Ultimate shear strength of intact and cracked stiffened panels

The present paper focuses on the ultimate shear strength analysis of intact and cracked stiffened panels. Several potential parameters influencing the ultimate shear strength of intact panels are discussed, including the patterns and amplitudes of initial deflection, the slenderness and aspect ratios of the plates, and the boundary conditions defined by the torsional stiffness of support members. An empirical formula for the ultimate shear strength of intact stiffened panels is proposed based on parametric nonlinear finite element analyses in ANSYS. Furthermore, the ultimate shear strength characteristics of cracked stiffened panels are investigated in LS-DYNA with the implicit method. Three types of cracks are considered, namely vertical crack, horizontal crack and angular crack. A simplified method is put forward to calculate the equivalent crack length. And the formula for the ultimate shear strength of cracked stiffened panels is derived on the basis of the formula for intact stiffened panels.     

Influence of corrosion on the ultimate compressive strength of steel plates and stiffened panels

This study concentrates on a comparison between steel plate and stiffened panels subject to localised corrosion. A finite element analysis is used to investigate the effect of random corrosion on the compressive strength capacity of marine structural units. Variables include the extent of corrosion; slenderness ratio and aspect ratio. A corrosion prediction model is incorporated to determine the thickness reduction with time. Corrosion-induced volume loss results in a greater reduction of ultimate strength for slender plates compared to stiffened panels, up to 45%, showing the structural element selection can strongly influence the accuracy of the estimated corrosion damage effect.     

Validation of the equivalent plate thickness approach for ultimate strength analysis of stiffened panels with non-uniform plate thickness

The stiffened plate structures in ships and ship-shaped offshore installations often consist of non-uniform plate thicknesses. Nonlinear finite element methods are usually employed to predict structural strength for such panels. However, the introduction of non-uniform plate thicknesses renders such calculations difficult when analytical methods and design equations are used. The authors have suggested an equivalent plate thickness method that is based on the weighted average approach to analyse the strength of stiffened panels with non-uniform plate thicknesses. In the present paper, the validity of the equivalent plate thickness method to the ultimate strength analysis of stiffened panels with non-uniform plate thicknesses is checked through nonlinear finite element method computations. It is concluded that the equivalent plate thickness method is accurate for the panel ultimate strength analysis under combined biaxial compression and lateral pressure loads.     

Ultimate strength of stiffened aluminium panels with predominantly torsional failure modes

The aim of this paper is to investigate the ultimate strength of aluminium plates with flatbar stiffeners with a torsional buckling or tripping failure mode. The formulations for torsional buckling of stiffeners in steel plating are still debated. Compared with steel structures, the ultimate strength of aluminium structures is sensitive not only to residual stresses and initial deformations, but also to the deterioration of mechanical strength in heat-affected zones (HAZ). In the present paper, the ultimate strength of stiffened aluminium panels with predominantly torsional failure modes is investigated by experimental and theoretical analysis. Stiffened panels made of the aluminium alloy AA5083-H116 and AA6082-T6 are considered. Various height of flatbar and various thickness of plate and stiffener were studied. The test results are compared with numerical predictions by using the finite element code ABAQUS (ABAQUS Version 5.7 (1997)), considering the influence of initial deflections, welding residual stresses and HAZ. The influence of HAZ and residual stresses on the ultimate strength of stiffened aluminium panels with the actual failure mode is discussed in detail. The numerical predictions are also compared with strength of material formulations used in DNV Rules for Classification of High Speed and Light Craft (Rules for classification of high speed and light craft, Hull structural design (1996)), NORSOK (Design of steel structures (1998)) all for steel, using the relevant values of the modulus elasticity and yield strength of aluminium, as well as EUROCODE 9 (Eurocode 9, Part 1-1: General rules (1998)).     

