A triangular finite element using Laplace transform for viscoelastic laminated composite plates based on efficient higher-order zigzag theory

To predict the time-dependent behaviors of viscoelastic laminated composites, a three-node multilayered plate element is developed based on the efficient higher-order plate theory (EHOPT), which was originally proposed by Cho and Parmerter. With the help of the Laplace transform, the integral form of the constitutive equation in the time domain is reduced to an algebraic equation in the Laplace domain. Thus, the structures and advantages of the EHOPT can be preserved in viscoelastic laminated composites in the Laplace domain. Since the time dimension is transformed to Laplace domain, the finite element discretization is only used in the spatial domain. A nonconforming three-node triangular element is employed to implement the viscoelastic EHOPT for finite element analysis. To pass the proper bending and shear patch tests in arbitrary mesh configurations, the modified shape function developed by Specht is applied and converted into Laplace domain. Therefore, the final numerical results, which is obtained by using inverse Laplace techniques, always converge to the corresponding analytical solutions. In order to verify the efficiency and accuracy of the present study, some numerical examples for long-term creep and relaxation processed are performed. The present viscoelastic finite element of composite laminates provides a powerful tool to accurately investigate the responses of the viscoelastic and time-dependent mechanical behaviors of composite laminates.