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Steel and Composite Structures
  Volume 31, Number 5, June10 2019 , pages 469-488

Nonlinear bending of functionally graded porous nanobeam subjected to multiple physical load based on nonlocal strain gradient theory
Yang Gao, Wan-shen Xiao and Haiping Zhu

    We in this paper study nonlinear bending of a functionally graded porous nanobeam subjected to multiple physical load based on the nonlocal strain gradient theory. For more reasonable analysis of nanobeams made of porous functionally graded magneto-thermo-electro-elastic materials (PFGMTEEMs), both constituent materials and the porosity appear gradient distribution in the present expression of effective material properties, which is much more suitable to the actual compared with the conventional expression of effective material properties. Besides the displacement function regarding physical neutral surface is introduced to analyze mechanical behaviors of beams made of FGMs. Then we derive nonlinear governing equations of PFGMTEEMs beams using the principle of Hamilton. To obtain analytical solutions, a two-step perturbation method is developed in nonuniform electric field and magnetic field, and then we use it to solve nonlinear equations. Finally, the analytical solutions are utilized to perform a parametric analysis, where the effect of various physical parameters on static bending deformation of nanobeams are studied in detail, such as the nonlocal parameter, strain gradient parameter, the ratio of nonlocal parameter to strain gradient parameter, porosity volume fraction, material volume fraction index, temperature, initial magnetic potentials and external electric potentials.
Key Words
    bending; functionally graded porous materials; nonlocal strain graded theory; multiple physical load
(1) Yang Gao, Wan-shen Xiao:
State Key Laboratory of Advanced Design and Manufacturing for Vehicle Body, Hunan University, Changsha, 410082, China;
(2) Haiping Zhu:
School of Computing, Engineering and Mathematics, Western Sydney University, Locked, Bag 1797, Penrith, NSW 2751, Australia.

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