The asymptotic homogenization method applied to the elastostatic model of functionally graded microperiodic Euler-Bernoulli beams
DOI:
https://doi.org/10.5902/2179460X90550Keywords:
Euler-Bernoulli beam, Asymptotic homogenization method, Formal asymptotic solution, Homogenized and local problemsAbstract
This work presents the application of the asymptotic homogenization method to a problem which models the mechanical equilibrium of functionally graded microperiodic Euler-Bernoulli beams clamped at both ends and subjected to a microperiodic distributed load. The five-term formal asymptotic solution is obtained in terms of the solution of the homogenized problem and the periodic solutions of the local problems, for whose existence a new result is presented. Analytical expressions for the homogenized and local solutions are provided. The exact solution of the problem, which is seldom available, is also provided for comparison purposes.
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Bakhvalov, N. & Panasenko, G. (1989). Homogenisation: Averaging Processes in Periodic Media: Mathematical Problems in the Mechanics of Composite Material. (MASS Series, 1st ed.). Springer Netherlands.
Bensoussan, A., Lions, J., & Papanicolau, G. (1978). Asymptotic Analysis for Periodic Structures. (MAEE series, 5th vol.). North Holland.
Ciouranescu, D. & Donato, P. (2000). An Introduction to Homogenization. (17th vol.). Oxford University Press.
Huang, Z., Xing, Y., & Gao, Y. (2020). A two-scale asymptotic expansion method for periodic composite Euler beams. Composite Structures, 241:112033.
Rao, S. S. (2016). Mechanical Vibrations. (6th ed.). Harlow: Pearson.
Silva, D. M., P´erez-Fern´andez, L. D., Molter, A., & Bravo-Castillero, J. (2023). M´etodo de homogeneizac¸ ˜ao assint´otica aplicado ao modelo de vigas de Euler-Bernoulli est´atico. Anais da Jornada de Matem´atica e Matem´atica Aplicada. S˜ao Paulo, SP, Brazil, 4.
Tartar, L. (2009). The General Theory of Homogenization: A Personalized Introduction. UMILN. (UMILN series, 7th vol.). Springer.
Torquato, S. (2002). Random Heterogeneus Materials: Microstructure and Macroscopic properties. (IAM series, 16th ed.). Springer
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