Size effects of functionally graded moderately thick microplates: A novel non-classical simple-FSDT isogeometric analysis

Published on Nov 1, 2017in European Journal of Mechanics A-solids3.786
· DOI :10.1016/J.EUROMECHSOL.2017.08.008
Shuo Liu5
Estimated H-index: 5
(Hohai University),
Tiantang Yu32
Estimated H-index: 32
(Hohai University),
Tinh Quoc Bui54
Estimated H-index: 54
(TITech: Tokyo Institute of Technology)
Sources
Abstract
Abstract This paper presents an effective plate formulation coupling the merits of isogeometric analysis (IGA) and a new non-classical simple first-order shear deformation theory (SFSDT) for static bending, free vibration, and buckling of functionally graded (FG) moderately thick microplates. In contrast to the conventional first-order shear deformation theory (FSDT), the new SFSDT adopted here inherently owns several advantages such as free from shear-locking, capturing the shear-deformation effect, and fewer unknowns. In order to capture the small scale effects, we thus introduce a non-classical SFSDT based on a modified couple stress theory. The requirement for C 2 -continuity in terms of the non-classical SFSDT is straightforwardly treated with the aid of inherent high-order continuity of non-uniform rational B-spline (NURBS), which serves as basis functions in our IGA framework. Numerical examples are presented and the obtained numerical results reveal that the deflection decreases while the frequency and buckling load increase with decreasing the plate thickness. Results also show that the small size effect can lead to an increase of microplate stiffness.
📖 Papers frequently viewed together
3,633 Citations
4 Authors (Shuo Liu, ..., Shifeng Xia)
48 Citations
2,098 Citations
References48
Newest
#1Son Thai (La Trobe University)H-Index: 7
#2Huu-Tai Thai (La Trobe University)H-Index: 46
Last. Vipulkumar Ishvarbhai Patel (La Trobe University)H-Index: 20
view all 4 authors...
Abstract This paper presents a robust numerical model, which takes into account both size-dependent and shear deformation effects, for the bending, buckling and free vibration analyses of functionally graded microplates. The size-dependent effect is captured by using the modified strain gradient elasticity theory with three length scale parameters, whilst the shear deformation effect is accounted by using the third-order shear deformation theory. The rule of mixture is employed to describe the d...
65 CitationsSource
#1Shuo Liu (Hohai University)H-Index: 5
#2Tiantang Yu (Hohai University)H-Index: 32
Last. Shifeng Xia (Hohai University)H-Index: 3
view all 4 authors...
Abstract The paper presents an effective thin plate formulation based on isogeometric analysis (IGA) and a non-classical Kirchhoff plate theory to study static bending, free vibration, and buckling behaviors of homogeneous and functionally graded microplates. The small scale effects are captured using a non-classical Kirchhoff plate theory which is developed based on a modified couple stress theory. The requirement for C 1 -continuity in terms of the non-classical Kirchhoff plate theory is strai...
48 CitationsSource
#1Kulmani Mehar (NITR: National Institute of Technology, Rourkela)H-Index: 18
#2Subrata Kumar Panda (NITR: National Institute of Technology, Rourkela)H-Index: 29
Last. Trupti Ranjan Mahapatra (KIIT: KIIT University)H-Index: 19
view all 4 authors...
ABSTRACTIn this article, the nonlinear vibration frequencies of functionally graded carbon nanotube-reinforced composite doubly curved shell panels under elevated thermal environment are numerically investigated using finite element method. The doubly curved carbon nanotube-reinforced shell panel has been modeled mathematically using higher-order kinematics theory and Green–Lagrange geometrical nonlinear strains. The properties of the individual constituents of the graded composite are assumed t...
52 CitationsSource
#1Tiantang Yu (Hohai University)H-Index: 32
#2Shuohui Yin (XTU: Xiangtan University)H-Index: 18
Last. Nuttawit Wattanasakulpong (Mahanakorn University of Technology)H-Index: 16
view all 5 authors...
Abstract Practical applications such as airplane wings are usually subjected to combined thermal and mechanical loads, and they hence are prone to buckling failure. Preceding works on the buckling of advanced materials, e.g., functionally graded materials, under combined thermal and mechanical loads are rather rare in literature. In this paper, we report new numerical results of thermal-mechanical buckling of functionally graded rectangular and skew plates (FGPs) under combined thermal and mecha...
68 CitationsSource
#1Hoang X. Nguyen (Northumbria University)H-Index: 9
#2Tuan V. Nguyen (Vietnamese-German University)H-Index: 118
Last. Thuc P. Vo (Northumbria University)H-Index: 36
view all 6 authors...
