Three-dimensional transient heat conduction in a functionally graded thick plate with a higher-order plate theory and a meshless local Petrov-Galerkin method.

*(English)*Zbl 1143.74321Summary: We analyze transient heat conduction in a thick functionally graded plate by using a higher-order plate theory and a meshless local Petrov-Galerkin (MLPG) method. The temperature field is expanded in the thickness direction by using Legendre polynomials as basis functions. For temperature prescribed on one or both major surfaces of the plate, modified Lagrange polynomials are used as basis and additional terms are added to these expansions to exactly match the given temperatures. Partial differential equations for the evolution of the coefficients of the Legendre polynomials are reduced to a set of coupled ordinary differential equations (ODEs) in time by a MLPG method. The ODEs are integrated by the central-difference method. The time history of evolution of the temperature at the plate centroid and through-the-thickness distribution of the temperature computed with the fifth-order plate theory are found to agree very well with those obtained analytically.

##### MSC:

74F05 | Thermal effects in solid mechanics |

74S30 | Other numerical methods in solid mechanics (MSC2010) |

74K20 | Plates |

80A20 | Heat and mass transfer, heat flow (MSC2010) |