Exact solution for hygro-thermo-mechanical creep and recovery of viscoelastic laminated beam

Abstract

In order to predict the creep and recovery behaviors of for viscoelastic laminated beam in hygro-thermo-mechanical (HTM) coupled condition, an exact analytical solution is proposed. This solution considers two effect mechanisms: temperature and humidity, including the expansion difference and the variation of viscoelastic properties. In the analytical model, the stresses and displacements of each lamina are described based on the hygro-thermo-elasticity theory combined with the Boltzmann superposition. By employing series expansion, the transfer matrix method, and Laplace transform, the solution is determined analytically. Notably, the entire process of Laplace inverse transformation is carried out analytically without relying on any numerical approximations. The comparison analysis indicates that the proposed solution is more computationally efficient than the finite element counterpart and is more accurate than the solutions based on transverse shear deformation assumption. By analyzing the components of the proposed solution, a modified superposition principle applicable to HTM coupled conditions and a superposition principle for creep recovery are derived. In the end, the HTM coupled behavior, the bending creep and recovery as well as the optimization of expansion coefficient are investigated in detail.