Keywords: linear viscoelastic, simplified unit cell method, multi-scale analyses, micromechanics, laminated composite plates.

In this paper viscoelastic laminated composite plates are analysed with a multi-scale algorithm including micro- and macro-scales. At a micro-scale an analytical method is used to obtain the overall properties of the composite material which consist of an isotropic viscoelastic matrix and a transversely isotropic fiber. The simplified unit cell method (SUCM) is used to predict these properties. This method is basically the same as the method of cells (MOC) which Aboudi [1] used to predict composite material properties. One of the advantages of SUCM is its closed form solution which makes multi-scale analyses easier. Viscoelastic behavior of the matrix is modelled using the Boltzmann superposition principle and the compliance of the viscoelastic material defined by a Prony series which is calibrated using experimental data for linear viscoelastic behaviour. At a structural level the differential quadrature (DQ) method is used to solve the governing equations of motion of the laminated composite plates. The DQ method was introduced by Bellman and his associates in the early of 1970s [2,3] following the concept of integral quadrature. The basic concept of the DQ method is that any derivative at a mesh point can be approximated by a linear summation of all the functional values of the nodes along a mesh line. Multi-scale analyses includes obtaining viscoelastic compliance of the matrix; then the SUCM obtains the properties of composite materials using new matrix compliance; then the stiffness of the laminated plate is calculated and DQ is used to solve the laminated plate equations of motion. This process continues until the end of the time duration. Classical laminated plate theory (CLPT) is applied to derive the governing equations of the plate and because for linear viscoelastic analysis the applied loads are small enough to ignore higher order terms in strains, there is just one equation which must be solved to determine displacements and stresses. Micromechanical results are validated using experimental data [4]. Displacements and stresses for different volume fractions with respect to time are given.

1

J. Aboudi, "Micromechanical Characterization of the Nonlinear Viscoelastic Behavior of Resin Matrix Composites", Composites Science and Technology, 38, 371-386, 1990.

2

R.E. Bellman, J. Casti, "Differential Quadrature and long-term integration", J Math Anal Appl, 34, 235-238, 1971. doi:10.1016/0022-247X(71)90110-7

3

R.E. Bellman, B.G. Kashef, J. Casti, "Differential quadrature: a technique for the rapid solution of nonlinear partial differential equations", J Comput Phys, 10, 40-52, 1972. doi:10.1016/0021-9991(72)90089-7

4

M.E. Tuttle, H.F. Brinson, "Prediction of the Long-Term Creep Compliance of General Composite Laminates", Experimental Mechanics, 26, 89-102, 1986. doi:10.1007/BF02319961

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