Topology Optimization of Thin-Walled Structures Using a Direct Approach: Validation and Industrial Application
DOI:
https://doi.org/10.70567/mc.v42.ocsid8345Keywords:
Topology Optimization, MITC4, Thin-walled structures, Geometrically nonlinear behaviorAbstract
The present work addresses topology optimization applied to thin-walled structures modeled with MITC4 shell finite elements under geometrically nonlinear behavior. The problem is formulated as the minimization of the structural end compliance subject to a volume constraint, with the aim of obtaining lightweight designs without compromising the mechanical response. The developed numerical tool was validated against benchmark results available in the literature for both in-plane and outof- plane responses, demonstrating the versatility and robustness of the adopted formulation. Finally, an industrially relevant application is presented on a B-pillar panel of an automotive chassis, where optimized lightweight components were obtained under different admissible solid material fractions, while maintaining compliance with the required service conditions.
References
Albanesi A.E., Álvarez Hostos J.C., Fachinotti V.D., y Volpe N.J. Design of metadevices based on isotropic materials for eigenfrequency recovery in lightened structures. Journal of Vibration and Control, 31:1377–1390, 2025. http://doi.org/https://doi.org/10.1177/10775463241244469.
Bathe K.J. Finite Element Procedures. Prentice Hall, 1996.
Behrou R., Lotfi R., Carstensen J.V., Ferrari F., y Guest J.K. Revisiting element removal for density-based structural topology optimization with reintroduction by heaviside projection. Computer Methods in Applied Mechanics and Engineering, 380:113799, 2021. http://doi.org/https://doi.org/10.1016/j.cma.2021.113799.
Bendsøe M.P. y Kikuchi N. Generating optimal topologies in structural design using a homogenization method. Computer Methods in Applied Mechanics and Engineering, 71:197– 224, 1988. http://doi.org/10.1016/0045-7825(88)90086-2.
Bourdin B. Filters in topology optimization. International Journal for Numerical Methods in Engineering, 50:2143–2158, 2001. http://doi.org/https://doi.org/10.1002/nme.116.
Bruns T.E. y Tortorelli D.A. Topology optimization of non-linear elastic structures and compliant mechanisms. Computer Methods in Applied Mechanics and Engineering, 190:3443–3459, 2001. http://doi.org/https://doi.org/10.1016/S0045-7825(00)00278-4.
Buhl T., Pedersen C.B.W., y Sigmund O. Stiffness design of geometrically nonlinear structures using topology optimization. Structural and Multidisciplinary Optimization, 19:93–104, 2000. http://doi.org/https://doi.org/10.1007/s001580050089.
Dvorkin E.N. y Bathe K.J. A continuum mechanics based four-node shell element for general nonlinear analysis. Engineering Computations, 1:77–88, 1984. http://doi.org/http://dx.doi.org/10.1108/eb023562.
Feng F., Xiong S., Kobayashi H., Zhou Y., Tanaka M., Kawamoto A., Nomura T., y Zhu B. Nonlinear topology optimization on thin shells using a reduced-order elastic shell model. Thin-Walled Structures, 197:111566, 2024. http://doi.org/https://doi.org/10.1016/j.tws.2024.111566.
Guest J.K., Prévost J.H., y Belytschko T. Achieving minimum length scale in topology optimization using nodal design variables and projection functions. International Journal for Numerical Methods in Engineering, 61:238–254, 2004. http://doi.org/https://doi.org/10.1002/nme.1064.
Sigmund O. A 99 line topology optimization code written in matlab. Struct Multidisc Optim, 21:120–127, 2001. http://doi.org/https://doi.org/10.1007/s001580050176.
Simo J. y Fox D. On a stress resultant geometrically exact shell model. part i: Formulation and optimal parametrization. Computer Methods in Applied Mechanics and Engineering, 72:267–304, 1989. http://doi.org/https://doi.org/10.1016/0045-7825(89)90002-9.
Simo J., Fox D., y Rifai M. On a stress resultant geometrically exact shell model. part ii: The linear theory; computational aspects. Computer Methods in Applied Mechanics and Engineering, 73:53–92, 1989. http://doi.org/https://doi.org/10.1016/0045-7825(89)90098-4.
Stegmann J. y Lund E. Nonlinear topology optimization of layered shell structures. Structural and Multidisciplinary Optimization, 29:349–360, 2005. http://doi.org/https://doi.org/10.1007/s00158-004-0468-y.
Svanberg K. The method of moving asymptotes—a new method for structural optimization. International Journal for Numerical Methods in Engineering, 24:359–373, 1987. http://doi.org/https://doi.org/10.1002/nme.1620240207.
Zheng J., Yang X., y Long S. Topology optimization with geometrically non-linear based on the element free galerkin method. International Journal of Mechanics and Materials in Design, 11:231–241, 2015. http://doi.org/https://doi.org/10.1007/s10999-014-9257-y.
Álvarez Hostos J.C., Fachinotti V.D., y Peralta I. Computational design of thermo-mechanical metadevices using topology optimization. Applied Mathematical Modelling, 90:758–776, 2021. http://doi.org/https://doi.org/10.1016/j.apm.2020.09.030.
Downloads
Published
Issue
Section
License
Copyright (c) 2025 Argentine Association for Computational Mechanics

This work is licensed under a Creative Commons Attribution 4.0 International License.
This publication is open access diamond, with no cost to authors or readers.
Only those papers that have been accepted for publication and have been presented at the AMCA congress will be published.

