Abstract
In this study, a new and efficient computational approach based on isogeometric analysis (IGA) and refined plate theory (RPT) is proposed for the geometrically nonlinear analysis of functionally graded (FG) microplates. While the microplates’ size-dependent effects are efficiently captured by a simple modified couple stress theory (MCST) with only one length scale parameter, the four-unknown RPT is employed to establish the displacement fields which are eventually used to derive the nonlinear von Kámán strains. The NURBS-based isogeometric analysis is used to construct high-continuity elements, which is essentially required in the modified couple stress and refined plate theories, before the iterative Newton-Raphson algorithm is employed to solve the nonlinear problems. The successful convergence and comparison studies as well as benchmark results of the nonlinear analysis of FG microplates ascertain the validity and reliability of the proposed approach. In addition, a number of studies have been carried out to investigate the effects of material length scale, material and geometrical parameters on the nonlinear bending behaviours of microplates.
Highlights
Classical elasticity has been well established and played a crucial role in the development of the material models and structural responses in various engineering fields ranging from mechanical to bio-engineering
The plates which are made of isotropic material and functionally graded material (FGM) with mixtures of ceramic and metal shown in Table 1 are used
The presented results, that are generated from different values of material length scale ratio /h and material index n, are compared with those reported by Kim and Reddy [29] who employed general third-order theory for element formulation of functionally graded (FG) microplates
Summary
Classical elasticity has been well established and played a crucial role in the development of the material models and structural responses in various engineering fields ranging from mechanical to bio-engineering. The non-local elasticity was initially proposed by Erigen [10] and Erigen and Edelen [11] who assumed that the stress of a point in an elastic body depends on the strain at that point and, theoretically, at all other points in the continuum While this theory considers the interactions between atoms, it includes the internal length scale in the constitutive equations as a material parameter [12]. In the last few years, the studies of the behaviours of microplates employing MCST and different plate theories have been enriched with a wealth of numerical solutions and analytical approaches Reddy and his colleagues have successfully developed finite element models to analyse the behaviours of microplates with and without nonlinearity [28, 38, 39].
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