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

Thai, Son, Thai, Huu-Tai, Vo, Thuc and Nguyen-Xuan, H. (2017) Nonlinear static and transient isogeometric analysis of functionally graded microplates based on the modified strain gradient theory. Engineering Structures, 153. pp. 598-612. ISSN 0141-0296

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Thai et al - Nonlinear static and transient isogeometric analysis of functionally graded microplates based on the modified strain gradient theory AAM.pdf - Accepted Version
Available under License Creative Commons Attribution Non-commercial No Derivatives 4.0.

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Official URL: http://dx.doi.org/10.1016/j.engstruct.2017.10.002

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 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.

Item Type: Article
Uncontrolled Keywords: Isogeometric Analysis, Modified strain gradient theory, Geometrical nonlinearity, Functionally graded microplate
Subjects: H300 Mechanical Engineering
Department: Faculties > Engineering and Environment > Mechanical and Construction Engineering
Depositing User: Paul Burns
Date Deposited: 18 Sep 2019 16:57
Last Modified: 11 Oct 2019 13:16
URI: http://nrl.northumbria.ac.uk/id/eprint/40739

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