Buckling Of Stiffeners Research Articles

Experimental and Numerical Prediction of Collapse of Flatbar Stiffeners in Aluminum Panels

Flatbar stiffeners are attractive in stiffened plates from a fabrication point of view. Flatbars are susceptible to torsional buckling and collapse. Current approaches to assess torsional buckling strength are uncertain. For instance, formulations for torsional buckling of stiffeners in steel panels are still debated. Compared to steel structures, the strength of aluminum structures is influenced not only by the residual stresses and initial imperfections, but also reductions in mechanical properties in heat-affected zones (HAZ). In the present paper, an experimental and numerical investigation of the torsional buckling strength of longitudinal stiffeners in aluminum (aluminum alloy 5083-H116 and 6082-T6) panels subjected to axial compression is conducted. The experimental results are presented and compared with numerical predictions by using finite element method code ABAQUS, considering the influence of the HAZ and actual initial deflections. The effect of the HAZ on the torsional buckling strength of t...

Experiments on interactive buckling in optimized stiffened panels

Five aluminium blade stiffened panels of three different geometries were tested in compression in a displacement controlled loading apparatus. Panel designs were achieved using VICONOPT, a fast-running optimization package based on linear eigenvalue buckling theory, and embrace two different design philosophies. The panels were loaded beyond initial buckling to collapse, and the effects of initial overall imperfections were monitored. In all cases the final failure showed evidence of significant interaction between buckling modes. The tests draw particular attention to a violently unstable and unpredictable form of failure, involving a combination of overall and stiffener buckling, which can occur even when initial buckling in the skin has the effect of pushing the panel in the opposite sense.

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)).

Development of Generalised Boundary Conditions for the Buckling of Composite Panel

This paper gives details of theoretical investigations into the buckling behaviour of uniformly compressed rectangular composite panel with the two unloaded edges elastically restrained. The theoretical elastic buckling analysis employs a semi-numerical approach, the finite strip method. This general method of approach is to postulate a fifth degree polynomial function which describe the buckled form of the panel. Based on the principle of minimum potential energy, the strain energies of the restraining medium along the unloaded edges are evaluated in term of matrix form. This elastic restraint stiffness matrix can be added directly onto the existing stiffness matrix. To utilize the Rayleigh-Ritz method, coefficients in the deflection series are evaluated. Hence the elastic buckling stiffness of the composite panel are obtained.

ISUM Rectangular Plate Element with New Lateral Shape Functions (2nd Report)

An ISUM rectangular plate element with new shape functions for its lateral deflection under longitudinal/transverse thrust has been developed in the 1st Report. In this report, the ISUM plate element is combined with beam-column elements to model stiffened plates, and its applicability is extended to biaxial thrust.The fundamental collapse behaviour of stiffened plates is investigated by FEM analyses. The ISUM approach is formulated considering the collapse characteristics. A new modelling technique to evaluate overall buckling of stiffeners with attached plating as well as local plate buckling is proposed. Results for longitudinal and biaxial thrust show the applicability and accuracy of this approach.

Postbuckled behavior of composite isogrid stiffened shell structure

This paper investigated reliability of a postbuckled composite isogrid stiffened shell structure under a compression load. The outside diameter of the isogrid cylinder was 624.8 mm, the length was 368.3 mm and the total weight of the cylinder was 3.24 kg. A finite element buckling analysis result was compared with the axial compression experimental data. The average critical buckling load of 186.56 kN was obtained by using the Patran finite element analysis (FEA). The isogrid shell was modeled using 3-node triangular elements and the stiffeners were modeled using 4-node quad elements with a total of 504 nodes and 900 elements. The postbuckled isogrid cylinder was compression tested to the failure load of 177.35 kN. The postbuckled cylinder continued to resist compression loading even after one or more stiffeners had fractured. The testing evaluation revealed that the stiffener buckling was the critical failure mode and it has been demonstrated to be tolerant to structural damage due to the multiplicity of load paths. The lower experimental bucking load was due to the small imperfections in the cylinder but this problem can be overcome by advancement in the manufacturing methods.

Response of stiffened and unstiffened plates subjected to blast loading

This paper describes the results of dynamic analyses carried out on both stiffened and unstiffened panels using both simplified and advanced analytical techniques. For unstiffened panels with in-plane restraint along their edges, the dynamic response of an imperfect panel was predicted using a large displacement elastic analysis based on Lagrange's equation, with the panel being treated as a shallow shell. For stiffened panels, the finite element (FE) technique was used to establish the validity of using the simplified technique to predict the inter-stiffener panel displacements for a simply supported panel. A parametric study has been carried out to analyse the effects of in-plane boundary conditions, local stiffener buckling and initial imperfections on the overall response. The significant effect of boundary conditions is demonstrated by including the actual boundary conditions of a test frame in the finite element modelling of a large-scale stiffened floorplate panel used in an experimental test series.

Local Buckling of Stiffeners in Ship Plating

The aim of the present study is to analytically investigate the characteristics of local buckling of the stiffener web in the stiffened panels under uniaxial compressive loads. A plate-stiffener combination model is used as representative of the stiffened panel. The elastic buckling condition for the stiffener web is analytically derived by solving the characteristic value problem involving the governing differential equation under the corresponding loading and boundary conditions. A series of analyses of stiffener web buckling strength for varying proportions of plating and web/flange is carried out. Based on the computed results, a basic investigation of stiffener web buckling is made. Closed-form approximate expressions for predicting the buckling strength of the stiffener web are derived taking into account the influence of rotational restraints at the plate-stiffener web connection and stiffener web-flange intersections. Design considerations for potentially preventing buckling of the stiffener web are then discussed. The computed basic results for the stiffener web buckling coefficient are documented.

