Thin-shell-theory solutions for the static structural response of circular-sections shaped corrugated laminates

Abstract

The study considers a corrugated laminate with dimensions far larger than the length of one periodic unit cell and at regions where edge effects have decayed. Then, the linear elastic structural properties of the corrugated laminate are presented by a substitute plate A~B~D~ matrix. Its entries are found by subjecting a unit cell model to the load cases which correspond to the entries of the plate deformation vector, and then calculating the reacting stress resultants. The enforced deformations are all states of generalized plane strain with respect to the span direction. A corrugation pattern consisting of circular segments and the assumption, that thin shell theory is valid for the modeling, facilitates finding of exact solutions even though the base laminate may exhibit all possible stiffness couplings. The exact interior solutions include displacements, plate deformations, stresses, and reaction forces from which the calculation of the substitute plate matrix follows naturally. The paper explains all derivations and gives results for a representative general laminate, studying the model limitations and illuminating on which mechanical effects are not naturally captured by thin shell theory. A parameter study on a non-symmetric cross-ply laminate is performed to identify the main effects caused by increasing corrugation amplitude. Rationales for the systematic deviations of thin-shell-theory from solid-volume-modeling predictions of some substitute-stiffness matrix entries are presented by using simplified analytical modeling.