Integral Stiffeners Research Articles

Experimental study of GFRP stiffened plates with and without large opening under combined axial and pressure loading

GFRP stiffened panels forms the basic component of ship hulls, decks, submarines, offshore oil platforms etc., GFRP stiffened panels used in ship hulls and decks are subjected to axial loading due to buoyancy and pressure loading due to cargo. GFRP stiffened plate dimensions considered in this study are the scaled down dimensions of a cargo ship. Aluminium moulds with and without opening are fabricated for casting GFRP stiffened panels. GFRP stiffened panels with integral stiffeners are manufactured using hand lay-up process. A unique lay-up pattern was adopted to achieve the monolithic behaviour of stiffeners and plate. Fabrication of GFRP stiffened panels by manual hand layup process leads to formation of indentations. These imperfections are determined using the LVDTs attached to imperfection measurement setup. The measured imperfections are compared with the allowable imperfection values available for steel in BS 5400, because limiting imperfection values are not available for FRP. Openings are necessary for access and maintenance in ship hulls, decks etc. The presence of openings can lead to loss in strength and stiffness of the GFRP stiffened panels. In this study, GFRP stiffened panels with and without opening are tested for different combinations of axial and pressure loading. Axial loads are applied using two hydraulic jacks and measured using two load cells which are fabricated to prevent eccentricity while applying axial load. Pressure loads are applied using inflatable air balloons with and without opening fabricated for this study. Load capacity, failure strain, failure patterns of GFRP stiffened panels under different load combinations are presented. Failure locations of GFRP stiffened panels with and without opening various load combinations are discussed. Reduction in load capacity, span to deflection ratio and loss in stiffness due to opening is calculated.

Inverse anamorphosis and multi-map techniques for free topology generation of curved self-stiffened panels using skeleton-based integral soft objects

In the present paper, an improved procedural method for the generation of curved, arbitrarily conformed self-stiffened panels using skeleton-based integral soft objects is presented. The proposed approach extends the application of integral soft objects to curved mesh surfaces by operating an inverse anamorphic mapping of special-purpose displacement fields applied orthogonally to the patched surface representing the curved structural domain. An efficient parallel procedure, able to evaluate the vector field of normals at mesh nodes of the host domain, is preliminary illustrated. Several multi-map techniques are subsequently exploited to generate arbitrary protrusions on different curved mesh surfaces, either open or closed. • Integral stiffeners can now be produced on curved meshes, either open or closed. • No support geometry is required or employed by the method. • A large collection of stiffening objects is available; further objects may be added. • The method does not require re-meshing, just fast morphing. • The whole method (procedures and database) is GPGPU compliant.

Experimental and Numerical Studies of Low-Profile, Triangular Grid-Stiffened Plates Subjected to Shear Load in the Post-Critical States of Deformation.

Constant developments in manufacturing technology have made it possible to introduce integrally stiffened elements into load-bearing, thin-walled structures. The application of thin-walled elements with integral stiffeners potentially increases buckling and critical loads to maintain the mass of the structure and lower production costs. This paper presents the results of experimental investigations and numerical Finite Element Modelling (FEM) analyses of low-profile, isosceles grid stiffened, aluminium alloy plates subjected to pure shear load. Conducted research included analysing buckling and post-buckling states of deformation, taking into account both geometrical and physical nonlinear effects. Use of the Digital Image Correlation (DIC) system during the experimental tests created representative equilibrium pathways and recorded displacement field distributions over the plate surface. The model was initially validated against the experimental results. The results for the stiffened plate were compared to the reference structure in the form of a smooth plate with equivalent mass. Comparative analyses included examining the displacement fields and stress efforts over the plates. The stiffening configuration under examination increased the critical buckling load by 300% in comparison to the unstiffened structure with the same mass. Obtained results also indicate potential problems with areas of concentrated stress in the case of an incorrect geometry design near to the boundary conditions.

A Location Method Using Sensor Arrays for Continuous Gas Leakage in Integrally Stiffened Plates Based on the Acoustic Characteristics of the Stiffener.

This paper proposes a continuous leakage location method based on the ultrasonic array sensor, which is specific to continuous gas leakage in a pressure container with an integral stiffener. This method collects the ultrasonic signals generated from the leakage hole through the piezoelectric ultrasonic sensor array, and analyzes the space-time correlation of every collected signal in the array. Meanwhile, it combines with the method of frequency compensation and superposition in time domain (SITD), based on the acoustic characteristics of the stiffener, to obtain a high-accuracy location result on the stiffener wall. According to the experimental results, the method successfully solves the orientation problem concerning continuous ultrasonic signals generated from leakage sources, and acquires high accuracy location information on the leakage source using a combination of multiple sets of orienting results. The mean value of location absolute error is 13.51 mm on the one-square-meter plate with an integral stiffener (4 mm width; 20 mm height; 197 mm spacing), and the maximum location absolute error is generally within a ±25 mm interval.

