Modified state space method for bending creep and recovery behaviors of viscoelastic orthotropic laminated plate

Abstract

A modified state space method (SSM) is proposed first to solve the analytical solution of viscoelastic orthotropic laminated (VOL) plate under time-varying load. This modification extends the applicability of traditional SSM from elastic materials to viscoelastic materials by resolving a limitation of the traditional SSM, where computing the exponential function of the state space matrix is infeasible. In the analytical model, the long-term stresses and displacements are established based on the orthotropic elasticity theory combined with the Boltzmann superposition. The convolution within the governing equation is resolved through Laplace transform. By using the proposed modified SSM, the general solution for each viscoelastic lamina is derived out, by separating the complex variable of Laplace transform out from the state space matrix. The analytical solution is ultimately derived using series expansion, transfer matrix method and inverse Laplace transform. The proposed model can provide long-term creep stress distribution in the VOL plate by creep deflection data from experiment. The comparison with existing results indicates the proposed solution exhibits greater accuracy than simplified solutions and higher efficiency compared to the finite element method. At last, the bending creep and recovery behaviors of the VOL plate are investigated in detail.