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Modified nonlocal couple stress isogeometric approach for bending and free vibration analysis of functionally graded nanoplates

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Abstract

In this article, isogeometric analysis (IGA) based on the modified nonlocal couple stress theory (MNCST) is introduced to study bending and free vibration characteristics of functionally graded (FG) nanoplates placed on an elastic foundation (EF). The MNCST is a combination of nonlocal elasticity theory and modified couple stress theory to capture the small-size effects most accurately, hence this theory considers both softening and stiffening effects on responses of FG nanoplates. A higher order refined plate theory is adapted, because it satisfies parabolic distributions of transverse shear stresses across the nanoplate thickness and equals zero at the top and bottom surfaces without requiring shear correction factors. The governing equations are obtained using Hamilton's principle from which deduce the equations determining the natural frequency and displacement of the FG nanoplates. Several comparison studies are conducted to verify the proposed model with other results in the literature. Furthermore, the influence of nonlocal parameters, material length parameters, boundary conditions, material volume exponent on the bending, and free vibration response of FG nanoplates are fully studied.

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Acknowledgements

The authors gratefully acknowledge the financial support granted by the Scientific Research Fund of Ho Chi Minh City Open University for this project.

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Authors and Affiliations

  1. Advanced Structural Engineering Laboratory, Department of Structural Engineering, Faculty of Civil Engineering, Ho Chi Minh City Open University, Ho Chi Minh City, Vietnam

    Quoc-Hoa Pham & Phu-Cuong Nguyen

  2. Faculty of Mechanical Engineering, Le Quy Don Technical University, Hanoi, Vietnam

    Van Ke Tran & Trung Thanh Tran

  3. Faculty of Civil Engineering, Ho Chi Minh City University of Technology (HCMUT), 268 Ly Thuong Kiet Street, District 10, Ho Chi Minh City, Vietnam

    Qui X. Lieu

  4. Vietnam National University Ho Chi Minh City (VNU-HCM), Linh Trung Ward, Thu Duc City, Ho Chi Minh City, Vietnam

    Qui X. Lieu

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Pham, QH., Nguyen, PC., Tran, V.K. et al. Modified nonlocal couple stress isogeometric approach for bending and free vibration analysis of functionally graded nanoplates. Engineering with Computers 39, 993–1018 (2023). https://doi.org/10.1007/s00366-022-01726-2

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