Three-dimensional analysis for static bending and free vibration of functionally graded rectangular plate

The state equation of functionally graded rectangularplate were established with the state variables of three displacementcomponents and three stress components, based on the three-dimensionallinear elastic theory by using of state space method. Considering simplysupported boundary conditions, the static bending and free vibrationproblems of a three-dimensional functionally graded rectangular plate werenumerically solved by shooting method with that the material propertiesthrough the thickness coordinate are assumed to obey the exponent lawdependence. Effects of the volume fraction distributions of constituentmaterials, and thickness-to-side ratio of functionally graded rectangularplate on the dynamical and static responses were studied. The presentalgorithm can be used to research the three-dimensional elastic response offunctionally graded materials.