Modified state space method for long-term behavior of viscoelastic laminated angle-ply plate

Abstract

This work proposes a modified state space method (SSM) to develop the analytical solution for viscoelastic laminated angle-ply plates subjected to long-term loading situations. Within the analytical model, the plate’s stresses and displacements are governed by orthotropic elasticity theory combined with Boltzmann superposition. The convolution within the governing equation is resolved through the application of Laplace transform. The modified SSM is proposed to provide a general solution for each lamina by extracting the complex variable of the Laplace transform from the state space equation. This modification addresses a limitation of the traditional SSM where the exponential function of the state space matrix is computationally infeasible to calculate. The analytical solution of the laminated angle-ply plate is ultimately derived using the transfer matrix method followed by the inverse Laplace transform. Through comparative analysis, it is observed that the proposed solution exhibits greater accuracy than simplified solutions and higher efficiency compared to the finite element method. In addition, the work explores the bending creep and recovery behaviors of viscoelastic laminated angle-ply plate under various parameters.