Asymptotic homogenization with finite elements for an orthotropic radially microperiodic sphere

Authors

DOI:

https://doi.org/10.5902/2179460X73779

Keywords:

Rapidly Oscillating Coefficients, Asymptotic Homogenization, Finite Elements, Microperiodic Sphere

Abstract

This paper proposes a semi-analytical methodology that combines the asymptotic homogenization method (AHM) with the finite elements method (FEM) to solve boundary-value problems with rapidly oscillating coefficients. This approach is motivated by the convergence difficulties observed when this type of problem is addressed directly via FEM, whereas the AHM has shown to be efficacious for obtaining good generic approximations of the exact solution. Illustratively, this AHM-FEM methodology is developed for the mechanical equilibrium problem of a radially microperiodic orthotropic sphere under hydrostatic pressure, which allows its validation by comparing with the AHM analytical solution. Specifically, the effective coefficients and the homogenized and local problems are calculated via AHM, and then their analytical and FEM solutions are obtained. Finally, to validate the semianalytical methodology, the generic solutions are applied in an example and, from the obtained results, a comparison is made between the analytical AHM solution and the semi-analytical AHM-FEM solution.

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Author Biographies

João Geraldo Menezes de Oliveira Neto, Federal University of Sergipe

Civil Engineer graduated from the Federal University of Sergipe (UFS). Currently studying for a Master's degree in Structural Engineering at the School of Engineering of São Carlos (EESC-USP)

Fabio Carlos da Rocha, Federal University of Sergipe

Graduated in Civil Engineering from the Federal University of Sergipe (2006), master's (2009) and doctorate (2015) in Sciences with emphasis in Structural Engineering from the School of Engineering of São Carlos - University of São Paulo. He is currently professor of the Superior Magisterium of the Department of Civil Engineering at the Federal University of Sergipe and coordinator of the Graduate Program in Civil Engineering PROEC/UFS 2020/2022. 

Leslie Darien Pérez Fernández, Federal University of Pelotas

He holds a degree in Mathematics from the University of Havana (2001), a Master's degree in Mathematics from the University of Havana (2006) and a Ph. Since March 2013 he has been a professor at the Department of Mathematics and Statistics at the Institute of Physics and Mathematics of the Federal University of Pelotas (DME-IFM-UFPel) and, since July since 2015, he is a member of the permanent faculty of the Graduate Program in Mathematical Modeling (PPGMMat-IFM-UFPel). He is a member of the research group on Optimization, Control and Nonlinear Analysis (DME-IFM-UFPel).

Maria do Socorro Martins Sampaio, University of the State of Amazonas

Graduated in Civil Engineering from the Federal University of Amazonas - FT/UFAM (2006), Master (2009) and PhD (2014) in Structural Engineering from the University of São Paulo - EESC/USP. She developed a post-doctorate at the School of Engineering of São Carlos - EESC/USP from 01/2014 to 01/2016. She is currently a professor of the Civil Engineering course at the Superior School of Technology at the State University of Amazonas (EST/UEA).

Julián Bravo Castillero, National Autonomous University of Mexico

Doctor Julián Bravo Castillero is a Senior Researcher at the National Autonomous University of Mexico, at the Institute for Research in Applied Mathematics and Systems, in its academic unit in the state of Yucatán, Mexico, Mérida, Yucatán. He has carried out teaching and research internships at various institutions in Germany, Brazil, Colombia, Cuba, Spain, France, and Mexico.

References

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Published

2023-12-01

How to Cite

Oliveira Neto, J. G. M. de, Rocha, F. C. da, Pérez Fernández, L. D., Sampaio, M. do S. M., & Bravo Castillero, J. (2023). Asymptotic homogenization with finite elements for an orthotropic radially microperiodic sphere. Ciência E Natura, 45(esp. 3), e73779. https://doi.org/10.5902/2179460X73779

Issue

Vol. 45 No. esp. 3 (2023): ENMC/ECTM/MCSul/SEMENGO

Section

Special Edition

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