The symplectic system method in the stress analysis of 2D elasto-viscoelastic fiber reinforced composites

With the aid of the variational method and Laplace transformation, the symplectic system method is employed into two-dimensional elastic-viscoelastic fiber reinforced composites. The fundamental eigenfunctions of the governing equations are generalized to the time domain. Therefore the problem can be discussed directly in the time domain, and the iterative application of Laplace transformation is not needed. Using this method, all the stress components of the inner fiber and outer matrix, and hence the stress transfer in the interface between the fiber and matrix, are expressed analytically. The results obtained by the approach are accurate, because all the boundary conditions prescribed on the surfaces and ends of the composites can be satisfied. Numerical example demonstrate that both the shear stress and the normal stress decrease with time due to the viscoelastic property of the matrix, and that stress concentration occurs near the end.