Bending analysis of FG plates using a general third-order plate theory with modified couple stress effect and MLPG method.

*(English)*Zbl 1403.74113Summary: Meshless local Petrov-Galerkin analysis of functionally graded plates based on a general third-order shear deformation plate theory with a modified couple stress effect is presented. Governing equations of problem are a fourth-order partial differential equations system which derived in terms of eleven generalized displacement variable, by applying the principle of virtual displacements. The moving least-squares approach is used for approximation of unknown variables and the Gauss weight function is employed as test function for obtaining local weak form. The Gauss-Legendre quadrature method is utilized for numerical integration of weak equations. Static bending results of a simply-supported plate is obtained for various power law index and length scale parameter, and is compared to analytical solutions that shows high accuracy in results.

##### MSC:

74S05 | Finite element methods applied to problems in solid mechanics |

65M60 | Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs |

74K20 | Plates |

##### Keywords:

meshless local Petrov-Galerkin method; general third-order plate theory; modified couple stress effect; functionally graded plate; moving least-square approximation
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\textit{V. S. Khorasani} and \textit{M. Bayat}, Eng. Anal. Bound. Elem. 94, 159--171 (2018; Zbl 1403.74113)

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