. Guarino, A. Milazzo, A discontinuous Galerkin formulation for nonlinear analysis of multilayered shells refined theories, International Journal of Mechanical Sciences, 255 (2023), 108426. https://doi.org/10.1016/j.ijmecsci.2023.108426
[11] E. Carrera, A. Pagani, R. Azzara, R. Augello, Vibration of metallic and composite shells in geometrical nonlinear equilibrium states, Thin-Walled Structures. 157 (2020) 107131. https://doi.org/10.1016/j.tws.2020.107131
[12] K. Sze, X. Liu, S. Lo, Popular benchmark problems for geometric nonlinear analysis of shells, Finite Elements in Analysis and Design. 40 (2004) 1551–1569. https://doi.org/10.1016/j.finel.2003.11.001