Bending and free vibration analyses of multi-directional functionally graded plates in thermal environment: A three-dimensional Isogeometric Analysis approach. (1st September 2022) - Thai, Son; Nguyen, Vu X.; Lieu, Qui X.
Abstract: This study presents a three-dimensional numerical approach to analyze the bending and free vibration behavior of multi-directional functionally-graded plates under the effect of thermal environment. The effective material properties are temperature dependent and the temperature field within the plate's volume are determined directly based on a generalized heat transfer equation. The governing equations for static bending and free vibration analyses are developed based on the three-dimensional elasticity theory. The Isogeometric Analysis approach is utilized to discretize the weak forms of heat transfer equation, static bending equation and free vibration equation. A iterative scheme is proposed to heat transfer problems with material being dependent on temperature. Rectangular and circular plates are investigated to validate the efficiency of Isogeometric Analysis approach on modeling and analyzing aspects. Various numerical examples are also presented to validate the accuracy of the proposed approach and investigate the influences of material variation profiles, thickness ratios, temperature rise, and boundary conditions on thermal responses of the plates. Highlights: An accurate 3D numerical model based on IGA approach is developed. Bending and free vibration responses of MFGM plates under thermal environment are investigated. An iterative procedure is proposed to solve heat transfer problems. Influences of material variations, temperature rise, thickness ratios, and boundary conditions are investigated.