Elsevier

Thin-Walled Structures

Volume 43, Issue 10, October 2005, Pages 1550-1566
Thin-Walled Structures

Ultimate compressive strength design methods of aluminum welded stiffened panel structures for aerospace, marine and land-based applications: A benchmark study

https://doi.org/10.1016/j.tws.2005.06.003Get rights and content

Abstract

The high strength-to-weight advantage of aluminum alloys has made it the material of choice for building airplanes and sometimes for the construction of land-based structures. For marine applications, the use of high-strength, weldable and corrosion resistant aluminum alloys have made it the material of choice for weight sensitive applications such as fast ferries, military patrol craft, luxury yachts and to lighten the top-sides of offshore structures and cruise ships. And while, over the last two decades, the ultimate limit state (ULS) design approach has been widely adopted in the design of aerospace and land-based (steel) structures, it is just recently being considered as a basis for the structural design and strength assessment of ships and offshore structures. Practical ULS methods or design codes are available in the aerospace and civil engineering industries, but they are just now being developed for use by the marine industry. The present paper compares some useful ULS methods adopted for the design of aerospace, marine and land-based aluminum structures. A common practice for aerospace, marine and civil engineering welded stiffened panel applications is discussed.

Introduction

There exist common issues in the structural design of airplanes, ships and land-based structures that usually are addressed differently. Most of the issues are different due to the inherent nature of the structures in themselves and in particular due to the loads, structural response, geometries and fabrication practices for each of these types of structures.

However, ships, airplanes and some land-based structures share a common aspect in that they use the stiffened panel as the building block of the primary load-carrying structure. The design of large parts of ship and airplane structures is primarily driven by compressive strength, where for civil transport aircraft the structural response of the upper wing and the lower fuselage shell may be likened to the structural behavior of a ship's hull girder (bottom, deck and side shells).

The structural stability of these thin-walled structures subjected to compressive loads is dependent on the buckling strength of the structure as a whole and of each structural member. For stiffened aerospace panels (high span-to-thickness ratio), the onset of buckling usually takes place in the skin, i.e., plating between stiffeners.

Marine stiffened panels are designed with sturdier stiffeners (e.g. bulb-flats or tees) so that they may meet other modes of failure rather than elastic panel buckling [1]. In both cases, the stiffness of the panel as a whole is significantly reduced after buckling, where the ultimate strength of the panel has normally not yet been reached since the panel enters into a post-buckling regime, a complex inelastic process being better described as panel failure or collapse. The final collapse state called the ultimate limit state can be formed by a combination of local buckling phenomena for plating and stiffeners or by a global ‘folding’ (or overall buckling) of the panel. In any case, the ultimate strength is not reached until the load versus end-shortening curve reaches its maximum, at which point several local buckling phenomena can already be active.

The design of aerospace stiffened panels under compressive loads needs methods which can predict buckling, post-buckling and ultimate strength behavior. These methods are based on Euler's column buckling analysis and Timoshenko's theory on the elastic stability of plates and shells [2].

These aerospace methods, where needed, combined with a correction for material plasticity, can easily predict the onset of buckling of perfect panels. While it may be possible to consider geometric imperfections as parameters of influence in these methods, it is not straightforward to take into account other types of imperfections such as thermo-mechanically affected zones (TMAZ, also described as HAZ, heat affected zones) and residual stresses from welding.

Marine structural design analysis has historically been simplified and experience-based. This is due to the intrinsic nature of ships, being hand crafted, generally one-off, large and relatively cheap structures that are subjected to complex load interactions between two distinct fluid mediums. In marine structural design, it has been common practice to assess only the onset of buckling adjusted by a plasticity correction, where acceptance is based on empirically derived stress level allowances with no real measure of the post-buckling and ultimate strength margin.

