Buckling Of Panels Research Articles

Nonlinear thermo-mechanical behaviour of soft core sandwich panels – Creep effects

Sandwich panels can be subjected to significant changes in ambient temperature, which develop and sustain over certain time periods and lead to creep of the core material, and consequently to changes in the internal stresses and deformations with time. This paper deals with this issue with focus on the geometrically nonlinear aspects of structural behaviour. A theoretical model is developed, which combines the concepts of the principle of superposition of viscoelasticity, with the high-order sandwich theory (HSAPT), and the temperature dependency of the viscoelastic material properties. The nonlinear HSAPT formulation accounts for the deformability of the core in shear and through its thickness and it is based on large displacement kinematics of the face sheets. The convolution integral of viscoelasticity is converted into a rheological generalized Maxwell model after the expansion of the relaxation moduli into Prony series with temperature-dependence terms, which enables the solution of the governing equations through an incremental step-by-step time analysis without the need to store the response history. The capabilities of the model are demonstrated through numerical examples. It is shown that the creep of the core material can lead to bifurcation buckling of the sandwich panel under sustained temperatures that are smaller than the critical temperature obtained under an instantaneous increase of temperature.

Stress-Strain State and Buckling Problems of Structurally-Anisotropic Aircraft Panels Made of Composite Materials in View of Production Technology

The main relations of a mathematical model for analyzing the stress-strain state and buckling of structurally-anisotropic panels made of composite materials are proposed. The mathematical model of a stiffening rib being in one-side contact with the skin is refined. One takes into account the influence of panel production technology, namely, residual thermal stresses and preliminary tension of reinforcing fibers. Exact analytical solutions for boundary value problems with the resolvent eight order equation are considered. The influence of the structure parameters on the level of stresses, displacements, buckling forces for bending and torsion modes has analyzed.

Elastic buckling of a cylindrical panel with symmetrically varying mechanical properties – Analytical study

The subject of the paper is a cylindrical panel with symmetrically varying mechanical properties in the thickness direction. The nonlinear hypothesis of deformation of the straight line normal to the panel neutral surface is assumed. Based on the principle of stationary potential energy differential equations of equilibrium are obtained. The system of the equations is analytically solved and the critical loads of cylindrical panel are derived. Moreover, a simplified model of the cylindrical panel without shear effect is formulated. The results of critical loads for example structures are calculated and presented in Tables.

Evolutionary Design of Engineering Constructions

The basic information required to utilize one of possible computation tools/algorithms (mainly the evolution strategy) to solve a wide class of real practical engineering optimization problems is presented and discussed in the present paper. The effectiveness of the considered method is demonstrated by the possibility of the use of different form of objective functions, various and numerous nonlinear constraints and different types of design variables (continuous, discrete, real, integer). The sensitivity of the algorithm to the choice of the evolution strategy parameters is also discussed herein. The generality of the evolution strategy is illustrated by the analysis of various examples dealing with: the design of helical springs, the buckling of cylindrical composite panels and the buckling of pressure vessels with domed heads.

Mechanical models for local buckling of metal sandwich panels

Modern design methods for sandwich panels must attempt to maximise the potential of such systems for weight reduction, thus achieving highly optimised structural components. A successful design method for large-scale sandwich panels requires the consideration of every possible failure mode. An accurate prediction of the various failure modes is not only necessary but it should also utilise a simple approach that is suitable for practical application. To fulfil these requirements, a mechanics-based approach is proposed in this paper to assess local buckling phenomena in sandwich panels with metal cores. This approach employs a rotational spring analogy for evaluating the geometric stiffness in plated structures, which is considered with realistic assumed modes for plate buckling leading to accurate predictions of local buckling. In developing this approach for sandwich panels with metal cores, such as rectangular honeycomb cores, due account is taken of the stiffness of adjacent co-planar and orthogonal plates and its influence on local buckling. In this respect, design-oriented models are proposed for core shear buckling, intercellular buckling of the faceplates and buckling of slotted cores under compressive patch loading. Finally, the proposed design-oriented models are verified against detailed non-linear finite-element analysis, highlighting the accuracy of buckling predictions.