Large deflection orthotropic plate approach to develop ultimate strength formulations for stiffened panels under combined biaxial compression/tension and lateral pressure

This paper uses the large deflection orthotropic plate approach to develop the ultimate strength formulations for steel stiffened panels under combined biaxial compression/tension and lateral pressure loads, considering the overall (grillage) buckling collapse mode. The object panel has a number of one-sided small stiffeners in either one or both orthogonal directions. The stiffened panel is then modeled as an equivalent orthotropic plate, for which the various elastic constants characterizing structural orthotropy are determined in a consistent systematic manner using classical theory of elasticity. The panel edges are considered to be simply supported. The influence of initial deflections is taken into account. The membrane stress distribution inside the panel under combined uniaxial loading (in either longitudinal or transverse direction) and lateral pressure is analyzed by solving the nonlinear governing differential equations of large deflection orthotropic plate theory. It is presumed that the panel collapses when the most highly stressed boundary location yields, resulting in closed-form expressions for the ultimate strength of the stiffened panel. Based on the insights previously developed through numerical studies, the panel ultimate strength interaction formulation between biaxial loads, with lateral pressure regarded as a secondary load component is then proposed as a relevant combination of the two sets of panel ultimate strength formulations, i.e. one for combined longitudinal axial load and lateral pressure and the other for combined transverse axial load and lateral pressure. The validity of the proposed ultimate strength formulations is verified by a comparison with nonlinear finite element and other numerical solutions.     

The buckling characteristics of some integrally formed bead stiffened composite panels

Composite panel stability can easily be improved by using vertical male beads. In this paper, new methods of stabilizing techniques used for the panels, webs and ribs of composite structures are studied. A parametric study is performed to assess the effects of important design considerations such as, bead length, number of beads, bead radius, bead depth and bead spacing on the initial buckling load of the panels. The results show that, there is an optimum bead spacing for each panel containing more than one bead which can be estimated using a simple equation. Integration of vertical beads with a length of less than 0.5 times the panel's length has no significant effect on the buckling load. There are no significant changes on the buckling loads of the beaded panels with bead depths greater than 0.6 times the bead radius. In this investigation, the instability of the nose and main ribs of a light airplane wing structure made of woven E-glass material and stiffened by P.V.C foam core and vertical male beads are also studied using experimental methods. The experimental results show that we can easily improve the buckling capability of the panels and webs by using vertical male beads instead of sandwiched construction. It is estimated that this would cause a weight reduction of about 50% and a manufacturing time reduction of about 50%.     

Buckling and ultimate strength criteria of stiffened shells under combined loading for reliability analysis

The work presented in this paper forms part of a broader task in establishing a guide to serve as technical documentation for buckling and ultimate strength assessment of various types of marine structural components using the best state-of-the-art knowledge for extreme environmental loading. This paper concentrates on buckling and ultimate strength assessment of ring stiffened shells and ring and stringer stiffened shells involving various modes of buckling and under various loading like axial compression, radial pressure and combined loading. Comparisons are made with screened test data, which have realistic imperfections and various radius to thickness ratio values in the range generally used in offshore structures. The statistical data of model uncertainty factors in terms of bias and coefficient of variation (COV) are calculated and may be used in a further reliability study. Comparisons are also made with the codified rules, API BUL 2U and DNV buckling strength of shells.     

Compressive tests on stiffened panels of intermediate slenderness

Test results are presented of eight stiffened panels subjected to axial compression until collapse and beyond. The specimens are three-bay stiffened panels with associated plate made of very high tensile steel S690. The use of this very high strength steel led to the unconventional solution of using U stiffeners and this paper aims at understanding the difference of performance of this stiffener type as compared with the conventional ones. Four different configurations are considered for the stiffeners, which are made of mild or high tensile steel for bar stiffeners and mild steel for ‘L’ and ‘U’ stiffeners. The influence of the stiffener's geometry on the ultimate strength of the stiffened panels under compression is analyzed.     

Empirical formulations for predicting the ultimate compressive strength of welded aluminum stiffened panels

The present study was undertaken by the support from Ship Structure Committee (http://www.shipstructure.org), a North American-based interagency research and development committee, in association with SR-1446 project, and also from Alcan Marine, France. Empirical expressions are developed for predicting the ultimate compressive strength of welded aluminum stiffened panels used for marine applications. Existing data of the ultimate compressive strength for aluminum stiffened panels experimentally and numerically obtained by the SR-1446 project is used for deriving the formulations which are expressed as functions of two parameters, namely the plate slenderness ratio and the column (stiffener) slenderness ratio. The formulae implicitly include the effects of weld induced initial imperfections, and softening in the heat affected zone.     

