Keywords: stability analysis, composite material, damage, shell structures, finite element modelling.

This paper presents an approach for the stability analysis of stringer-stiffened fibre reinforced polymer panels under axial compression based on the finite element method. In the first part we discuss the necessary modifications of shell formulations to model layered shear-elastic thin shell structures allowing for an arbitrary stacking sequence and furthermore a variable position of the reference plane along the thickness. A main goal of the paper is the modeling of damaged structures. Here intralaminar and interlaminar damage may occur. Different ply discount models with constant knock-down factors are employed to account for ply failure which can occur as fibre fracture, matrix cracking, or fibre-matrix shear failure. Finally a modified material law using so called knock-down factors is derived. The interlaminar damage, here especially delamination of layers and particularly debonding of stiffeners from the skin of stiffened panels, is modeled via so-called two- or three-dimensional interface elements in which a cohesive zone approach is implemented. Material laws for the cohesive zone are discussed and a special exponential cohesive law is presented which is history-dependent in order to prevent restoration of cohesion. The interpenetration of the crack faces is avoided using a penalty contact formulation. The algorithms developed are applied to two examples were experimental data are available. The first example presents the simulation of axial compression tests for single-stiffener panels whereas the second example shows the simulation of a curved multi-stiffener panel again under axial compression. The pre- and post-buckling response of these composite structures are calculated with an arc-length as well as dynamic solution algorithms in case of multi-buckling. The response of the structures is governed by the complex intra- and inter-laminar damage behaviour. The performance and applicability of the proposed models are described in detail and the results are compared to the experiments.

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