An Enhanced Global–Local Higher-Order Model for Thermal Expansion Analysis of Laminated Panels Reinforced by Carbon Nanotubes

Carbon nanotubes (CNTs) are added to the matrix according to proper distribution configurations by many researchers to improve the stiffness of laminated composites. However, the distribution configurations of CNTs may induce dramatic changes in displacements and stresses, which significantly affect structural safety. Moreover, such issues have received little attention at present because existing theoretical models encounter difficulties in accurately predicting dramatic changes in stresses of these structures. To accurately analyze the thermal expansion behaviors of laminated panels reinforced by CNTs, an equivalent single-layer higher-order model is proposed in which in-plane displacements are constructed by superimposing the second local displacements onto a smooth cubic varying field. Transverse normal deformation should be considered for the thermal expansion behavior of the laminated plate; therefore, a smooth cubic distribution along the thickness is adopted in the transverse displacement field. The layer-dependent displacement parameters can be expressed using global displacement variables by applying compatible conditions of displacements and stresses. Based on the proposed model, analytical solutions for laminated composites are obtained using Navier's technique. The capability of the proposed model is verified by comparing the results of the proposed model with the exact solutions and the three-dimensional finite element model. The effect of the distribution configuration and volume fraction of CNTs on the thermomechanical behavior of the composite panels is studied based on the present model. Numerical results show that the distribution configuration and volume fraction of the CNTs significantly influence the distributions and magnitudes of stresses.