Reflection and transmission of guided ultrasonic plate waves by vertical stiffeners.

Ultrasonic guided waves are very useful for structural health monitoring. They have the potential to interrogate and detect damage in a structure over a large area with few transducers. Guided plate modes (Lamb waves) are used and proposed for damage detection at a distance in semi-monococque structures such as airplane fuselages and spacecraft structures. The interaction of guided plate waves with stiffening members such as ribs, stringers, or the integral stiffeners used in spacecraft structures limits the distance over which structural health monitoring non-destructive evaluation systems can detect damage. This paper develops a simple explanatory model for the scattering of low-order ultrasonic Lamb waves crossing a stiffening device. The model illuminates the underlying mechanics of waves crossing a stiffener. The model shows that stop-bands for transmission of S(0) (longitudinal pressure) waves across a stiffener line up with flexural resonances of the stiffener. It also demonstrates why transmission of A(0) (flexural) waves is more complicated and harder to predict. The model is shown to agree well with both boundary element method calculations and experimental measurements.

Improved stress intensity factors for selected configurations in cracked plates

In this paper improved stress intensity geometry factors are determined for four key geometric configurations. They were developed using a p-version finite element method program. Two-dimensional uniaxially loaded plates are investigated, with either: an edge crack, a crack approaching a hole, or a crack propagating from a hole after ligament failure. The three-dimensional problem of a through crack in an integral stiffener approaching a junction, under uniaxial tension, is also considered. The resulting normalised stress intensity factor data are provided as compact equations or presented in tabular form.

Potential applications of peen forming finite element modelling

► A finite element methodology was applied for peen forming of aerospace components. ► The method combines dynamic and static simulations to lower computational cost. ► The response of complex parts to sequential forming treatments was predicted. ► This reduces the dependence of process development upon costly experimental testing. ► This approach has great potential at different stages of the component lifecycle. Peen forming is a versatile and flexible manufacturing process commonly used in the aerospace industry to shape wing skins and rockets panels. Development of peening parameters needed to obtain a specific component shape can be both costly and challenging due to the use of empirical methods which involve large quantities of physical experiments coupled with trial and error processing of prototype components. Many iterations are often required to get the desired shape with no guarantee that a specific component geometry can be achieved. Reliable numerical simulations could substantially reduce the time, cost and risk associated with process development. The purpose of this study is to further investigate the use of numerical tools to model the peen forming process. This work combines static and dynamic simulation techniques to predict the development of curvature on representative wing skin panels that include features such as integral stiffeners. This work illustrates the considerable potential of finite element simulations to determine the process parameters needed to produce a component design, and substantially reduce the dependence upon physical testing.

Guided plate wave scattering at vertical stiffeners and its effect on source location

This paper examines guided wave transmission characteristics of plate stiffeners and their influence on the performance of acoustic noise source location. The motivation for this work is the detection of air leaks in manned spacecraft. The leaking air is turbulent and generates noise that can be detected by a contact-coupled acoustic array to perform source location and find the air leak. Transmission characteristics of individual integral stiffeners are measured across a frequency range of 50–400kHz for both high and low aspect-ratio rectangular stiffeners, and comparisons are made to model predictions which display generally good agreement. It is demonstrated that operating in frequency ranges of high plate wave stiffener transmission significantly improves the reliability of noise source location in the plate. A protocol is presented to enable the selection of an optimal frequency range for leak location.

Analysis and optimization of externally stiffened crush tubes

Nonlinear finite element analysis is used to investigate the quasi-static axial collapse response of cylindrical tubes which are externally stiffened by multiple identical rings. The rings divide the long tube into a series of short thin-walled tubes. It is assumed that the size and shape of integral stiffeners are controlled through a machining process. The effects of various geometric parameters such as wall thickness, ring spacing, ring thickness and width on the collapse response, crush force and energy absorption of monolithic, integrally stiffened steel tubes are studied and used as a general framework for a design optimization study. Through design and analysis of computer experiments, global metamodels are developed for the mean crush force and energy absorption, using the radial basis function approximation technique. Using both single- and multi-objective design optimization formulations, optimum designs for different response characteristics are found. The crush mode in the form of progressive collapse or buckling is found to heavily depend on the ratio of stiffener spacing to stiffener height as well as the ratio of wall thickness to stiffener thickness. The optimization results show the viability of externally stiffened tubes as efficient energy absorbers.

