Decay rate of Saint-Venant end effects for multilayered orthotropic strips

Saint-Venant decay rate of end effects is investigated for generally laminated orthotropic strips under self-equilibrated end loads. The problem is governed by a fourth-order partial differential equation for the Airy stress function with discontinuous coefficients at the layer interfaces, where displacements and traction continuities are imposed. The solution is found in the form of product of an exponentially decaying function along the strip and an unknown function defined over its total height. External face and interface conditions are used to obtain the characteristic equation for the eigenvalues governing the decay rate of end effects along the strip. For orthotropic and strongly orthotropic sandwich strips the transcendental eigenvalue equation is explicitly given. The case of laminated strips with periodic layout is finally considered. Making use of the homogenization method, both effective elastic constants and expressions for the local stress variation at the layer level are obtained. Numerical calculations confirm that the eigenvalues of the homogenized material are the asymptotic values of those of periodically laminated strips when the number of layers increases. Moreover, homogenization method is shown to be very powerful also in the calculation of local stress distributions. 0 1997 Elsevier Science Ltd.