A semi-analytical model for global buckling and postbuckling analysis of stiffened panels

A computational model for global buckling and postbuckling analysis of stiffened panels is derived. The loads considered are biaxial in-plane compression or tension, shear, and lateral pressure. Deflections are assumed in the form of trigonometric function series, and the principle of stationary potential energy is used for deriving the equilibrium equations. Lateral pressure is accounted for by taking the deflection as a combination of a clamped and a simply supported deflection mode. The global buckling model is based on Marguerre’s nonlinear plate theory, by deriving a set of anisotropic stiffness coefficients to account for the plate stiffening. Local buckling is treated in a separate local model developed previously. The anisotropic stiffness coefficients used in the global model are derived from the local analysis. Together, the two models provide a tool for buckling assessment of stiffened panels. Implemented in the computer code PULS, developed at Det Norske Veritas, local and global stresses are combined in an incremental procedure. Ultimate limit state estimates for design are obtained by calculating the stresses at certain critical points, and using the onset of yielding due to membrane stress as the limiting criterion.     

Residual ultimate strength of cracked steel unstiffened and stiffened plates under longitudinal compression

This paper numerically deals with the influence of cracks (in terms of length and location) on the ultimate compressive strength characteristics of unstiffened and stiffened plate elements used in thin-walled structures. The cracks were presumed to be through-thickness, having no contact between their faces and no propagation was allowed. A series of nonlinear finite element analyses was conducted using ANSYS commercial finite element code in which the Newton–Raphson method has been employed to solve the nonlinear governing equations.This study indicates that the length of cracks and especially its location can significantly affect the ultimate strength characteristics of unstiffened and stiffened plate elements subjected to axial compressive action.     

The computational post-buckling analysis of fuselage stiffened panels loaded in shear

Fuselage panels are commonly fabricated as skin-stringer constructions, which are permitted to locally buckle under normal flight loads. The current analysis methodologies used to determine the post-buckling response behaviour of stiffened panels relies on applying simplifying assumptions with semi-empirical/empirical data. Using the Finite Element method and employing non-linear material and geometric analysis procedures it is possible to model the post-buckling behaviour of stiffened panels without having to place the same emphases on simplifying assumptions or empirical data. Previous work has demonstrated that using a commercial implicit code, the Finite Element method can be used successfully to model the post-buckling behaviour of flat riveted panels subjected to uniform axial compression. This paper expands the compression modelling procedures to flat riveted panels subjected to uniform shear loading, investigating element, mesh, idealisation and material modelling selection, with results validated against mechanical tests. The work has generated a series of guidelines for the non-linear computational analysis of flat riveted panels subjected to uniform shear loading, highlighting subtle but important differences between shear and compression modelling requirements.     

Influence of initial distortion on the structural stress in 3 mm thick stiffened panels

This paper investigates the effect of initial distortion on the structural stress in 3 mm thick stiffened panels. The influence of initial distortion shape as well as magnitude is studied under axial tension and compression using geometrically non-linear finite element analysis. Different levels of structures are analyzed starting from the plate strips to an actual panel in order to understand how the structural response of thin initially distorted panel builds up. This way the difference between having initial distortion in one or two directions as well as the effect of boundary conditions becomes visible. The results reveal high non-linearity in the behavior of plate strip models and relatively linear behavior of actual plates and panel models in typical fatigue relevant ranges. This is due to support that the actual structures get from having initial distortion in two directions and from surrounding structures. In case of panels the most important effect on structural stresses near the transverse butt weld is the shape of the initial distortion. The second important is the magnitude of initial distortion and significantly less relevant is the straightening effect, i.e. decrease in structural to nominal stress ratio under loading.     

Buckling analysis of stiffened circular cylindrical panels using differential quadrature element method

Differential quadrature element method (DQEM) for buckling analysis of stiffened circular cylindrical panels subjected to axial uniform compressive stresses is presented for the first time. The methodology and procedures are worked out in detail. The circular cylindrical panel and the stiffeners are treated separately. Governing differential equations are derived based on the equilibrium of the panel and the stiffener, and on compatibility conditions along the interface of panel elements and stiffeners. Torsional stiffness of the stiffener is ignored. Circular cylindrical panels with a stringer stiffener or a chordwise stiffener are analyzed by the DQEM, and the results are compared with previously published data to verify the established methodology and procedures. Some new results are presented for the circular cylindrical panels with two orthogonal stiffeners.     

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

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.     

