Elsevier

Composite Structures

Volume 94, Issue 2, January 2012, Pages 654-663
Composite Structures

Semi-analytic probabilistic analysis of axially compressed stiffened composite panels

https://doi.org/10.1016/j.compstruct.2011.08.033Get rights and content

Abstract

The influence of scattering input parameters on the response of axially compressed stiffened composite panels is investigated. In order to estimate the stochastic distributions and the correlations between the first buckling load (or local buckling load), the global buckling load and the collapse load, a semi-analytic probabilistic analysis is performed. A procedure is given for evaluating the probability of failure of stiffened panels from the determined stochastic distributions, and probabilistically justified safety factors are derived.

Introduction

Stiffened fiber composite panels as part of aircraft fuselage provide great weight saving potential. However, under axial compression stiffened panels show a complex buckling behavior, which, for instance, has been demonstrated by the experimental work of Zimmermann et al. [1]. For stringer dominated designs, the first point of instability is reached when the skin between the stringers starts to buckle. The structural stiffness decreases slightly, but the load still can be increased. With the onset of global buckling, which corresponds to a lateral deflection of the stringers, the stiffness is reduced significantly.

Within the European projects POSICOSS and COCOMAT (see [2] and [3]) simulation tools and design guidelines have been developed to exploit the load carrying capability of stiffened composite panels, especially beyond the first buckling load. Still, safety factors are required to account for uncertainties or stochastic influences of the important parameters, respectively. The new design guidelines propose to divide the global buckling load λGB by a safety factor γ and to make sure that the onset of degradation λOD is beyond the design load λd.λd=min(λGB/γ,λOD)

Ghilai et al. [4] propose to have a safety region of 10–20% of the global buckling load, which is equivalent to a safety factor of 1.11–1.25. This provides additional weight savings compared to the commonly used safety factor of 1.5. Yet, investigations on the reliability or probability of failure, respectively, are lacking for the new design approach. Lee et al. [5] investigated the robustness of stiffened panels probabilistically, taking into account the scattering input parameters, but they did not derive safety factors from their investigations.

Within the MAAXIMUS project [6], the Institute of Structural Analysis at the Leibniz Universität Hannover investigates the scattering of the first buckling load or local buckling load, the global buckling load and the onset of degradation, which can start either before or after global buckling (see Fig. 1). With knowledge about the stochastic distribution of buckling loads, a lower bound of the load carrying capability can be defined by choosing the probability of failure. Hence, probabilistically justified safety factors and the reliability of the structure are obtained.

In the present paper, the sensitivities and the stochastic distributions of the first buckling load, the global buckling load and the onset of degradation due to scattering input parameters are determined. For this, a fast semi-analytic probabilistic procedure is used, which has been proposed and validated for buckling of cylindrical shells by Kriegesmann et al. [7]. As compared with the investigations in [7], now material failure is regarded additionally, which causes a more challenging, deterministic analysis. Furthermore, now multiple objective values are considered, namely the buckling loads and the onset of degradation, which requires an enhancement of the existing methods for taking into account the joint distribution of these objective values. Therefore, a new concept for determining the probability of failure of stiffened panels is given, which then is validated using Monte Carlo simulation. Based on these results, probabilistically justified safety factors can be derived.

Section snippets

Scatter of input parameters

For the present work, a set of panels is considered, which has been manufactured and tested at the German Aerospace Center (Deutsches Zentrum für Luft und Raumfahrt, DLR) in Braunschweig [1]. For the probabilistic analysis geometric imperfections of skin, deviations of wall-thickness, material properties and fiber orientation are regarded as scattering input parameters.

Numerical buckling analysis

The determination of the buckling loads is done within a geometrically non-linear, numerical simulation using the finite element code ABAQUS.

Probabilistic analysis

Given an objective function g(x) that is a function of a random vector X with the probability density function fX(x). The cumulative distribution function Fg of g is given byFg(g(x))=x:g(x)gfX(x)dx

In the work presented, the objective function is the local or global buckling load, or the onset of degradation, and the random vector describes all scattering input parameters. Given the cumulative distribution function of the load carrying capability and a desired level of reliability, the design

Results

The methods described in Sections 3 Numerical buckling analysis, 4 Probabilistic analysis are applied to panel P12–P14 of the set of stiffened panels given in [1]. From the load–displacement curves given in [1], the global buckling loads of the panels tested are determined according to the stiffness reduction criterion (see Section 3.2) and are given in Table 9.

Conclusions

A probabilistic analysis of axially compressed fiber composite stiffened panels has been performed taking into account geometric imperfections, imperfect boundary conditions, deviation of wall-thickness and fiber orientation as well as scattering material properties. The probabilistic sensitivity analysis shows that geometric imperfections, radius, and wall-thickness have the most significant influences on first buckling load, global buckling load and onset of degradation. For the probabilistic

Acknowledgments

The work presented has been done within the framework of the MAAXIMUS project, which is supported by the European Commission. The support of the EC and of the partners of the MAAXIMUS consortium is acknowledged. Furthermore, the excellent experimental work that has been performed at the German Aerospace Center in Braunschweig is gratefully acknowledged.

References (20)

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