Instability Of Panels Research Articles

Segmental instability failures in transmission line towers

This paper presents the results of the detailed studies conducted on premature failures of transmission line towers during full-scale testing. Configuration and proportioning of base width, hamper width, the height of each segment and selection of bracing patterns play a vital role in providing geometric stability to the tower. In the present study, three towers of different voltage clauses failed during testing, investigated and found that geometric instability caused the premature failure. In the case of a 500 kV tower with a rectangular configuration, the staggered bracing pattern continuously for multiple segments for about 20 m height without a diaphragm bracing in between caused geometric instability in the tower. Nonlinear FEA results of the tower modelled with diaphragm bracing showed that tower failure can be prevented by introducing diaphragm bracing at different heights. The 400 kV double circuit dead-end type tower with a 15 m height bottom segment and 161 kV suspension towers analysed based on the conventional static analysis ignoring geometric instability failed prematurely and FE analysis clearly shows the failure due to geometric instability. It is recommended to divide the single segment into two segments such that the included angle between the leg and primary bracing member can be increased, and thereby additional moments in the leg members are reduced by making the bracing member contribute to sharing the shear. The code recommended minimum included angle of 15° between the leg and primary bracing member is only a guiding parameter for the designers. Based on this study, it is recommended that the designers shall check the tower geometry for segmental / panel instability by modelling and nonlinear FE analysis of the tower with beam elements in place of conventional space truss elements.

Minimum stiffness criterion for ring frames of stringer frame stiffened shell structures

Stringer frame stiffened shell structures have been able to establish themselves as primary structures of aerospace applications because of their high ratio of load carrying capacity to weight. Unfortunately, this advantage goes hand in hand with a high level of complexity in the design of such structures. This is due to the many design variables and the complex physical behaviour caused by the interaction of stringer, frame and shell. Despite the many research activities carried out, the behaviour of such a structure under axial compression is not fully understood yet and reliable methods for an efficient calculation are lacking. In particular, the state-of-the-art sizing of frames is still based on an empirical method established in the 1950s. Within this paper, new minimum stiffness criteria are developed for the sizing of frame stiffener of stringer frame stiffened shell structures under axial compression. A novel but not fully reliable sizing method and a novel calculation method for the calculation of the panel instability load serve as a basis. For the derivation of a criterion, two different approaches are chosen and compared to each other. One approach incorporates the frame stiffnesses locally, whereas the other on a global level. Geometrically non-linear finite element analyses are performed to verify the proposed approach. The results reveal that the local consideration of the frame stiffness does not represent the physical behaviour of the shell sufficiently, whereas the minimum stiffness criterion, which incorporates the frame stiffness on a global level, delivers excellent predictions of the minimum frame stiffness.

Parametric Instability of Functionally Graded Porous Cylindrical Panels under the Effect of Static and Time-Dependent Axial Loads

This work presents an analytical study of the parametric instability of cylindrical panels containing functionally graded porous exposed to static and dynamic periodic axial loads under simply supported boundary conditions. Based on Hamilton’s principle, the governing equation of motion by using first-order shear deformation theory (FSDT) has been obtained. By applying the Galerkin technique, an excitation frequency expression is derived, which helps identify areas of instability of functionally graded porous cylindrical panels. Numerical simulations are used to validate the analytical results. Eventually, the impacts of the porosity coefficient, porosity distribution method, static and dynamic periodic axial loads, panel angle, circumferential wave number, and cylindrical panel characteristics on the region of instability are displayed in the section of results and discussions. The findings show that when the porosity is further from the surface, the more stable the structure is. Furthermore, a small angle of the cylindrical panels gives a better dynamic response than a large angle. In addition, increased static and dynamic loads lead to an expansion of areas of instability.

Improved approach for the panel buckling calculation of stiffened shell structures with torsional stiff stringer

Primary structures of aerospace applications are often constructed as stringer frame stiffened shell structures because of their high load carrying capacity. Recent research activities on the design of such shells have shown that the design is a demanding task due to the mostly interdependent design variables. Furthermore, the calculation of panel instability is only possible with numerical simulation software demanding high computational costs. Recently, an efficient approach was developed with promising results. This work is taken up to be analysed in more detail. Study structures with differentiating stiffnesses are defined. Findings show high deviations in the prediction of panel instability for increasing axial stiffness of the shell. The reason is found to be the insufficient consideration of prebuckling deformations resulting from the reduced structural model. Improvements to the method are suggested: The reduced structural model is changed and the formerly Ritz formulation is converted into a finite element formulation. One panel of the shell is discretized by the derived one dimensional element. The influence of skin buckling on the structural behaviour is taken into account. An adapted smeared stiffener theory is used in an iterative calculation routine. Geometrically non-linear verification computations are conducted using commercial finite element simulation software. The suggested adjustments lead to a capturing of the size effect and a significant improvement of the method. Excellent results for the prediction of panel instability with reasonable error margins are delivered.