The isogeometric analysis associated with a novel quasi-3D shear deformation theory is proposed to investigate size-dependent behaviours of functionally graded microplates. The modified couple stress theory with only one material length scale parameter is employed to effectively capture the size-dependent effects within the microplates. Meanwhile, the quasi-3D theory which is constructed from a novel seventh-order shear deformation refined plate theory with four unknowns is able to consider both...
151 CitationsSource
#1Shuohui Yin (XTU: Xiangtan University)H-Index: 18
#2Tiantang Yu (Hohai University)H-Index: 32
Last. Sohichi Hirose (TITech: Tokyo Institute of Technology)H-Index: 16
view all 5 authors...
Buckling and vibration of FGM cracked plates with internal cracks and voids are studied.Extended isogeometric analysis with NURBS basis and Reissner-Mindlin theory is developed.The internal defects are modeled by using enrichment methods and level sets.Effects of gradation materials, crack length, etc. on critical buckling and frequency of FGM plate are significant.The accuracy of the XIGA for FGM cracked plates with internal defects is high. The critical buckling parameters and natural frequenc...
64 CitationsSource
#1Shuohui Yin (XTU: Xiangtan University)H-Index: 18
#2Tiantang Yu (Hohai University)H-Index: 32
Last. Satoyuki Tanaka (Hiroshima University)H-Index: 22
view all 5 authors...
Abstract Numerical investigation of buckling and free vibration of functionally graded plates considering in-plane material inhomogeneity is presented in this paper. A novel and effective approach based on isogeometric analysis (IGA) and higher-order shear deformation theory (HSDT) is developed for fulfilling that purpose, analyzing the critical buckling parameter and natural eigenvalues of functionally graded plates involving the in-plane material inhomogeneity. The HSDT allows us to account fo...
69 CitationsSource
#1Reza Ansari (University of Gilan)H-Index: 69
#2A. Norouzzadeh (University of Gilan)H-Index: 16
Abstract The size-dependent static buckling responses of circular, elliptical and skew nanoplates made of functionally graded materials (FGMs) are investigated in this article based on an isogeometric model. The Eringen nonlocal continuum theory is implemented to capture nonlocal effects. According to the Gurtin–Murdoch surface elasticity theory, surface energy influences are also taken into account by the consideration of two thin surface layers at the top and bottom of nanoplate. The material ...
77 CitationsSource
#1Nicholas Fantuzzi (UNIBO: University of Bologna)H-Index: 51
#2Francesco Tornabene (UNIBO: University of Bologna)H-Index: 69
Abstract Engineering applications in conventional numerical modeling are investigated by domain decomposition techniques because, generally, structural components do not have a regular shape. The most common and versatile numerical approach, in this regard, is the Finite Element (FE) method, which uses low order polynomials and the variational formulation for the solution of the differential problem. In contrast with the classic approach, the present paper shows a strong form collocation method ...
75 CitationsSource
#1Reza Ansari (University of Gilan)H-Index: 69
#2Raheb Gholami (IAU: Islamic Azad University)H-Index: 39
Abstract The present study deals with the nonlinear postbuckling and free vibration of third-order shear deformable rectangular nanoplate with various edge supports in the pre- and post-buckling regimes incorporating the surface effects. The Gurtin–Murdoch surface stress elasticity theory in conjunction with the third-order shear deformation plate theory is used for the size-dependent mathematical modeling of the nanoplates. The von Karman-type kinematic nonlinearity is used to consider the nonl...
37 CitationsSource
Cited By47
Newest
#1Shuo Liu (HIT: Harbin Institute of Technology)H-Index: 6
#2Kaifa Wang (HIT: Harbin Institute of Technology)H-Index: 12
Last. Chunwei Zhang (Qingdao University)H-Index: 32
view all 5 authors...
Modern electronic devices are usually subjected to thermo-mechanical loads and prone to buckle during their operation. Thermo-mechanical stability is a crucial standard for their reliable applications. This paper explores the size effect on the thermo-mechanical behavior of the organic solar cells. An effective isogeometric analysis method combined with modified couple stress theory is presented. The thermo-mechanical buckling load-bearing capacities of the organic solar cells subjected to vario...
Source
#1Hamed Farahmand (IAU: Islamic Azad University)H-Index: 4
#2P. Yasaie (IAU: Islamic Azad University)
In this study, the buckling analysis of moderately thick porous micro-plate is investigated to predict instability of the micro-plate using strain gradient theory and two-variable refined plate theory termed two-variable strain gradient theory (TV-SGT). The governing equations and new boundary conditions are achieved. Also, the Navier solution technique is utilized to obtain analytical solutions for the simply supported moderately thick porous rectangular micro-plates. The non-dimensionalized cr...