Simultaneous cost and weight minimization of composite-stiffened panels under compression and shear

An approach is presented to determine the part configuration that minimizes the cost and weight of composite-stiffened panels under combined compression and shear loads. The stiffened panel is designed so that no overall, bay, or stiffener buckling occurs under the applied loads. Skin and stiffener material failure conditions and manufacturing constraints are also imposed. The stiffened panel cost and weight are minimized for a variety of stiffener cross-sectional shapes. A set of near-optimum (in a Pareto sense) configurations is determined. The final optimum configuration is selected from this set by minimizing a weight and cost penalty function.

Inelastic analysis of panel collapse by stiffener buckling

A previous paper [1] proposed an elastic tripping model using a Rayleigh-Ritz approach with 4 d.f. This paper extends the elastic model into the inelastic range, using deformation theory and an iterative and incremental formulation. Nonetheless, because of the efficiency of the Rayleigh-Ritz formulation, the solution is very rapid, even for ordinary PCs. The method can be used for analyzing the flexural-torsional and lateral-torsional buckling (“tripping”) behavior of flanged stiffeners subjected to axial compression, end moment, uniform lateral pressure and any combination of these. The effects of cross-sectional distortion, postbuckling behavior of the plate (incorporated by considering the plate effective width) and plasticity are included. Results obtained using the method are shown to be in good agreement with experimental results, and to be more accurate than other methods.

Behaviour of axially loaded lipped channel

Thin plates have a stable post buckling behaviour so that its failure load is materially higher than its buckling load. This characteristics makes thin plates very suitable structural elements in lighweight structures. For a thin-walled channel which consists of a system of connected thin plates, the structure will develop local, torsional, flexural buckling or a combination of these modes under axially compressive loads. Either buckle of an individual plate component or buckle as a system of connected plates may cause a reduction in the stiffness of the section. Hence, a lower load carrying capacity is expected. In this paper, the finite strip method is employed to investigate the buckling behaviour of axially loaded lipped channels. In the formulation, by modifying the displacement function, the buckling solution of other end support conditions besides the simply supported case is obtained. Furthermore, utilizing the eigenvectors from the elastic buckling solution, the lower bound method is used to evaluate the initial post buckling stiffness of an adequately edged stiffened thin-walled channel.

Wind‐Buckling Approach for RC Cooling Towers

The equations of the bending and stability theories for the orthotropic shell are solved using the finite element method (FEM). A biaxial material law for concrete and a nearly bilinear stress‐strain diagram for reinforcing steel were considered. Taking a layered ring element the influence of bending moments together with the membrane forces can be followed under increasing load up to the failure of concrete or steel. At each level the buckling factor can be calculated considering the stress dependent orthotropic buckling stiffness. The method of calculation developed is applied to two large cooling tower shells, one under wind load according to German code DIN 1055 and the other one under unusually high wind pressures, as those considered in the U.S.A. According to the wall thickness taken the buckling load factor drops to half or less of the value obtained assuming a linear elastic behavior. This high reduction is mainly due to orthotropy and the descending tangent modulus near the ultimate load.

Ultimate Strength Analysis of Double Bottom Structure by “Idealized Structural Unit Method”

In a previous paper, two of the authors have developed an effective method for the ultimate strength analysis of large size structures. The method is named as “Idealized Structural Unit Method”.In the method, a large size element with idealized nonlinear character was necessary and an example element, “Girder Element”, was developed. In this paper, this method is applied to double bottom structures. The state of two-dimensional stress in the tank top and the bottom shell plating is considered. Conditions for buckling of these plates are established and its post buckling stiffness is determined. The condition for their ultimate strength and stiffness at the ultimate strength are determined in connection with the girder element.An example structure is analysed and the results of the analysis are presented.

Design of an aircraft utilizing fiberglass reinforced plastic primary structure.

A description is presented of the salient structural features and technical approach employed in the design of a high-performance light aircraft stressed to 8 g limit loads. This design exercise is analytical in scope only and is intended to show the feasibility of constructing primary airframe structures from fibrous composite materials. The results of minimum weight analyses of both fluted core and honeycomb core sandwich panels are presented, and their use in the selection of final sandwich geometry is detailed. Curves are presented showing the variation in elastic properties with changes in fiber orientation angle for typical basic laminate patterns employed in the air-frame components. The tradeoff in fiber orientation angle to obtain the best balance between transverse buckling stiffness and longitudinal stretching stiffness is discussed, together with expected strength performance of the oriented fiber laminates under static and dynamic loadings.

Structural synthesis capability for integrally stiffened waffle plates

Structural synthesis has been denned as the rational directed evolution of a structural configuration, which in terms of a denned criterion, efficiently performs a set of specified functional purposes. An automated, minimum weight, optimum design capability for rectangular, simply supported waffle plates subjected to a multiplicity of inplane load conditions is presented. The synthesis involves six design parameters (total depth, back-up sheet thickness, stiffener thickness in the x and y directions, and stiffener spacing in the x and y directions). The behavior constraints are provided primarily by elastic stability failure modes. In particular, gross instability of the waffle plate, buckling of the back up sheet panel, and stiffener buckling are prevented in each of several load conditions while seeking a minimum weight design configuration. Side constraints in the form of upper and lower bounds on the design parameters due to external considerations (such as space limits and manufacturing capabilities) are provided. The mathematical programming problem to which this structural synthesis problem leads has the following characteristics: 1) relative minima; 2) nonlinear inequality constraints; 3) a multitude of side constraints; and 4) nonlinear merit function. Numerical results for several symmetric as well as unsymmetrical waffle-plate optimum designs are presented. The results of the waffle-plate synthesis study support the contention that structural synthesis capabilities for complex structural configurations of current and future importance are feasible. Amn a b bx by Ca DI Z>2