Thermoelastic stability of thin CNT-reinforced composite cylindrical panels with elastically restrained edges under nonuniform in-plane temperature distribution

In order to fill the evident lack of investigations on nonlinear response of nanocomposite curved panels under nonuniform temperature, this paper aims to analyze the nonlinear thermoelastic stability of cylindrical panels made of carbon nanotube (CNT) reinforced composite, rested on elastic foundations and subjected to sinusoidal-type in-plane temperature distribution. Reinforcement is carried out through functional rules of CNT volume fraction. An extended rule of mixture is adopted to estimate the effective properties of CNT-reinforced composite. Governing equations are derived based on classical shell theory accounting for von Kármán–Donnell nonlinearity, initial imperfection, interactive pressure from elastic foundation, and preexisting lateral pressure. In addition, the elasticity of in-plane constraints of boundary edges is included. Approximate analytical solutions are assumed to satisfy simply supported boundary conditions and Galerkin procedure is adopted to derive nonlinear closed-form relation between thermal load and deflection. Parametric studies are carried out and interesting remarks are obtained. The present study finds that, unlike case of uniform temperature rise, thermal instability of cylindrical panels under sinusoidal temperature distribution still occurs even though all edges are movable and load carrying capacity is the weakest for an intermediate value of CNT volume fraction. Under sinusoidal temperature distribution, the cylindrical panel may be deflected at the onset of loading and, for the most part, has no longer bifurcation-type buckling response. Furthermore, small values of preexisting external pressure have beneficial influences on the stability of nanocomposite cylindrical panels under nonuniform thermal loads.

Panel buckling of stiffened shell structures with torsional stiff stringer

Stringer frame stiffened shell structures are frequently used as primary structures of aerospace applications. They show a high load carrying capacity combined with a low mass. The design is complex because of three reasons: Firstly, there exists a high number of design variables making the design of such a shell very demanding using numerical methods such as the finite element method. Secondly, such a shell can exhibit different local instabilities before failing globally. And thirdly, the calculation of the panel instability load is not fully possible yet, especially when using closed and therefore torsional stiff stringer stiffener. Within this paper, a novel approach for the calculation of the panel instability load of stringer frame stiffened shell structures with torsional stiff stringer under axial compression is introduced. The novelty is expressed in the consideration of transverse shear and prebuckling deformations. It is shown that in contrast to unstiffened shell structures both aspects cannot be neglected and have a significant influence on the buckling load. The classical smearing method is expanded and used in a consecutive utilization of the Ritz method to calculate the panel instability load. Geometrically non-linear finite element analyses are performed to validate the novel approach and establish a domain of applicability. The suggested approach delivers excellent results for the prediction of the panel instability load.

Dynamic instability of curved variable angle tow composite panel under axial compression

Variable angle tow (VAT) composites have demonstrated better performance in buckling and post-buckling over straight fiber composites based on the mechanics of load redistribution from critical regions to supported edges. In this work, the dynamic instability behavior of a curved VAT composite panel subjected to periodic axial compression load is investigated. The governing energy functional of a curved symmetric VAT panel under external loading is derived using Donnell's shallow shell theory. Later, the discretized equations of motion are derived using the Rayleigh–Ritz method combined with the generalized differential integral quadrature method (GDIQM). Initially, the pre-buckling problem is solved by applying a uniform compression load to compute the stress resultant distribution which is used to evaluate the buckling load of the curved VAT panel. Subsequently, the dynamic/parametric instability region of a curved VAT panel subjected to periodic axial compression load is determined using Bolotin's first-order approximation. Then, the dynamic instability performance is evaluated for a curved VAT panel with linear fiber angle distribution and compared with straight fiber laminates. Finally, the influence of fiber angle orientation, the radius of curvature, aspect ratio and plate boundary conditions on the dynamic instability of VAT panel is presented.

