Variable Kinematic Model for the Analysis of Functionally Graded Material plates

By Erasmo Carrera, Salvatore Brischetto, A. Robaldo. 2008

269 citations recorded by the source corpus.

This work addresses the static analysis of functionally graded material plates subjected to transverse mechanical loadings. The unified formulation and principle of virtual displacements are employed to obtain both closed-form and finite element solutions. The use of the unified formulation permits a large variety of plate models with variable kinematic assumptions to be compared in the same framework. These differ according to the order of the expansion in the thickness direction and the variable description: the order of the expansion ranges from 1 to 4, thus covering first-order as well as higher-order theories; the description of the unknowns can be equivalent single layer or layerwise. The dependence of the material data on the thickness direction was introduced by employing thickness functions that are derived from the Legendre polynomials that are used in the layerwise case. The proposed approach is independent of the used transition function, and as a result, any continuous variations of the material properties in the thickness direction may be easily implemented. The obtained solutions (closed form and finite element) are validated through comparison with three-dimensional exact solutions and other available solutions. These show the limitations of classical plate theories as well as the convenience of the use of the proposed variable kinematic models for the analysis of functionally graded material plates.

Subfields: Civil and Structural Engineering, Mechanics of Materials

View Paper: https://www.semanticscholar.org/paper/5f4206cb7c4e4277595b3540526b0e1ebf3d008b

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In Civil and Structural Engineering

In Mechanics of Materials

Citations in the corpus

Exact elasticity solution for natural frequencies of functionally graded simply-supported structures (2013, methodology): “Hosseini-Hashemi et al. (2011) used the Reddy third-order shear deformation plate theory.”
A nth-order shear deformation theory for the bending analysis on the functionally graded plates (2013, background): “6110 Carrera et al. (2008) 0.”
A critical review of recent research on functionally graded plates (2013, background): “[105], Brischetto [106] and Brischetto and Carrera [107].”
Effects of thickness stretching in functionally graded plates and shells (2011, methodology): “The 3D solution is given by Kashtalyan [4] for a/h = 3, while for the other thickness ratios, a quasi-3D solution is provided, as described in [27].”
Performance of CUF Approach to Analyze the Structural Behavior of Slender Bodies (2012, methodology): “This formulation has been developed over the last decade for plate/ shell models (Carrera 1995, 2002, 2003; Carrera et al. 2008), and it has recently been extended to beam modelings (Carrera and Giunta 2010).”
Variable kinematic models applied to free-vibration analysis of functionally graded material shells (2010, methodology): “Details can be found in previous authors’ works [11],[20] and [21].”