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Thin-walled cylindrical shells under axial compression load are prone to buckling. The influencing factors leading to a reduction of the buckling load are a major design challenge. The sensitivity to imperfection increases with rising slenderness. In literature, cylinders with the same parameters and different slenderness are rarely tested in a larger number of samples. In this contribution, seven cylindrical shells, six of them nominally identical, are tested on two different test rigs and compared with twelve specimens with a smaller radius and same wall thickness from a previous series of tests. It is shown how the imperfection sensitivity is dependent on the R/t-ratio. Additionally, it is demonstrated how the quality of the test set ups corresponds with the achieved buckling load. Finally, the suitability of selected design approaches is determined based on the test results. Based on that, recommendations for the choice of a suitable approach are given. [ABSTRACT FROM AUTHOR]

• Single-stringer specimens are manufactured with a Double-Double stacking sequence. • Tapered specimens are manufactured using the card-sliding technique. • Specimens undergo compression loading, inducing skin buckling, and collapse. • Tapered specimens show evidence to enhance resistance to skin-stringer separation. This paper presents the work on six single-stringer specimens manufactured using the card-sliding technique with non-crimp fabrics and adopting a Double-Double (DD) stacking sequence. These specimens, representative of sub-structure level components, are used to investigate post-buckling and failure in aerospace structures. Two specimens maintain a constant thickness cross-section, while four are tapered, two of which incorporate a Teflon insert in the stringer flange. All specimens are tested under compression loading conditions, inducing skin buckling, skin-stringer separation, and eventual collapse. Numerical simulations are validated by experimental results and serve to analyze the specimens behavior and the failure mode. The load versus displacement curves of both experimental tests and Finite Element Method (FEM) analyses are compared, along with the out-of-plane displacement field. Subsequently, the observed failure modes are discussed, focusing on the various mechanisms that occurred and considering the impact of flanges and stiffener tapering. Both the FEM simulations and experimental tests demonstrate good agreement, with the flanges tapering revealing notable results. This offers promising evidence of a viable solution to optimize aeronautical structures and enhance resistance to skin-stringer separation. [ABSTRACT FROM AUTHOR]

The buckling mode of helicoidal composite panel are non-axisymmetric, resulting its different capability to resist loads in different orientation and the irregular buckling mode after curvilinearly stiffened. A method was proposed to design asymmetric curved stiffeners considering the local displacement gradient of the buckling mode shape. The displacement gradient depends on the bending stiffness and yields a better optimization. The basic unit of the stiffener family includes two stiffeners that pass through the midpoint of the panel; the remainder can be formed from this unit via translation. A simply supported curved grid-stiffened panel using uniaxial compression or shear loads under multiple load cases was addressed, and an integrated design framework was developed to obtain the designs. The curved grid-stiffened helicoidal composite panel yields a weight reduction of up to 13.26% compared to angle-grid designs under uniaxial compression and 11.68% for shear loads in multiple load cases. [ABSTRACT FROM AUTHOR]

Abstract This paper deals with the buckling behavior of corrugated thin plates made of multilayer functionally graded (FG) graphene nanoplatelets (GPLs) reinforced nanocomposites (FG-GPLRC) within the framework of classical plate theory. The GPLs are uniformly dispersed in each individual layer with its weight fraction following a layer-wise variation along the thickness direction. The effective Young modulus of each layer is determined by the modified Halpin-Tsai model while the Poisson's ratio is predicted based on the rule of mixture. It is assumed that the plate is subjected to either compression or shear or both on the edge. Analytical critical buckling solutions are obtained for both unilateral buckling when the plate is resting on a rigid foundation and bilateral buckling without the constraint of the foundation. A parametric study is conducted to investigate the influences of distribution pattern, geometry, size, and weight fraction of GPL nanofillers as well as the corrugated profile and rigid foundation on the buckling performance of the plate. It is found that the buckling resistance of the corrugated plate can be effectively enhanced by adding a small amount of GPLs into the matrix according to FGX distribution pattern and when the inclination angle is 45 degrees. [ABSTRACT FROM AUTHOR]