The design of aerospace and land-based structures is by and large carried out based on the ultimate limit state (ULS) design approach (commonly referred to as the load-resistance factor design (LRFD) approach). Recently, the ULS design approach has also widely been adopted for steel marine structures [3]. It is recognized that the ULS design approach is useful for the design of aluminum structures for marine applications, and practical design formulae have been derived together with some relevant considerations in terms of mechanical properties, initial imperfections and HAZ effects (e.g. [4], among others).

In aerospace design, minimum weight is of primary concern and airworthiness regulations permit the use of true post-buckling design, for metallic structures. It has therefore become common practice to assess the onset of buckling through non-linear plate theory, and the ultimate strength through the engineering theory of Euler–Johnson [5].

Recent developments in building of aerospace, marine and land-based structures are trending towards a common practice of design and fabrication. Welding is gaining interest for building aerospace and civil engineering structures. In the predominantly ‘steel culture’ marine industry, current economic and environmental considerations drive a need for weight savings that presses towards more effective material and design choices, meaning greater applications of aluminum alloys and the ULS design method.

This paper studies the differences between ultimate strength prediction methods adopted for design and strength assessment of aerospace, marine and land-based structures. A common practice for design of aerospace, marine and land-based structures is discussed.

Section snippets

General

Aluminum aerospace stiffened panels are designed based on post-buckling and ultimate strength behavior, implying that the skin is allowed to buckle locally for loads lower than the ultimate panel strength. The overall panel geometry is optimized so that compressive loads are transferred through to the stiffeners. Since plastic deformation is allowed at ultimate load, the post-buckling analysis becomes both geometrically non-linear and elastic-plastic.

Besides the local buckling (or crippling) of

General

Theoretically, the primary modes of overall failure for a stiffened panel subject to predominantly compressive loads are categorized into six types, namely [3]:

  • Mode I: overall collapse of plating and stiffeners as a unit

  • Mode II: biaxial compressive collapse

  • Mode III: beam-column type collapse (due to flexural buckling of the plate-stiffener combination section)

  • Mode IV: local buckling of stiffener web

  • Mode V: tripping (lateral or torsional buckling of stiffener alone or a combined

General

Aluminum alloys are also used for building some types of land-based structures. The civil engineering industry adopted LRFD (or ULS design) approach over two decades ago. Therefore, ULS design codes for aluminum structures as well as steel bridge structures in civil engineering industry have been well documented in contrast to marine industry which is now attempting to develop such ULS codes.

Useful simplified methods or formulations for predicting the ultimate strength of land-based aluminum

Finite element analyses

Geometrically non-linear elasto-plastic finite element analysis is the only method capable of simulating the succession of all buckling phenomena that occur during the quasi-static compression of a stiffened panel. To predict the ultimate strength of thin-walled structures, plate-shell elements that account for both membrane and bending stiffness are employed.

The mesh size must be fine enough to capture long-wave-length buckling modes, such as torsional buckling, also accounting for continuity

General

For a total of 13 aluminum stiffened panels subjected to axial compressive loads, that have experimental results of their ultimate strength, various ULS prediction methods noted above are now compared. A number of 6 candidate methods are considered, as will be indicated in Table 4. For aerospace design methods described above, only the Euler–Johnson (E–J) method is adopted.

It should be noted that the present theoretical predictions of ultimate strength, by the various methods discussed, are

Concluding remarks

In the present paper, a comparison of the various methods for ULS predictions of aluminum stiffened panels used for aerospace, marine and civil engineering applications has been made.

A total of 13 aluminum stiffened panels (11 marine panels and two aerospace panels), where mechanical collapse testing data is available, were studied. It is to be noted that the theoretical predictions including FEA were undertaken using the ‘minimum’ specified properties of material instead of real properties of

Acknowledgements

Part of the present work was undertaken with the support of US Office of Naval Research (Grant No. N00014-03-1-0761). The first author is pleased to acknowledge the support. The effort of Dr Young Il Park regarding the computations of ALPS/ULSAP and the Paik–Duran empirical formulae is appreciated. Part of the present paper has been presented at the 9th International Symposium on Practical Design of Ships and Other Floating Structures held in Germany during 12–17 September 2004.

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