Exactness of formal asymptotic solutions of a Dirichlet problem modeling the steady state of functionally-graded microperiodic nonlinear rods

• Autorzy: Décio Roberto M.S. , Pérez-Fernández Leslie D. , Bravo-Castillero Julián

Identyfikatory

DOI

10.17512/jamcm.2019.3.04

• Języki publikacji: EN

Abstrakty

EN

In their usual form, homogenization methods produce first-order approximations of the exact solutions of problems for differential equations with rapidly oscillating coefficients which model the physical behavior of microstructured media. However, there is need of approximations containing higher-order terms when the usual first-order approximations, which are formed by superposing a macroscopic trend and a local perturbation, are not capable of reproducing the local details of the exact solutions. Here, two-scale asymptotic solutions with second-order terms are provided for a Dirichlet problem modeling the steady state of functionally-graded microperiodic nonlinear rods. The need of considering higherorder terms is illustrated through numerical examples for various power-law nonlinearities.

Słowa kluczowe

EN

asymptotic homogenization; power-law nonlinearity; functionally-graded rods

PL

stan ustalony; problem Dirichleta; metoda homogenizacji; rozwiązanie asymptotyczne

• Wydawca: Wydawnictwo Politechniki Częstochowskiej
• Czasopismo: Journal of Applied Mathematics and Computational Mechanics
• Rocznik: 2019
• Tom: Vol. 18, nr 3
• Strony: 45--56
• Opis fizyczny: Bibliogr. 25 poz. rys., tab.

Twórcy

autor

Décio Roberto M.S.

• Programa de Pós-Graduação em Modelagem Matemática, Universidade Federal de Pelotas Pelotas-RS, Brazil

autor

Pérez-Fernández Leslie D.

• Instituto de Física e Matemática, Universidade Federal de Pelotas Pelotas-RS, Brazil

autor

Bravo-Castillero Julián

• Instituto de Investigaciones en Matemáticas Aplicadas y Sistemas, Universidad Nacional Autónoma de México Ciudad de México, Mexico

Bibliografia

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Uwagi

Opracowanie rekordu w ramach umowy 509/P-DUN/2018 ze środków MNiSW przeznaczonych na działalność upowszechniającą naukę (2019).