Source
#1Chao Zhou (DUT: Dalian University of Technology)H-Index: 4
#2Dongqi An (DUT: Dalian University of Technology)H-Index: 4
Last. Rui Li (DUT: Dalian University of Technology)H-Index: 28
view all 5 authors...
Abstract This paper presents a first attempt to explore the symplectic superposition method for analytic buckling solutions of non-Levy-type moderately thick rectangular plates, which were hard to tackle by classical semi-inverse methods. In contrast with the conventional Lagrangian-system-based expression that is solved in the Euclidean space, this study describes the issue in the Hamiltonian system for treatment in the symplectic space. The follow-up solution procedure involves the conversion ...
4 CitationsSource
#1Shuo Liu (HIT: Harbin Institute of Technology)H-Index: 6
#2Kaifa Wang (HIT: Harbin Institute of Technology)H-Index: 12
Last. Chunwei Zhang (Qingdao University)H-Index: 32
view all 5 authors...
This paper presents a non-classical refined shear deformation theory model in conjunction with the isogeometric analysis for the static bending, free vibration, and buckling behaviors of multilayered microplates. The modified couple stress theory is used to account for the small-scale effect. Taking a five-layer (Al, P3HT: PCBM, PEDOT: PSS, ITO, and Glass) organic solar cell as an example, it is found that the small-scale effects lead to a decrease in deflection, but an increase in the natural f...
Source
#1Pham Toan Thang (Ton Duc Thang University)H-Index: 16
#2Phuong Tran (RMIT: RMIT University)H-Index: 32
Last. Trung Nguyen-Thoi (Ton Duc Thang University)H-Index: 55
view all 3 authors...
Abstract In this research paper, as initial endeavors, the vibrational responses of functionally graded carbon nanotube-reinforced composite (FG-CNTRC) nanoplates taking into account the effect of nonlocal parameter and strain gradient coefficient are investigated. The study aims at developing mathematical modeling via an analytical solution to FG-CNTRC nanoplate structure with allowance for the nonlocal strain gradient effect. The four types of CNT distribution are used and compared in the cont...
6 CitationsSource
#1Licheng Li (Chongqing University)
#2Yinsong Pan (Chongqing University)
Last. Arash Arabmarkadeh (TMU: Tarbiat Modares University)H-Index: 1
view all 3 authors...
This research deals with the nonlinear forced vibration analysis of cylindrical micro-panels (CMP) under the modified strain gradient shell theory using the higher-order finite element method. The ...
1 CitationsSource
#1Sadegh Ghamsari Esfahani (IUT: Isfahan University of Technology)H-Index: 1
#2Saeid Sarrami-Foroushani (IUT: Isfahan University of Technology)H-Index: 7
Last. Mojtaba Azhari (IUT: Isfahan University of Technology)H-Index: 20
view all 3 authors...
Abstract This paper is focused on the application of a novel reproducing kernel particle finite strip method (RKP-FSM) for the static, mechanical and thermal buckling, and free vibration analyses of rectangular functionally graded (FG) plates with different boundary conditions and internal supports. Conventional reproducing kernel particle method (RKPM) is incorporated into the finite strip method (FSM), and the governing equations are derived based on the first-order shear deformation theory (F...
2 CitationsSource
#1Y.S. Joshan (IITD: Indian Institute of Technology Delhi)H-Index: 3
#2L.K. Sharma (Thapar University)
Last. R. K. Godara (Thapar University)H-Index: 4
view all 4 authors...
Abstract In the present article, the couple stress models in the non-polynomial framework are developed and employed to examine the structural response characteristics of composite micro-plates. The length scale effects in the micro-laminates are considered using the couple stress theory. The trigonometric, inverse-trigonometric, hyperbolic, inverse-hyperbolic and exponential shear shape functions are considered to model transverse shear deformation effects in micro-plates. The Hamilton principl...
1 CitationsSource
In this paper, two-variable refined plate theory and strain gradient theory (SGT) are adopted and termed (TV-SGT) for buckling analysis of moderately thick microplate. The TV-SGT embraces both shear and micro-effects simultaneously and, therefore, does not need the shear correction factor. Notably, the governing equations and new boundary conditions are derived using variational approach. Moreover, the boundary conditions are generalized for complicated problems. The constitutive equations are s...
1 CitationsSource
#1Ehsan Arshid (University of Kashan)H-Index: 12
#2Saeed Amir (University of Kashan)H-Index: 19
Size-dependent vibration analysis of three-layered fluid-infiltrated porous curved microbeams, which are integrated with nanocomposite face sheets, is provided in this work. The effect of the fluid...
7 CitationsSource