Experimental and numerical studies on the buckling and post-buckling behavior of single blade-stiffened CFRP panels

The aim of this study is to experimentally investigate the stability behavior and failure characteristics of carbon fibre reinforced polymer (CFRP) composite panels with secondary bonded blade stiffener under compression. Various experimental techniques like 3D-digital image correlation (DIC), acoustic emission (AE), strain gaging and infrared thermography were employed together for capturing the buckling, post-buckling response and failure characteristics of test panels. The 3D-DIC technique was employed for determining the buckling and post-buckling displacement fields of the test panel. The strain gage data was used for accurate prediction of the onset of buckling phenomenon of the test panels. Parametric data obtained from the AE technique was analysed for identifying and classifying the various damage events encountered in the test panel. In addition, finite element simulation of the CFRP stiffened panel under compression was performed to validate the experimental post-buckling results. In this work, Hashin’s failure criteria was used to study the initiation of various failure modes in the critical regions of the stiffened panel. The proposed unified experimental approach can provide more insights on the post-buckling behavior and failure characteristics of single blade stiffened CFRP panels, thereby helping engineers in designing damage tolerant composite structures.

Semi-analytical model for the prediction of the post-buckling behaviour of unstiffened cylindrically curved steel panels under uniaxial compression

Owing to its structural efficiency stiffened steel curved panels are increasingly used in structural applications in civil, naval and offshore engineering. However, design provisions to predict their strength are practically non-existent. Consequently, the aim of this paper is to present a robust semi-analytical procedure for the prediction of the post-buckling behaviour of unstiffened cylindrically curved steel panels under uniform uniaxial compression. Nonlinear stability models based on large deflection theory incorporating initial imperfections and geometric nonlinearity are implemented. The problem is solved through the Rayleigh-Ritz method and the post-buckling solutions are obtained in order to assess local buckling of isotropic panels. Two distinct simply supported boundary conditions are considered, depending on the in-plane restraints of edges. The validity of these computational models is assessed with the results of finite element analyses for different curvatures and aspect ratios, yielding good results. Finally, design-oriented closed-form analytical expressions are derived based on single degree of freedom approximations.

Buckling and postbuckling of carbon nanotube-reinforced composite cylindrical panels subjected to axial compression in thermal environments

This paper presents an analytical investigation on the buckling and postbuckling behavior of thin composite cylindrical panels reinforced by single walled carbon nanotubes (SWCNTs), exposed to thermal environments and subjected to uniform axial compression. Material properties of isotropic matrix phase and carbon nanotubes are assumed to be temperature dependent, and effective properties of carbon nanotube-reinforced composite (CNTRC) are functionally graded in the thickness direction and estimated by extended rule of mixture. Governing equations are based on the classical thin shell theory taking von Karman-Donnell nonlinearity and initial geometrical imperfection into consideration. Approximate solutions are assumed to satisfy simply supported boundary conditions and Galerkin procedure is applied to derive explicit expressions of buckling loads and load-deflection relation. Effects of volume fraction and distribution type of carbon nanotubes, geometrical parameters, elevated temperature and initial imperfection on the nonlinear stability of CNTRC cylindrical panels are analyzed and discussed. The novelty of the present study is that closed-form results of buckling load and nonlinear load-deflection relation can be readily used to analyze the buckling and postbuckling behaviors of axially loaded CNTRC cylindrical panels.

