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Advances in Nano Research
  Volume 12, Number 5, May 2022 , pages 441-455

Nonlinear bending analysis of porous sigmoid FGM nanoplate via IGA and nonlocal strain gradient theory
Thanh Cuong-Le, Khuong D. Nguyen, Hoang Le-Minh, Phuong Phan-Vu, Phuoc Nguyen-Trong, Abdelouahed Tounsi

    This study explores the linear and nonlinear solutions of sigmoid functionally graded material (S-FGM) nanoplate with porous effects. A size-dependent numerical solution is established using the strain gradient theory and isogeometric finite element formulation. The nonlinear nonlocal strain gradient is developed based on the Reissner-Mindlin plate theory and the Von-Kármán strain assumption. The sigmoid function is utilized to modify the classical functionally graded material to ensure the constituent volume distribution. Two different patterns of porosity distribution are investigated, viz. pattern A and pattern B, in which the porosities are symmetric and asymmetric varied across the plate's thickness, respectively. The nonlinear finite element governing equations are established for bending analysis of S-FGM nanoplates, and the Newton-Raphson iteration technique is derived from the nonlinear responses. The isogeometric finite element method is the most suitable numerical method because it can satisfy a higher-order derivative requirement of the nonlocal strain gradient theory. Several numerical results are presented to investigate the influences of porosity distributions, power indexes, aspect ratios, nonlocal and strain gradient parameters on the porous S-FGM nanoplate's linear and nonlinear bending responses.
Key Words
    isogeometric analysis; nonlinear bending; nonlocal strain gradient; porosity; S-FGM nanoplate
Thanh Cuong-Le, Hoang Le-Minh, Phuong Phan-Vu, and Phuoc Nguyen-Trong,: Faculty of Civil Engineering, Ho Chi Minh City Open University, Ho Chi Minh City, Vietnam

Khuong D. Nguyen: Department of Engineering Mechanics, Faculty of Applied Science,
Ho Chi Minh City University of Technology (HCMUT), Ho Chi Minh City, Vietnam/ Vietnam National University, Ho Chi Minh City, Vietnam

Abdelouahed Tounsi: YFL (Yonsei Frontier Lab), Yonsei University, Seoul, Korea/ Department of Civil and Environmental Engineering, King Fahd University of Petroleum & Minerals, 31261 Dhahran, Eastern Province, Saudi Arabia/ Material and Hydrology Laboratory, University of Sidi Bel Abbes, Faculty of Technology, Civil Engineering Department, Algeria

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