Size-dependant behaviour of functionally graded microplates based on the modified strain gradient elasticity theory and isogeometric analysis

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 distributions of material phrases through the plate thickness. By using Hamilton's principle, the governing equations are derived and then discretized by employing an Isogeometric Analysis (IGA) approach, where the Non-Uniform Rational B-Splines (NURBS) basis functions are adopted to meet the C 2 −continuity requirement. Physical mesh convergence and verification studies are performed to prove the accuracy and reliability of the present model. In addition, parametric studies are also carried out to investigate the size effect in conjunction with the influences of gradient index, shear deformation effect and boundary conditions on the responses of microplates.

Modelling size-dependent bending, buckling and vibrations of 2D triangular lattices by strain gradient elasticity models: Applications to sandwich beams and auxetics

“…Altogether, literature on applications of non-classical continuum models to real materials, structures and systems is still very limited; some examples can be found in [32,33,34,35,36,37,38,39]. Regarding numerical methods and numerical analysis for the models of generalized continuum mechanics, literature is limited as well, although there are some successful endeavours including rigorous studies on solvability and convergence (for recent overviews and examples, see [40,41,25,42,26,43,44,45]).…”

Post-buckling of functionally graded microplates under mechanical and thermal loads using isogeomertic analysis

“…Hosseini et al [58] employed an analytical approach to study the buckling responses of an orthotropic multi-microplate system embedded in an elastic medium. Thai et al [59] also carried out a comprehensive investigation on linear bending, free vibration and buckling responses of FG microplates by using IGA approach. In addition, the behaviour of microplates under thermal loads was also examined based on the MST in some studies recently.…”

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

“…The linear components in above expressions can be found in [55], whilst the additional nonlinear components are given as follows…”

“…Although numerical solutions of the MST models have been recently developed using Chebyshev-Ritz method [53], the finite strip method [54] and the IGA method [55], these studies were limited to linear problems (linear bending [55], linear buckling [54] and linear free vibration [53,54]). In fact, the behaviour of microplates could undergo large deformations when heavier loads are imposed.…”