Nonlinear static and transient isogeometric analysis of functionally graded microplates based on the modified strain gradient theory

Thai, Son; Thai, Huu‐Tai; Vo, Thuc P.; Nguyen‐Xuan, H.

doi:10.1016/j.engstruct.2017.10.002

Cited by 45 publications

(11 citation statements)

References 60 publications

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“…Nguyen et al 40 developed an IGA-based numerical model for MCST-based FG micro-plates, including both shear and normal deformation effects. In the context of MSGT, Thai et al 41,42 presented IGA-based simulation models for the linear/nonlinear static and dynamic analysis of FG Reddy micro-plates. Using the IGA approach, Makvandi et al 43 investigated the behavior of second-and third-order gradient materials under edge and point displacement boundary conditions, respectively.…”

Section: Introductionmentioning

confidence: 99%

Strain gradient differential quadrature finite element for moderately thick micro‐plates

Zhang

Kong

et al. 2020

Numerical Meth Engineering

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Summary In this study, we integrate the advantages of differential quadrature method (DQM) and finite element method (FEM) to construct a C1‐type four‐node quadrilateral element with 48 degrees of freedom (DOF) for strain gradient Mindlin micro‐plates. This element is free of shape functions and shear locking. The C1‐continuity requirements of deflection and rotation functions are accomplished by a fourth‐order differential quadrature (DQ)‐based geometric mapping scheme, which facilitates the conversion of the displacement parameters at Gauss‐Lobatto quadrature (GLQ) points into those at element nodes. The appropriate application of DQ rule to non‐rectangular domains is proceeded by the natural‐to‐Cartesian geometric mapping technique. Using GLQ and DQ rules, we discretize the total potential energy functional of a generic micro‐plate element into a function of nodal displacement parameters. Then, we adopt the principle of minimum potential energy to determine element stiffness matrix, mass matrix, and load vector. The efficacy of the present element is validated through several examples associated with the static bending and free vibration problems of rectangular, annular sectorial, and elliptical micro‐plates. Finally, the developed element is applied to study the behavior of freely vibrating moderately thick micro‐plates with irregular shapes. It is shown that our element has better convergence and adaptability than that of Bogner‐Fox‐Schmit (BFS) one, and strain gradient effects can cause a significant increase in vibration frequencies and a certain change in vibration mode shapes.

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Section: Introductionmentioning

confidence: 99%

Strain gradient differential quadrature finite element for moderately thick micro‐plates

Zhang

Kong

et al. 2020

Numerical Meth Engineering

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“…In the present study, the MSGT is chosen to derive strain potential energy containing classical strain ε, dilatation gradient vector γ, symmetric rotation χ ðsÞ , and deviatoric stretch gradient η ð1Þ tensors (Mohammadimehr et al, 2018a). This theory can be written as follows (Thai et al, 2017)…”

Section: Micro-timoshenko Beam Based On Msgtmentioning

confidence: 99%

Magneto-mechanical vibration analysis of single-/three-layered micro-Timoshenko porous beam and graphene platelet as reinforcement based on modified strain gradient theory and differential quadrature method

Mohammadimehr

Mehrabi

Mousavinejad

2020

Journal of Vibration and Control

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This article discusses about vibration analysis of single-/three-layered microsandwich Timoshenko beams with porous core and graphene platelet–reinforced composite face sheets under magnetic field and elastic foundation based on the modified strain gradient theory. It is assumed that the material properties of matrix and reinforcement vary in thickness directions. Hamilton’s principle based on the energy approach is used to obtain the governing equations of motions. The equations of motions are solved using a numerical differential quadrature method for various boundary conditions. The obtained results of this study are compared with other previous research studies, and there is a good agreement between them. Moreover, the effects of different parameters such as length-to-thickness ratio, magnetic field, various distributions of graphene platelets and porous beams, and volume fractions of graphene platelets are studied on the dimensionless natural frequencies. In fact, the main idea of this work is combination of structure reinforcement with magnetic field and graphene platelets on the sandwich porous beams at microscale, and the effects of these parameters are developed on the dimensionless natural frequencies of the microbeam. The results of the present study demonstrate that applying magnetic field and increasing its intensity lead to enhance the natural frequency. Also, it is showed that graphene platelet reinforcement with one percent of weight fraction has an effective effect on the increasing dimensionless natural frequencies of the microporous beam. Thus, it can be predicted that graphene platelets can be used instead of nanotubes because they do not have the problem of nanotube accumulation and they are more economical than nanotubes.

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“…Therefore, geometrically nonlinear analysis is necessary to investigate the plate behavior. To solve such nonlinear problems, many methods have been introduced such as Picard method [9], Newton-Raphson method [10], modified Newton-Raphson method [11], modified Riks method [12], arclength technique [13], and other methods. Most of the above methods require many iterations to obtain nonlinear solutions.…”

Section: Introductionmentioning

confidence: 99%

Long short-term memory for nonlinear static analysis of functionally graded plates

Thai

Bui

2022

STCE

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This study presents an effective method based on long short-term memory to reduce the computational cost in nonlinear static analysis of functionally graded plates. Data points representing a load-deflection curve in a dataset are generated through isogeometric analysis (IGA). The order of these data points is always maintained as a sequential series of observations; therefore, it is referred to as a time series. Dataset is divided into three sets including training, testing, and prediction sets. Both training and testing sets are used for the training process by the long short-term memory to gain optimum weights. Based on these obtained weights, data points in the prediction set are directly predicted without using any analysis tools. The effectiveness and accuracy of the proposed method are demonstrated by comparing the obtained results to those of isogeometric analysis.

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Nonlinear static and transient isogeometric analysis of functionally graded microplates based on the modified strain gradient theory

Cited by 45 publications

References 60 publications

Strain gradient differential quadrature finite element for moderately thick micro‐plates

Strain gradient differential quadrature finite element for moderately thick micro‐plates

Magneto-mechanical vibration analysis of single-/three-layered micro-Timoshenko porous beam and graphene platelet as reinforcement based on modified strain gradient theory and differential quadrature method

Long short-term memory for nonlinear static analysis of functionally graded plates

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