Mechanical performance of two-way modular FRP sandwich slabs

This paper presents a modular GFRP sandwich assembly for two-way slab applications. The sandwich assemblies were built-up sections made from pultruded web-core box profiles incorporated between two flat panels, connected via adhesive bonding or novel blind bolts. Two different pultrusion orientations were examined: flat panels with pultrusion directions either parallel (unidirectional orientation) or perpendicular (bidirectional orientation) to the box profiles. The effects of pultrusion orientation, shear connection and the presence of foam core materials on strength and stiffness were investigated by testing two-way slab specimens until failure. Sandwich slabs with unidirectional orientation showed premature cracking of the upper panel between fibres, whereas those with bidirectional orientation showed local out-of-plane buckling of the upper flat panel. The unidirectional slab also showed greater bending stiffness than bidirectional slabs due to the weak in-plane shear stiffness provided by the web-core profiles, which introduced partial composite action between the upper and lower flat panels of the bidirectional slab. Finite element models and analytical techniques were developed to estimate deformation, failure loads and the degree of composite action, and these showed reasonable agreement with the experimental results.

Effect of stiffener damage caused by low velocity impact on compressive buckling and failure modes of T-stiffened composite panels

Effect of stiffener damage caused by Low Velocity Impact (LVI) on compressive buckling and failure load of the three T-stiffened composite panel was studied by experiment in this paper. Stiffener damages were introduced at four impact energy levels with the impact position located on the panel side over the middle stiffener. The impact experimental results show that the impact energy inducing the initial damage of the stiffened panel is about 34 J. With the increase of impact energy, the damage of the panel is slighter than Barely Visible Impact Damage (BVID), while the stiffener damage and stiffener/panel debonding are serious. The panel dent will not be visible until the stiffener is completely fractured under a higher energy impact. Compression after Impact (CAI) experimental results show that although the initial compression stiffness of the stiffened panel is not affected by the stiffener damage, the compressive stiffness decreases with the increase of compressive load due to the damage propagation of the impacted stiffener and buckling of panel. The failure loads decrease significantly when the damage of stiffener and the stiffener/panel debonding occur as the result of LVI, with a maximum drop of 44% compared to the undamaged specimen.

Experimental and numerical study on honeycomb sandwich panels under bending and in-panel compression

Sandwich structures have been extensively employed as lightweight composite components in aerospace and shipbuilding engineering for their high capacity of stiffness, strength and energy absorption. To explore the crushing behaviors of honeycomb sandwiches, both three-point bending (TPB) and in-panel compression (IPC) tests were performed on aluminum honeycomb sandwich panels in this study. The effects of several key structural parameters on crashworthiness characteristics and collapse mechanism were first explored through the experiments here. The experimental results divulged that crashworthiness and collapse mode of sandwich structures were greatly influenced by the structural parameters under the TPB test. The crash behaviors can be also affected by both structural and adhesive parameters in the IPC test. Through validating with the experimental data, the numerical models were established to capture some deformation and failure details in the crushing processes. Taking into account the adhesive interface in the finite element (FE) model, glue debonding was simulated for the IPC loading, which is in good agreement with the experimental results at the skin panel buckling. Based on the experimental results, theoretical solutions for the TPB test were also established to predict the peak load, energy absorption and collapse mode. This study provided a new basis for the further studies on the crashworthiness optimization of sandwich structures.

Deformations of Laminated Cylindrical Panels with Circular Holes

The present work is devoted mainly to investigation of the buckling and post-buckling behavior of the composite cylindrical panels under axial load. The influence of the diameter of the hole on the buckling strength is studied with the use of finite element method.

