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

Research output: Contribution to journalArticle

Standard

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.

In: Engineering Structures, Vol. 153, 15.12.2017, p. 598-612.

Research output: Contribution to journalArticle

Author

Bibtex - Download

@article{19e99cd65d0245eeace78d1f1725db77,
title = "Nonlinear static and transient isogeometric analysis of functionally graded microplates based on the modified strain gradient theory",
abstract = "The objective of this study is to develop an effective numerical model within the framework of an isogeometric analysis (IGA) to investigate the geometrically nonlinear responses of functionally graded (FG) microplates subjected to static and dynamic loadings. The size effect is captured based on the modified strain gradient theory with three length scale parameters. The third-order shear deformation plate theory is adopted to represent the kinematics of plates, while the geometric nonlinearity is accounted based on the von K{\'a}rm{\'a}n assumption. Moreover, the variations of material phrases through the plate thickness follow the rule of mixture. By using Hamilton{\textquoteright}s principle, the governing equation of motion is derived and then discretized based on the IGA technique, which tailors the non-uniform rational B-splines (NURBS) basis functions as interpolation functions to fulfil the C2-continuity requirement. The nonlinear equations are solved by the Newmark{\textquoteright}s time integration scheme with Newton-Raphson iterative procedure. Various examples are also presented to study the influences of size effect, material variations, boundary conditions and shear deformation on the nonlinear behaviour of FG microplates.",
keywords = "Isogeometric Analysis, Modified strain gradient theory, Geometrical nonlinearity, Functionally graded microplate",
author = "Son Thai and Huu-Tai Thai and Vo, {Thuc P.} and H. Nguyen-Xuan",
year = "2017",
month = dec,
day = "15",
doi = "10.1016/j.engstruct.2017.10.002",
language = "English",
volume = "153",
pages = "598--612",
journal = "Engineering Structures",
issn = "0141-0296",
publisher = "Elsevier",

}

RIS (suitable for import to EndNote) - Download

TY - JOUR

T1 - Nonlinear static and transient isogeometric analysis of functionally graded microplates based on the modified strain gradient theory

AU - Thai, Son

AU - Thai, Huu-Tai

AU - Vo, Thuc P.

AU - Nguyen-Xuan, H.

PY - 2017/12/15

Y1 - 2017/12/15

N2 - The objective of this study is to develop an effective numerical model within the framework of an isogeometric analysis (IGA) to investigate the geometrically nonlinear responses of functionally graded (FG) microplates subjected to static and dynamic loadings. The size effect is captured based on the modified strain gradient theory with three length scale parameters. The third-order shear deformation plate theory is adopted to represent the kinematics of plates, while the geometric nonlinearity is accounted based on the von Kármán assumption. Moreover, the variations of material phrases through the plate thickness follow the rule of mixture. By using Hamilton’s principle, the governing equation of motion is derived and then discretized based on the IGA technique, which tailors the non-uniform rational B-splines (NURBS) basis functions as interpolation functions to fulfil the C2-continuity requirement. The nonlinear equations are solved by the Newmark’s time integration scheme with Newton-Raphson iterative procedure. Various examples are also presented to study the influences of size effect, material variations, boundary conditions and shear deformation on the nonlinear behaviour of FG microplates.

AB - The objective of this study is to develop an effective numerical model within the framework of an isogeometric analysis (IGA) to investigate the geometrically nonlinear responses of functionally graded (FG) microplates subjected to static and dynamic loadings. The size effect is captured based on the modified strain gradient theory with three length scale parameters. The third-order shear deformation plate theory is adopted to represent the kinematics of plates, while the geometric nonlinearity is accounted based on the von Kármán assumption. Moreover, the variations of material phrases through the plate thickness follow the rule of mixture. By using Hamilton’s principle, the governing equation of motion is derived and then discretized based on the IGA technique, which tailors the non-uniform rational B-splines (NURBS) basis functions as interpolation functions to fulfil the C2-continuity requirement. The nonlinear equations are solved by the Newmark’s time integration scheme with Newton-Raphson iterative procedure. Various examples are also presented to study the influences of size effect, material variations, boundary conditions and shear deformation on the nonlinear behaviour of FG microplates.

KW - Isogeometric Analysis

KW - Modified strain gradient theory

KW - Geometrical nonlinearity

KW - Functionally graded microplate

U2 - 10.1016/j.engstruct.2017.10.002

DO - 10.1016/j.engstruct.2017.10.002

M3 - Article

VL - 153

SP - 598

EP - 612

JO - Engineering Structures

JF - Engineering Structures

SN - 0141-0296

ER -