Edge Effects in Laminated Composite Plates

Abstract

The attenuation of self-equilibrated edge stress states into the interior of a laminated plate composed of an arbitrary number of bonded, elastic, anisotropic layers is investigated in the context of Saint-Venant’s principle using the exponential decay results of Toupin, Knowles, and Horgan. To model the plate’s behavior, a semianalytical method is used with finite element interpolations over the thickness and exponential decay into the plate’s interior. The formulation leads to a second-order algebraic eigensystem whose eigenvalues are the characteristic inverse decay lengths, and corresponding right eigenvectors depict the displacement distributions of self-equilibrated traction states. Orthogonality relations between these right and left eigenvectors of the adjoint system are established. An eigenvector expansion for representing arbitrary self-equilibrated edge tractions is then presented. This approach is useful in revealing the interlaminar effects and their decay rates in a laminated composite plate under plane strain. Two examples are provided where the interlaminar phenomena due to eigenstates of self-equilibrated edge stress are illustrated.

A spectral dynamic stiffness method for free vibration analysis of plane elastodynamic problems

“…The notations l, s, ξ, γ ls are the same as those in Eq. (16). It is apparent that the two MFBF correspond to the first derivatives of each other with respect to ξ.…”

“…Therefore, the two MFBF of Eqs. (16) and (17) form a conjugate pair. The above conjugate property is a crucial factor which will be used in the current SDSM development to cope with the 90 • phase different between U and V and between the BCs.…”

“…(11) can be appropriately expressed by the combination of two series with the aid of the two type of MFBF given by Eqs. (16) and (17) as follows…”

“…The plane strain theory is also widely used in plane wave propagation problems [11], which have applications in non-destructive testing [12,13] and phononic crystal analysis [14]. Some other investigators have used the plane strain theory to study the mechanism of edge effects on the natural vibration and wave propagation properties of thick multi-layered plates [15,16]. As the natural mode shapes can be regarded as the standing waves of a structure with the prescribed boundary conditions, the plane strain free vibration can provide important information for wave propagation problems with respect to different boundary conditions or discontinuities.…”

“…Ahmed [8] used a generalised Fourier-series technique for the axisymmetric plane-strain vibrations of a thick-layered orthotropic cylinder. Dong et al [15,16] made use of a direct-iterative eigensolution technique to investigate the edge effects in laminated plates. However, most of the above analytical methods are limited to single rectangular or annular domain and thus can not be applied to complex geometries.…”