Long-term behavior of multilayered angle-ply plate structures with viscoelastic interlayer by state space method

Layered angle-ply plates bonded by viscoelastic adhesives exhibit time-dependent behavior when subjected to sustained loads, which is a common phenomenon in practical engineering. The present work proposes analytical solutions based on the exact elasticity theory for the long-term behavior of multilayered angle-ply plates considering viscoelastic interlayers. In the analytical model, each angle-ply layer involves nine independent orthotropic constants and is modeled on the basis of the three-dimensional (3D) elasticity theory. The interlayer exhibits viscoelastic property and is described by the standard linear solid model. The state space method is employed in order to solve the stresses and displacements for the plate, and the convolution equation for viscoelasticity is figured out by Laplace transform. The results of numerical examples show that the present solution is convergent rapidly and is consistent with the finite element solution. The effects of the viscoelastic material constants, the layer angle and the orthotropic constants on the long-term stresses and displacements in the plate are studied thoroughly by use of the present solution.