Compressive strength of composite laminates with delamination-induced interaction of panel and sublaminate buckling modes

Compression After Impact (CAI) strength is critical to the safety and weight of carbon fibre aircraft. In this paper, the standard aerospace industry practice of using separate analyses and tests for panel buckling and CAI strength is challenged. Composite panels with a range of stacking sequences were artificially delaminated and subject to compression testing in a fixture that allowed local sublaminate and global panel buckling modes to interact. Compared to panels without delamination, interaction of buckling modes reduced panel buckling strains by up to 29%. Similarly, compared to delaminated panels restrained against panel buckling, interaction reduced delamination propagation strains by up to 49%. These results are the first to indicate that restriction of interaction during CAI testing is unconservative and therefore potentially unsafe. A novel integration of an analytical Strip model, for sublaminate buckling driven delamination propagation, and a Shanley model, for determining increased local strain due to sublaminate-buckling-induced panel curvature, is used to calculate the reduction in strength due to buckling mode interaction. Assuming a typical sublaminate post to pre-buckling stiffness ratio of 0.65, the difference in integrated model and experimental results is<11% – a level of accuracy that will allow the integrated model to drive initial design studies.

Revisiting the structural collapse of a 52.3 m composite wind turbine blade in a full‐scale bending test

AbstractFull‐scale structural tests enable an in‐depth understanding of how composite blades respond to specific applied loads. Blade strength can be validated, and necessary modifications can be made to improve structural performance and/or reduce blade weight. This study revisits the structural collapse of a 52.3 m composite blade with new research content. Specifically, the present work examines the chain of events captured in the video record of the blade collapse and provides direct phenomenological evidence of how the blade collapsed in its ultimate limit state. In addition, three‐dimensional strains are investigated by reconstructing the root transition region of the blade using solid brick elements in a finite element analysis. The strain components responsible for particular failure characteristics are identified. The structural response of the blade is investigated numerically. Interactive failure phenomena associated with strains, local buckling and material failure are examined in detail. The study shows that local buckling of the sandwich panels with unbalanced construction drives progressive failure of the composite materials and eventually leads to blade collapse owing to significant failure of the load‐carrying spar cap. Design modifications of the blade are proposed and validated with the test of a new blade. With respect to the latest DNV GL standard, this study notes a possible method to predict delamination and skin/core debonding failures. This study also recommends the use of three‐dimensional solid elements in finite element analysis, especially when the strength and failure of large blades are of concern. Copyright © 2017 John Wiley &amp; Sons, Ltd.

Buckling and Ultimate Strength Assessment of Ship Hull Layered Composite Panels

Parametric study to evaluate the influence of the sides ratio on the axial buckling and postbuckling behaviour of the layered composite plates used in ship deck structure, is presented. In the deck structure, the plates (outlined by two pairs of longitudinal and transversal stiffeners) have obviously quadrilateral shape (from triangle to quadratic shapes). The presence of the in-plane loading, occurred from the ship hull general bending, may cause buckling of layered panels. The parametric calculus was performed for various values of ratio between the minimum and maximum value of the sides. The numerical analysis on the trapezoidal plates is presented, including the graphical results for all values of loading and side ratios.

Numerical Investigation on the Effect of Thermo-mechanical Tensioning on the Residual Stresses in Thin Stiffened Panels

In shipbuilding industry, thin plates are widely used to maintain the minimum hull weight and to increase the fuel efficiency. These thin plates, when welded, are more prone to buckling distortions. So, it is very much important to predict these buckling distortions beforehand and try to mitigate them in the fabrication stage rather than doing it later. By doing this, the competitiveness in cost and time can be increased. In this study, a numerical investigation on the reduction of buckling distortions in the fabrication of orthogonal stiffened panels as used in shipbuilding was conducted. A method of in-process distortion mitigation technique, named as thermo-mechanical tensioning (TMT) was introduced to reduce the compressive residual stress in the far-field zone. The detail stress development mechanism in TMT process is discussed here. Commercially available finite element software ANSYS® 15 was used for calculations. The simulations revealed that the peak tensile stresses in the weld zone and the corresponding far-field compressive residual stresses get significantly reduced by the implementation of TMT. Thus, with reduction of compressive residual stress, buckling of such stiffened panels is effectively mitigated.

