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Steel and Composite Structures
  Volume 45, Number 3, November10 2022 , pages 331-348

Effects of size-dependence on static and free vibration of FGP nanobeams using finite element method based on nonlocal strain gradient theory
Quoc-Hoa Pham and Phu-Cuong Nguyen

    The main goal of this article is to develop the finite element formulation based on the nonlocal strain gradient and the refined higher-order deformation theory employing a new function f(z) to investigate the static bending and free vibration of functionally graded porous (FGP) nanobeams. The proposed model considers the simultaneous effects of two parameters: nonlocal and strain gradient coefficients. The nanobeam is made by FGP material that exists in un-even and logarithmic-uneven distribution. The governing equation of the nanobeam is established based on Hamilton's principle. The authors use a 2-node beam element, each node with 8 degrees of freedom (DOFs) approximated by the C1 and C2 continuous Hermit functions to obtain the elemental stiffness matrix and mass matrix. The accuracy of the proposed model is tested by comparison with the results of reputable published works. From here, the influences of the parameters: nonlocal elasticity, strain gradient, porosity, and boundary conditions are studied.
Key Words
    finite element method; functionally graded porous material; nanobeam; nonlocal strain gradient theory; refined higher-order deformation theory
Quoc-Hoa Pham and Phu-Cuong Nguyen: Advanced Structural Engineering Laboratory, Department of Structural Engineering, Faculty of Civil Engineering, Ho Chi Minh City Open
University, Ho Chi Minh City, Vietnam

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