Instability and vibration analyses of FG cylindrical panels under parabolic axial compressions

This paper presents the semi-analytical development of the dynamic instability behavior and the dynamic response of functionally graded (FG) cylindrical shallow shell panel subjected to different type of periodic axial compression. First, in prebuckling analysis, the stresses distribution within the panels are determined for respective loading type and these stresses are used to study the dynamic instability behavior and the dynamic response. The prebuckling stresses within the shell panel are the same as applied in-plane edge loading for the case of uniform and linearly varying loadings. However, this is not true for the case of parabolic loadings. The parabolic edge loading produces all the stresses (

Parametric instability behavior of tow steered laminated quadrilateral plates using isogeometric analysis

For the first time, the parametric instability regions of variable stiffness laminated composite quadrilateral plates subjected to uniform in-plane loadings are studied. The static as well as time-varying inplane loadings are assumed distributed throughout the whole geometry. The isogeometric analysis finite element formulation based on non-uniform rational B-splines is developed in order to address the dynamic instability of quadrilateral panels. The problem has been formulated by utilizing the principle of virtual work based on first order shear deformation plate theory. In terms of tow-steered reinforcements, the fiber orientations in every lamina is assumed to change linearly in the panel longitudinal direction. In order to demonstrate the capabilities of the developed formulation in predicting the structural parametric dynamic behavior, some representative results are obtained and compared with those available in the literature. The effects of geometry layout, loading frequency and amplitude, changes in curvilinear fiber orientations, and material orthogonality on the parametric instability regions are studied by applying Bolotin's first order approximation.

Nonstationary transversal vibrations of thermoelastic web with a constant velocity motion

We consider axial movements of elastic web performing small transversal vibrations. We take into account thermal loadings on the moving web (panel) and determine the critical temperature providing the divergence (instability) of thermoelastic panel. We perform an analysis of non-stationary vibrations of the panel. Solving dynamical problem is based on application of Galerkin’s method. As an example, we present the analytical solution to the problem of nonstationary thermoelastic panel vibrations for the case of two shape functions.

Flutter of rectangular simply supported plates at low supersonic speeds

Aeroelastic instability of skin panels, known as panel flutter, can occur in the form of coupled-mode or single-mode flutter. While the first type of flutter usually occurs in one eigenmode (composed of the first and the second natural modes in vacuum) and yields well-studied nonlinear limit cycle oscillations, the single mode flutter can occur in several simultaneously growing eigenmodes, leading to complex nonlinear panel dynamics, including different co-existing limit cycles, periodic and non-periodic higher-mode oscillations. Structural nonlinearity and linear aeroelastic growth mechanism play the major role in this dynamic.While the linear panel flutter boundaries in the two-dimensional formulation have been studied in detail, there are only few investigations of the boundaries in the three-dimensional case. Since the linear growth mechanism plays an essential role in nonlinear oscillations, its comprehensive study is an important step toward understanding of complex dynamics of skin panels in the three-dimensional case. In this paper, we investigate the flutter boundaries of rectangular panels simply supported at all edges, and use potential flow theory to calculate the unsteady pressure. The problem is considered in two formulations: a series of rectangular plates, attached to each other, and a single rectangular plate. Flutter boundaries of the first four modes are calculated, and their transformations with the change of the spanwise plate width are studied in detail.

Thermal Effects on Parametric Instability of Delaminated Woven Fabric Composite Curved Panels

The present study highlights the parametric instability characteristics of delaminated woven fabric composite curved panels under in-plane harmonic loadings exposed to the thermal environment. The equation of motion of the delaminated curved panel is reduced to a system of Mathieu–Hill equations with periodic coefficients. The development of the region of instability arises from Floquet’s theory and the solution is obtained using Bolotin’s approach by the finite element method (FEM). An eight-noded isoparametric finite element is developed considering the effects of delamination and thermal exposure of the composite panel for predicting the dynamic instability regions (DIRs). The first-order shear deformation theory (FSDT) is used for all the numerical computations. The results predicted from the present finite element analysis are validated with those available in the literature. The effects of static load factor, curvature, delamination, temperature and boundary conditions on the DIRs of curved composite panels are investigated. Noteworthy effects of these parameters on the parametric instability of composite panels are witnessed and discussed.