Abstract In the present paper, a methodology for determination of an approximate value of the lowest buckling load of the thin-walled column under compression and with an arbitrary cross-section, affected by initial imperfections, whose amplitude does not exceed half the thickness of the wall, using a load-axial shortening plot, is presented. It has been shown that the load corresponding to an alternation in rigidity of the real structure on the load-axial shortening plot determines the buckling load with high accuracy. The attained results have been compared to the values corresponding to the bifurcation load and the lowest buckling loads determined with commonly used methods based on post-buckling equilibrium paths (i.e., P-w method, P-w 2 method, inflection point method). The formulated problem of nonlinear buckling has been solved with the analytical-numerical method and the FEM. An influence of the imperfection amplitude on an approximate value of the lowest buckling load of laminated thin-walled structures has been analysed on the determined post-buckling equilibrium paths and the load-axial shortening plot. Non-symmetric configurations of laminate layers that additionally exhibit various types of the membrane and bending state coupling have been selected. Detailed computations have been conducted for short angle sections (i.e. angle columns) under uniform compression. [ABSTRACT FROM AUTHOR]

Staggered structure, where mineral crystals are arranged in a staggered manner in protein matrix, is the most representative microstructure in biological composites. Because of the elongated geometry and large aspect ratio of mineral crystals, their failure mechanism under compressive loading is predominantly controlled by buckling. The microstructural complexity, diversity of the constituent materials, and the complexity of buckling behaviors present substantial challenges for the precise forecasting of the buckling behavior of biological materials. In this paper, a novel method combining finite element analysis with machine learning is proposed. Specifically, based on the large dataset obtained using the finite element method, the buckling strength of biological staggered composites was rapidly predicted using a machine learning algorithm. Herein, the effects of microstructure and component materials on buckling behavior have been investigated systematically. The results indicate that the neural network models are highly accurate in predicting critical buckling strength. Aspect ratio and modulus ratio significantly affect the critical buckling strength of staggered structures according to the results of feature importance analysis. Additionally, the post-buckling modes of staggered structures exhibit heightened sensitivity to initial geometric defects, particularly in higher-order buckling modes. Our research provides valuable insights into fast and accurate prediction of the buckling behavior of biological composites and their design. [ABSTRACT FROM AUTHOR]

Composite cylindrical shells are widely used in space launch systems due to their high load-carrying capability and for being lightweight. However, these structures are prone to buckling phenomena at much lower loads than classical predictions for perfect cylinders. This work aims to develop data-driven empirical expressions to calculate the upper and lower bound values of cylindrical shells under linear compression loads with various boundary conditions together with various levels of bend/twist anisotropy. The inclusion of bend/twist coupling effects is a major development. To do so, the critical buckling load for laminated thin-walled cylindrical shells on elastic foundations with low, medium and high levels of bend/twist anisotropy were investigated. Then, an analysis-driven design approach is proposed to estimate the upper and lower bounds of buckling loads for axial, radial and tangential elastic foundations. Subsequently, parametric studies were performed with various combinations of bend/twist anisotropy and laminate thicknesses using Abaqus finite element models, and a comparison was made with the proposed data-driven empirical buckling load expressions. Finally, results show that the detrimental effect of boundary conditions and inherent bend/twist anisotropy could lead to a 61% reduction in buckling load, providing a need for detailed studies in this area. [ABSTRACT FROM AUTHOR]

Nonlinear and post-buckling behaviors of internally cracked functionally graded plates subjected to uniaxial compressive loading have been presented in this paper. A general nonlinear mathematical model for cracked functionally graded plates has been developed based on the first order shear deformation theory within the framework of von-Karman nonlinearity. To approximate the primary variables, Legendre polynomials are used in the current research. The crack is modelled by decomposing the entire domain of the plate into several sub-plates and therefore, a plate decomposition technique is applied. In this study, the penalty technique is used to enforce interface continuity between the sub-plates. The integrals of the potential energy are numerically computed by Gauss-Lobatto quadrature formulas to get adequate accuracy. Finally, the obtained non-linear system of equations is solved by the well-known Newton-Raphson technique. Results are presented to show the influence of crack length, various locations of crack, crack direction, boundary conditions and volume fraction index in nonlinear behavior of functionally graded plates. [ABSTRACT FROM AUTHOR]

