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A Chebyshev–Ritz solution for size-dependent analysis of the porous microbeams with various boundary conditions

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Abstract

This research proposes a Chebyshev–Ritz solution for analysing the size-dependent behaviour of porous microbeams. The displacement field is based on the higher-order beam theory, while the size-dependent effect is accounted for using the modified couple stress theory. Moreover, porous microbeams’ elasticity moduli and mass density are assumed to be graded in the thickness direction according to four distinct distribution patterns. The open-cell metal foam exemplifies a characteristic mechanical attribute that facilitates the determination of the interrelation between coefficients of density and porosity. To derive the governing equations, the Lagrange’s principle is employed. Four types of boundary conditions, including clamped–clamped, clamped-simply supported, clamped-free, and simply-supported, along with four porosity distribution types of the beam, are considered. The Chebyshev polynomial is developed to analyse the porous microbeams’ buckling, free vibration, and bending. Furthermore, the study discusses the impacts of the material length scale parameter, porosity, slenderness, boundary condition, and porosity type on their mechanical responses. Finally, some novel results are presented, which can serve as benchmarks for future studies.

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Acknowledgments

This work belongs to the project in 2023 funded by Ho Chi Minh City University of Technology and Education, Vietnam.

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Authors and Affiliations

  1. Faculty of Civil Engineering, Ho Chi Minh City University of Technology and Education, 1 Vo Van Ngan Street, Thu Duc City, Ho Chi Minh City, Vietnam

    Ngoc-Duong Nguyen

  2. Faculty of Engineering and Technology, Kien Giang University, 320A Route 61, Chau Thanh district, Kien Giang Province, Vietnam

    Thien-Nhan Nguyen

  3. CIRTech Institute, HUTECH University, 475A Dien Bien Phu Street, Binh Thanh District, Ho Chi Minh City, Vietnam

    Trung-Kien Nguyen

  4. School of Computing, Engineering and Mathematical Sciences, La Trobe University, Bundoora, VIC, 3086, Australia

    Thuc P. Vo

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Nguyen, ND., Nguyen, TN., Nguyen, TK. et al. A Chebyshev–Ritz solution for size-dependent analysis of the porous microbeams with various boundary conditions. Int J Mech Mater Des 19, 861–881 (2023). https://doi.org/10.1007/s10999-023-09666-5

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