Non-linear effective properties for web-core steel sandwich panels in tension

All-metal sandwich panels with a low weight-to-stiffness ratio provide the means to develop cost and energy efficient large-scale thin-walled structures such as ships. However, the modeling and computational effort for a three-dimensional (3-D) sandwich structures may be significant especially in the limit state analysis of ship structures. This can become a significant drawback especially in the conceptual design stage. To this end, we determine the load–displacement curves until tensile instability for orthotropic web-core sandwich panels under multi-axial tension loading. Load–displacement curves are determined by dividing sandwich panel into discrete members and analyzing each of the constituents separately. Combined response is obtained by rule of mixtures. Tensile instability of panel is assessed using analytical necking criteria. Validity of the analytically obtained curves is established by comparing them with those obtained by a 3-D Finite Element Modeling (FEM) of the unit cell. Analyses with the unit cells show that while stiffness of the orthotropic sandwich panels is strongly direction dependent, tensile instability of panels is direction independent and governed by the faceplates. The analytical curves are then implemented to ABAQUS UGENS subroutine to describe the non-linear mechanical shell section behavior in the framework of Equivalent Single Layer (ESL) theory. The subroutine was used to simulate the response of idealized accommodation deck, with and without of a cut-out, of a passenger ship. Good agreement in response was found between 3-D FEM and ESL.

Minimum stiffness criteria for ring frame stiffeners of space launch vehicles

Frame stringer-stiffened shell structures show high load carrying capacity in conjunction with low structural mass and are for this reason frequently used as primary structures of aerospace applications. Due to the great number of design variables, deriving suitable stiffening configurations is a demanding task and needs to be realized using efficient analysis methods. The structural design of ring frame stringer-stiffened shells can be subdivided into two steps. One, the design of a shell section between two ring frames. Two, the structural design of the ring frames such that a general instability mode is avoided. For sizing stringer-stiffened shell sections, several methods were recently developed, but existing ring frame sizing methods are mainly based on empirical relations or on smeared models. These methods do not mandatorily lead to reliable designs and in some cases the lightweight design potential of stiffened shell structures can thus not be exploited. In this paper, the explicit physical behaviour of ring frame stiffeners of space launch vehicles at the onset of panel instability is described using mechanical substitute models. Ring frame stiffeners of a stiffened shell structure are sized applying existing methods and the method suggested in this paper. To verify the suggested method and to demonstrate its potential, geometrically non-linear finite element analyses are performed using detailed finite element models.

Computational Modeling of Failure Patterns of Glass Panels with Imperfections Subjected to Air Blast

Glass fragments are a prime source of injury to occupants of buildings subjected to explosive events during which window glass breaks into either flying shards (annealed glass windows) or fragments (fully tempered glass). These account for injuries ranging from minor cuts to severe wounds. A successful blast-resistant glazing design requires balancing of the safety and security of the window panels with physical appearance and cost-effectiveness. Moreover, it should consider the principles of a reasonable degree of protection against explosive threats based on the proposed level of security and previous lessons learned. In this paper, explicit finite element method (FEM) with is used for modeling the window failure and investigate the failure patterns of annealed and fully tempered glass windows panels with embedded imperfections across the panel. For this purpose, the element-removal technique is utilized in accordance with the fracture micromechanics' principles and the brittle failure criteria of displacements; strains and stresses. The results of the analysis demonstrate that the response of the conventionally-framed window panels to blast loading cases depends upon the glazing technologies; blast load intensities; the glass types; and the location of imperfections. Through the application of element removal technique and stress redistributions at each infinitesimal time increment, the results of this paper further demonstrates that the existence of glass imperfections in the window panels will make them more vulnerable against the air blast overpressures for both annealed and fully-tempered glass panel cases: For fully tempered glass panels, the vulnerability arises from greater stress concentrations at the location of glass defects as well as higher brittleness of the panel itself when compared to the annealed glass panels. The results of this study show that the existence of defects along the edges will help in redistribution of the stresses in a way that the yield lines will pass through these imperfection locations. The general failure pattern for defective annealed glass panels subjected to small intensity air blast will be very similar to the failure pattern of homogeneous window panels yet with a faster pace. However, when subjected to a higher intensity air blast, the severity of the load will cause excessive rotation angles in the panel and subsequent computational divergence and instability. The panel failure will occur much faster and with different patterns compared to the case of annealed glass panels subjected to smaller intensity air blasts. KeywordsGlass; Air Blast; Safety; Window Panels; Fracture Mechanics; Crack Propagation

Parametric instability analysis of laminated composite curved shells subjected to non-uniform in-plane load

The parametric instability regions of laminated composite plate and cylindrical shells subjected to non-uniform in-plane axial end-loadings are studied. The static as well as varying parts of the end-loading assumed to vary according to parabolic distribution in the width of the panel. The dynamic instability of panels has been investigated by using a developed finite strip method (FSM). The problem has been formulated on the basis of principle of virtual work. The effects of loading distribution as well as boundary conditions and static loading on the instability regions of load frequency are studied by applying Bolotin’s first order approximation. In order to demonstrate the capabilities of the developed formulations and methods in predicting the structural parametric dynamic behavior, some representative results are obtained and compared with those in the literature wherever available.

