Optimización Topológica de Estructuras de Pared Delgada bajo un Enfoque Directo: Validación y Aplicación Industrial

Autores

DOI:

https://doi.org/10.70567/mc.v42.ocsid8345

Palavras-chave:

Optimización Topológica, MITC4, Estructuras de pared delgada, Campo no lineal geométrico

Resumo

El presente trabajo aborda la optimización topológica aplicada a estructuras de pared delgada, modeladas mediante elementos finitos de cáscara MITC4 en campo geométricamente no lineal. El problema se plantea como la minimización de la end compliance sujeta a una restricción de volumen, con el fin de obtener diseños aligerados sin comprometer la respuesta mecánica. La herramienta numérica desarrollada fue validada contra resultados disponibles en la literatura para respuestas tanto en el plano (in-plane) como fuera del plano (out-of-plane), demostrando la versatilidad y robustez de la formulación utilizada. Finalmente, se presenta una aplicación de interés industrial en un panel B de un chasis automotriz, donde se logró obtener piezas optimizadas de menor peso bajo diferentes fracciones de material sólido permitidas, manteniendo la satisfacción de las condiciones de servicio requeridas.

Referências

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.

Publicado

2025-12-04

Edição

Seção

Artigos completos da conferência MECOM 2025

Artigos mais lidos pelo mesmo(s) autor(es)