Fatigue, residual strength and non-destructive tests of an aging aircraft’s wing detail

This study concentrates on fatigue, residual strength and non-destructive tests of an aging aircraft’s wing detail of the Finnish Air Force’s Hawk Mk.51 jet trainer. The studied detail was the integral stiffener with a drain hole near the wing root. Fatigue tests were deemed necessary to verify experimentally the analytically observed short fatigue life, significant crack growth rates and eventually to re-assess the detail’s inspection period for the fleet jets. The results of the study have been utilized e.g. at the complementary type approval accomplished for the Finnish Air Force’s Hawk.

Response of Impacted Sandwich Panels with Integral Stiffeners

A study was conducted to determine the effect of integral stiffeners on the damage growth and ultimate strength of sandwich panels with impact damage. A total of 18 specimens with IM7/8552 [90/0]S facesheets cocured to 25-mm thick Nomex honeycomb core were impacted and tested in compression. All of the specimens were nominally 152 mm in width and 356 mm in length and were impacted at the center of the front facesheet. Damage growth was monitored via strain gages, and ultimate strength was compared against sandwich panels without integral stiffeners. When the integral stiffeners involved redistributing material in the facesheet, the damage in the resulting thinner facesheet often grew sooner and the ultimate strength was unaltered. When the internal stiffeners involved additional material, damage growth was delayed and the ultimate strength was increased to the point where the ultimate failure initiated away from the impact site.

The behaviour of damage tolerant hat-stiffened composite panels loaded in uniaxial compression

Damage tolerant hat-stiffened thin-skinned composite panels with and without a centrally located circular cutout, under uniaxial compression loading, were investigated experimentally and analytically. These panels incorporated a highly postbuckling design characterised by two integral stiffeners separated by a large skin bay with a high width to skin-thickness ratio. In both configurations, the skin initially buckled into three half-wavelengths and underwent two mode-shape changes; the first a gradual mode change characterised by a central deformation with double curvature and the second a dynamic snap to five half-wavelengths. The use of standard path-following non-linear finite element analysis did not consistently capture the dynamic mode change and an approximate solution for the prediction of mode-changes using a Marguerre-type Rayleigh-Ritz energy method is presented. Shortcomings with both methods of analysis are discussed and improvements suggested. The panels failed catastrophically and their strength was limited by the local buckling strength of the hat stiffeners.

Non-linear finite element modelling of an integrally stiffened composite panel

The progressive introduction of advanced fibre composite materials into aerospace structures has enabled significant performance improvements to be achieved. Structures using these materials are generally designed so that their behaviour is essentially linearly elastic through to failure. The realisation of further significant weight reductions in light-weight aerospace structures is highly dependent on design technologies which will enable postbuckling stiffened panels to be utilised in primary structures. The capabilities of the finite element code, MSC/NASTRAN, to predict the onset of buckling and subsequent postbuckling behaviour of a blade-stiffened fibre composite panel have been investigated. The panel consists of T300/914 carbon/epoxy unidirectional tape and is reinforced by integral stiffeners. Basic modelling techniques for the efficient analysis of such postbuckling assemblies are presented. It is concluded that the prediction of their performance requires specialist modelling skills and a sound understanding of the behaviour of the composite materials used in the structure.

Regularized formulation for optimal design of axisymmetric plates

This paper presents a regularized mathematical formulation, necessary conditions of optimality and solutions of problems of optimal design of solid, elastic, axisymmetric plates of prescribed total material volume. Single-purpose design criteria of minimum static compliance (maximum stiffness) and maximum frequency of free, transverse vibrations, are considered.The regularization, which alleviates some anomalies and difficulties encountered earlier in plate optimization problems, is based on a new compound plate model with two simultaneous design variables, namely, variable thickness of a solid part of the plate and variable concentration of a dense system of thin, integral stiffeners attached to the solid plate part. A numerical, optimality-criterion-based method of solution is developed for the problem, and several optimal designs are presented. The results are compared with results obtained from optimal design formulations applied heretofore, and substantiate the superiority of the new, regularized formulation.

A note on transverse vibrations of stiffened rectangular plates with edges elastically restrained against rotation

This note deals with the determination of the fundamental frequency of vibration of rectangular plates with edges elastically restrained against rotation. The plate is reinforced by a single integral stiffener placed along one of its center lines. It is assumed that the value of the parameter f/h (stiffener deph/plate thickness) is “moderate”.