A simplified method for elastic large deflection analysis of plates and stiffened panels due to local buckling

A computational model for analysis of local buckling and postbuckling of stiffened panels is derived. The model provides a tool that is more accurate than existing design codes, and more efficient than nonlinear finite element methods. Any combination of biaxial in-plane compression or tension, shear, and lateral pressure may be analysed. Deflections are assumed in the form of trigonometric function series. The deformations are coupled such that continuity of rotation between the plate and the stiffener web is ensured, as well as longitudinal continuity of displacement. The response history is traced using energy principles and perturbation theory. The procedure is semi-analytical in the sense that all energy formulations are derived analytically, while a numerical method is used for solving the resulting set of equations, and for incrementation of the solution. The stress in certain critical points are checked using the von Mises yield criterion, and the onset of yielding is taken as an estimate of ultimate strength for design purposes.     

The computational post buckling analysis of fuselage stiffened panels loaded in compression

Fuselage panels are commonly fabricated as skin–stringer constructions, which are permitted to locally buckle under normal flight loads. The current analysis methodologies used to determine the post buckling response behaviour of stiffened panels relies on applying simplifying assumptions with semi-empirical/empirical data. Using the finite element method and employing non-linear material and geometric analysis procedures, it is possible to model the post buckling behaviour of stiffened panels without having to place the same emphases on simplifying assumptions or empirical data. Investigation of element, mesh, idealisation, imperfection and solution procedure selection has been undertaken, with results validated against mechanical tests. The research undertaken has demonstrated that using a commercial implicit code, the finite element method can be used successfully to model the post buckling behaviour of flat riveted panels. The work has generated a series of guidelines for the non-linear computational analysis of flat riveted panels subjected to uniform axial compression.     

Ultimate strength formulations for stiffened panels under combined axial load, in-plane bending and lateral pressure: a benchmark study

This paper develops advanced, yet design-oriented ultimate strength expressions for stiffened panels subject to combined axial load, in-plane bending and lateral pressure. The collapse patterns of a stiffened panel are classified into six groups. It is considered that the collapse of the stiffened panel occurs at the lowest value among the various ultimate loads calculated for each of the collapse patterns. The panel ultimate strengths for all potential collapse modes are calculated separately, and are then compared to find the minimum value which is then taken to correspond to the real panel ultimate strength. The post-weld initial imperfections (initial deflection and residual stress) are included in the developed panel ultimate strength formulations as parameters of influence. The validity of the developed formula is confirmed by comparing with the mechanical collapse tests and nonlinear FEA. A comparison of the present method is also made with theoretical solutions from the Det Norske Veritas classification society design guideline. Important insights developed are summarized.     

An experimental study of ultimate compressive strength of transversely stiffened aluminium panels

An experimental investigation was carried out to determine the ultimate strength of welded stiffened aluminium panels in alloy 6082 T6 subjected to in-plane compressive loads normal to the directions of the stiffeners. This load case is not treated in the European standard for aluminium structures, Eurocode 9. A total of 21 panel specimens with various side aspect ratios and both open and closed stiffener sections were tested in a purpose made test rig. Great care was taken to ensure the rig gave very precise boundary conditions. The panels were manufactured by metal inert gas arc welding and friction stir welding. An extensive measurement program was carried out to determine the distribution of material strength and initial geometric imperfections. Small imperfection amplitudes were found. Tensile tests revealed variation in material properties, but the strength values were on average higher than the values stated in Eurocode 9. The panels failed by two different deformation modes; global flexural buckling and local buckling of the plate elements between the stiffeners.     

Buckling of laminated composite stiffened panels subjected to in-plane shear: A parametric study

The presence of in-plane loading may cause buckling of stiffened panels. An accurate knowledge of critical buckling load and mode shapes are essential for reliable and lightweight structural design. This paper presents some parametric studies on simply supported laminated composite blade-stiffened panels subjected to in-plane shear loading. A total of 450 models were analyzed using ANSYS 7.1 and a database is prepared for different plate and stiffener combinations. Studies are carried out by changing the panel orthotropy ratio, stiffener depth, pitch length (number of stiffeners), smeared extensional stiffness ratio of stiffener to that of the plate and extensional stiffness to shear stiffness ratio of the plate. Based on the studies, few important parameters influencing the buckling behaviour are identified and guidelines for better stiffener proportioning are developed, which will be helpful for the designer.