Hygrothermal effects on buckling of composite shell-experimental and FEM results

The effects of moisture and temperature on buckling of laminated composite cylindrical shell panels are investigated both numerically and experimentally. A quadratic isoparametric eight-noded shell element is used in the present analysis. First order shear deformation theory is used in the present finite element formulation for buckling analysis of shell panels subjected to hygrothermal loading. A program is developed using MATLAB for parametric study on the buckling of shell panels under hygrothermal field. Benchmark results on the critical loads of hygrothermally treated woven fiber glass/epoxy laminated composite cylindrical shell panels are obtained experimentally by using universal testing machine INSTRON 8862. The effects of curvature, lamination sequences, number of layers and aspect ratios on buckling of laminated composite cylindrical curved panels subjected to hygrothermal loading are considered. The results are presented showing the reduction in buckling load of laminated composite shells with the increase in temperature and moisture concentrations.

Buckling of uniaxially compressed composite anisogrid lattice cylindrical panel with clamped edges

An analytical solution of the buckling problem for a uniaxially compressed composite lattice cylindrical panel with the clamped edges is presented in this paper. The compressive load applied to the two opposite curved sides of the panel induces compression in the circumferential direction due to Poisson effect which is taken into account in this study. The lattice panel composed of the helical and hoop ribs is modelled as an equivalent orthotropic cylindrical panel with effective stiffness parameters. The deflection of buckled panel is described using the equations of the engineering theory of orthotropic cylindrical shells. The buckling equations are solved using the Galerkin method in which the displacements and deflection of the panel are approximated by the mode shape functions of a clamped-clamped beam. An analytical formula providing fast and reliable way of calculation of the critical buckling load is derived and applied to the analyses of the composite anisogrid panels with various parameters of lattice structures. The results are verified using a finite-element method. The mass efficiency of the lattice panels designed for a required critical load is analysed.

Robust simulation of buckled structures using reduced order modeling

Lightweight metallic structures are a mainstay in aerospace engineering. For these structures, stability, rather than strength, is often the critical limit state in design. For example, buckling of panels and stiffeners may occur during emergency high-g maneuvers, while in supersonic and hypersonic aircraft, it may be induced by thermal stresses. The longstanding solution to such challenges was to increase the sizing of the structural members, which is counter to the ever present need to minimize weight for reasons of efficiency and performance.In this work we present some recent results in the area of reduced order modeling of post- buckled thin beams. A thorough parametric study of the response of a beam to changing harmonic loading parameters, which is useful in exposing complex phenomena and exercising numerical models, is presented. Two error metrics that use but require no time stepping of a (computationally expensive) truth model are also introduced. The error metrics are applied to several interesting forcing parameter cases identified from the parametric study and are shown to yield useful information about the quality of a candidate reduced order model.Parametric studies, especially when considering forcing and structural geometry parameters, coupled environments, and uncertainties would be computationally intractable with finite element models. The goal is to make rapid simulation of complex nonlinear dynamic behavior possible for distributed systems via fast and accurate reduced order models. This ability is crucial in allowing designers to rigorously probe the robustness of their designs to account for variations in loading, structural imperfections, and other uncertainties.

Effects of variable thickness and imperfection on nonlinear buckling of sigmoid-functionally graded cylindrical panels

The use of variable thickness can help the designers and researches reduce the weight of the functionally graded (FG) panel structures. For cases where reduction of weight is of high importance, such as space structures, ocean engineering, this type of panel is the best choice. Hence, this paper analyzes the effect of the variable thickness on nonlinear buckling of imperfect cylindrical panels made of sigmoid-functionally graded material (S-FGM) under combined axial compression and external pressure. The governing equations are in nonlinear form based on the classical shell theory with the von Karman assumption. By applying Galerkin procedure and the Airy stress function, the resulting equations are solved to obtain closed form expressions for critical buckling load and load–deflection curves. In numerical results, effect of variable thickness, the volume fraction index, imperfection size, loading as well as the geometric parameters on the load–dimensionless deflection curves are discussed in details.