Flutter Analysis of Viscoelastic Panels in Supersonic Flow

In this paper, dynamic instability behavior of a linear viscoelastic panel in supersonic flow is investigated. The quasi-steady piston theory of supersonic flow is employed for the aerodynamic pressure. The partial differential governing equation of isotropic flat panel is derived by introducing viscoelastic structural damping based on Kelvins model. The panel governing equation is transformed into a set of ordinary differential equations via the Galerkin approach. First-order state equations are afterwards obtained and solved by means of a standard eigenvalue calculation. The dynamic instability of viscoelstic panels is predicted by the feature of characteristic roots. The phenomena of coupled-mode flutter without structural damping and single-mode flutter with structural damping induced by the supersonic flow are observed for the different dynamic pressure values. Results indicate that structural damping plays an important role for the stability of panels flutter. Flutter threshold keeps decreasing as viscoelastic structural damping is increased.

Finite element buckling analysis of laminated composite sandwich panels with transversely flexible core carrying attached elastic strip

In this article, a three-dimensional finite element model is proposed to study the effect of distributed attached mass with thickness and stiffness on the buckling instability of sandwich panels with transversely flexible cores. Unlike the previous works in the literature which have made use of unified displacement theories, the present model uses different types of finite elements to model the core and the face sheets. It utilizes shell elements for the face sheets and three-dimensional solid elements for the core which enables the model to account for the transverse flexibility of the structure. The motions of the face sheets and the core as well as the attached mass are related through defining constraint equations between the nodes of their respective finite elements based on the concept of master and slave nodes which is incorporated into the finite element analysis program ANSYS through a user-defined subroutine. The validated finite element model is then used to study the effects of size, thickness, material property, aspect ratio, and the position of the attached mass on the buckling load of a sandwich panel under different combinations of boundary conditions. The results presented in this study have hitherto not been reported in the literature.

DIMENSIONING OF ORTHOTROPICALLY STIFFENED CFRP SHELLS OF LARGE LAUNCH VEHICLES FOR LOAD INTRODUCTION AND STABILITY

The dimensioning of an orthotropically stiffened cylindrical CFRP shell subjected to the introduction of concentrated axial loads using rapid analytical methods is presented. For stress calculation the shell equations are simplified by applying the semibending theory and integrated by employing the transfer matrix method. Analytical approaches are used for stability verification. The dimensioning considers required constraints in the force flux distribution, strength of the laminate, general instability, panel instability (from ring frame to ring frame) and local instability. The rapid analytical methods allow mass optimization. The final design is confirmed by detailed FE analysis. A comparison of the FE analysis with the analytical results is shown.

Possible ‘panel instability’ in composite deck floor systems under fire

This paper describes a possible ‘panel instability’ in composite deck floor slabs under fire conditions. The phenomenon is characterised by a rapid increase in deflection of the whole composite floor system (steel beams and concrete deck) forming part of a continuous floor in a compartment fire. This is accompanied by a sudden loss in the thermally induced axial compression in a primary steel beam. The instability occurs when the moment capacity at the end of the composite section (comprising the profiled deck slab and the primary beam) is achieved, and the connection at the column changes from moment resisting (because of the composite action) to pinned. The end moment is the sum of, moment due to imposed load (constant); moment due to increasing gradient over the composite (increasing with temperature); and moment from the increased loading caused by expanding and bowing secondary beams pushing down on the primary beam (increasing with temperature). The moment resisting connections at the ends of the primary beam prevent secondary beam(s) from reaching their natural thermally displaced shape (determined by the temperature distribution in the composite secondary beam–slab section). When the moment capacity at the composite primary beam–column connection is reached, the secondary beams are instantly free to deflect. To the authors’ knowledge, this phenomenon has not been reported in other previous studies. Also the authors’ discovery of this phenomenon is entirely based on computational modelling without any experimental evidence, and much further work is required to ascertain that it would indeed occur under normal fires, loading and restraint conditions.