Thermally induced dynamic response of point-supported temperature-dependent FGM plates utilizing modified 2D Legendre Ritz method

This study investigates the thermally induced dynamic behavior of a rectangular plate with temperature-dependent functionally graded materials. The structure is supported by concentrated bearing points in addition to its boundary conditions—a configuration that significantly enhances structural performance but presents modeling challenges due to singularities. The Mori-Tanaka micromechanical procedure is used to calculate the equivalent material characteristics of the FGM. A high-temperature rapid heating is imposed to the plate outer facade, necessitating a solution for transient heat conduction. This is achieved using the generalized differential quadrature method and the Crank-Nicolson approach for spatial and temporal discretization. The resulting temperature variations, along with induced thermal forces and moments, are incorporated into the Lagrangian function of the system. The inclusion of point supports in the functional of Lagrange is achieved through the application of Lagrange multipliers. Employing a modified 2-dimensional Ritz algorithm relying on Legendre polynomials, the Lagrangian is minimized across the plate domain. Time-dependent responses are then obtained using the Newmark method. A frequency analysis is also performed. Validation against limited existing works demonstrates the accuracy of this approach, while further analysis highlights its effectiveness in tuning the dynamic response of point supported plates under thermal shock.