Affiliations: Weidlinger Associates, Inc., New York, NY, USA | Department of Civil and Environmental Engineering,
Louisiana State University, Baton Rouge, LA, USA
Abstract: We present a simple and efficient method for the analysis of shear
flexible isotropic and orthotropic composite shells. Classical thin shell
constitutive equations used in the explicit finite element code EPSA to model
homogenous isotropic shells using "through-the-thickness-integration" and
layered orthotropic composite shells [1–3,5] are modified to account for
transverse shear deformation. This effect is important in the analysis of thick
plates and shells as well as composite laminates, where interlaminar effects
matter. Transverse shear stresses are calculated using a linear normal strain
distribution, where first the shear forces are calculated and then the stresses
are calculated by means of the generalized section properties, i.e., first and
second moments of area. The formulation is a generalization of the analytical
method of analyzing composite beams. It is simple and computationally
inexpensive, and it yields accurate results without employing higher order
displacement interpolations. In the case of isotropic shells, the transverse
shear stresses are distributed parabolically, based on the assumption of linear
normal strain distribution through the thickness and on application of the
quadratic shape function to transverse shear strains. The transverse shear
stresses are included in the elastic-perfectly plastic yield function of the
Huber-Mises-Hencky type.
