Bending and extension of a multilayered plate with body forces and thermal loading

A multilayered plate composed of thin layers of isotropic materials is analyzed. The problem for the multilayered plate with body forces is formulated by using the lamination theory in which displacement fields are expressed in terms of in-plane displacements on a main plane and transverse displacement. Placing the main plane at an appropriate distance from the lower surface of the plate, a set of equilibrium equations is shown to be written in uncoupled forms, which are identical to those for an uncoupled plate such as a single layer plate. It is proved that the complete solutions of the multilayered plates subject to the specified in-plane resultant tractions or in-plane displacements on its whole boundary can be obtained from the sum of solutions for uncoupled plates. Closed form solutions are obtained for a circular laminate clamped or simply supported on its the boundary as well as for a rotating disk with a constant angular velocity. The calculations of thermoelastic stresses and displacements in multilayered plates are also discussed. Closed form solutions are obtained for a circular laminate with distributed temperature varying in the radial direction and through the thickness.