An investigation concerning optimal design of solid elastic plates

We consider the problem of maximizing the integral stiffness of solid elastic plates described by thin plate theory. Assuming the material volume and plate domain to be given, we use the plate thickness function as the design variable and take both maximum and minimum allowable thickness values into account. On the basis of a convenient tensorial formulation of the problem, where the governing equations are derived by variational analysis and constitute necessary conditions for stationarity, we develop an efficient and quite general numerical algorithm by means of which a number of stationary solutions for rectangular and axisymmetric annular plates with various boundary conditions are obtained.These numerical results enable us to investigate the optimization problem itself in terms of its major parameters, particularly the maximum and minimum values specified for the plate thickness. For problems associated with large ratios between these constraint values, plate designs with significant integral stiffeners are obtained. We find however, that these designs are only local optima and that a global optimal plate thickness function does generally neither exist within the class of smooth functions nor within the class of smooth functions with a finite number of discontinuities. In order to determine a global optimal solution associated with given thickness constraint values, it is therefore necessary to change the optimal design formulation. With implications for a number of similar two-dimensional optimization problems, our results offer valuable indications of the lines along which such changes should be performed.

On non-smoothness in optimal design of solid, elastic plates

In the present paper, minimum compliance design problems of thin, solid elastic plates are discussed. We follow up indications provided by numerical results obtained in a recent paper[1], and propose a new plate model, where a uniform plate is equipped with an infinite number of infinitely thin integral stiffeners. On the basis of this new plate model, numerical and analytical investigations of a new formulation of the minimum compliance design problem are carried out. It is demonstrated that the new formulation is, under certain conditions, superior to the corresponding traditional formulation for determining a possible global optimal solution for solid plates.Since both the new formulation and the traditional formulation are based on classical thin plate theory, the superiority of the new plate model over the corresponding smooth one directly implies that optimal thickness distributions for thin, solid, elastic plates, are generally not smooth functions, but functions with an infinite number of discontinuities.

Numerical Results for the Initial Buckling of Some Stiffened Panels in Compression

SummaryIn previous papers the basis of a matrix approach to the initial buckling or vibration of prismatic structures consisting of a series of thin flat rectangular plates rigidly connected together along their longitudinal edges has been developed. The present paper provides numerical results for the buckling, under uniform longitudinal compression, of a series of panels with unflanged or flanged integral stiffeners, or with Z-section stiffeners; the results are compared with those obtained by other methods and with published results, including an appropriate Royal Aeronautical Society Structures Data Sheet. It was found that considerable inaccuracies can arise from the usual methods of analysis and the authors believe that these justify the use of computer programmes, such as the ones used to obtain the results of this paper, at least at the final design stage.

Natural frequencies of stiffened rectangular plates

The natural frequencies of the first symmetric and first antisymmetric modes of a simplysupported rectangular plate are determined. The plate is reinforced by a single integral stiffener placed along one of its centre lines, the dimensions of the plate and stiffener cross-section being chosen so that the mass of the plate-stiffener combination remains constant. Two forms of stiffener cross-section are studied, namely, rectangular sections and T-sections. The ratio (frequency of stiffened plate/frequency of unstiffened plate of equal mass) is determined by the Ritz method using a two-term solution, for a wide range of ratios of ( a/b ) and (stiffener depth/plate thickness). The frequencies obtained by the Ritz method for the symmetric mode are compared with those found from the exact solution and are found to agree closely. The results show a maximum increase in frequency for the symmetric mode of about three times, whereas the frequency of the antisymmetric mode is generally lower than that of the unstiffened plate. An increase in the symmetric mode frequency and a decrease in the antisymmetric mode frequency, makes it possible for both modes to possess equal frequencies for a particular ( a/b ) ratio and a certain size of stiffener.

The Limitations of Wide Strut Analyses for Determination of the Optimum Proportions of Panels Having Unflanged Integral Stiffeners

Determination of the cross-sectional dimensions of panels of least weight typically follows the procedure set out by D. J. Farrar in this JOURNAL 20 years ago. Farrar made the assumption that for panels of least weight the flexural and local instability stresses were coincident. Using this he investigated the Z-section stringer-skin combination and later, using the same method, E. J. Catchpole studied the panel having unflanged integral stiffeners. In both cases the panel is treated as a wide strut, i.e. the flexural buckling load was taken to be the Euler buckling load, no account being taken of the effect of edge restraint.