Due to the non-uniform in-plane stress distribution, variable-stiffness panel with curvilinear fiber paths is a promising structural concept for cutout reinforcement of composite structures under axial compression, due to the more diverse tailorability opportunities than simply choosing the best straight stacking sequence. However, traditional representation methods of curvilinear fiber path are usually not flexible for cutout reinforcement. In this study, the flow field function containing a uniform field and several vortex fields is utilized to represent the fiber path due to its inherent non-intersect and orthotropic features, and a bi-level optimization framework of variable-stiffness panels considering manufacturing constraints is then proposed. A typical rectangular composite panel with multiple cutouts is established to demonstrate the advantage of proposed framework by comparison with other fiber path functions. Results indicate that the flow fiber path only needs few variables to finely represent the fiber path, which can provide satisfying and manufacturable fiber paths by combination use of curvature constraint. [ABSTRACT FROM AUTHOR]

Influence of axial compression load on buckling and free vibration characteristics of natural fiber fabric polymer composite beam is analyzed experimentally. Critical buckling strength, free vibration frequencies and modal loss factors are obtained and analyzed. It is found that buckling strength increases with number of layers of fabric in composite. It is also observed that weaving pattern of the fabric influences buckling strength of the composite and basket type woven fabric enhances the buckling strength compared to plain and herringbone woven fabric composites. Sandwich composites with glass fiber fabric facing layer and natural fiber fabric as core layer having higher buckling strength. Free vibration frequency reduces with increase in axial compression load while modal damping factor increases in the pre-buckling region. However, this behavior reverses in the post-buckling region. The load-deflection obtained experimentally is compared with finite element result obtained considering the geometric non-linearity. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

• A criterion for simulation of delamination is proposed. • An imperfection induced pre-buckling must be incorporated into failure analysis of open-hole laminate under in-plane compression. • Rules for selection of a scale factor for the pre-buckling analysis are set forth. • Various failures of notched laminate under compression are predicted with no parameter adjustment and no iteration. Failure prediction of open-hole laminates under compression still remains a great challenge. A number of unique mechanics theories for composites developed by the author are successfully applied to analyze in plane compression induced various failures of the notched laminates in this paper. A buckling mode must be incorporated into the analysis of the compression induced delamination, and the rules for selecting a scale factor for the buckling analysis through ABAQUS are established. To simulate delamination, the interlaminar matrix stress modification method is applied. A more pertinent criterion for delamination is proposed. When and where is delamination initiated, how can the initiated delamination be propagated and how much is the delaminated area to be attained can be easily reproduced. Intralaminar failures are estimated based on Bridging Model and the matrix true stress theory. The ultimate strength of a notched laminate is assumed when any primary layer element outside neighborhoods of the stress singularity and weak singularity points firstly attains an ultimate failure. A limited, if not the minimum, number of inputs are required all measurable independently and following existing standards with no data calibration. Except for the pre-buckling analysis, no iteration is needed for prediction of all the other failures. The predicted failure modes and ultimate compressive loads of several laminates with single or double holes agree well with our measured counterparts. [ABSTRACT FROM AUTHOR]

Sandwich structures are often used in space and aviation industry as energy absorption elements due to their load carrying capacity and light weight features. In experiments, it has been found that sandwich hemispherical structures have two different deformation modes referred as dimpling and flat mode under axial compression load. Deformation modes exercise a great influence on load carrying capacity of sandwich hemispherical structure. In this paper, theoretical models for two deformation modes of sandwich hemispherical structures under axial compression have been proposed. The reason for two different deformation modes observed in the compression tests has been explained. A finite element model has been set up and validated by the experimental results. Based on the numerical simulation results, buckling behaviors, load carrying capacities and displacements of top points of two different deformation modes have been compared. It is found that the load carrying capacity of the sandwich hemispherical structure under dimpling mode is about half of that under flat mode with very similar configurations. The deformation mode can be changed from dimpling to flat by adjusting the thicknesses of the out and inner metal sheets. This is a feasible and efficient way to improve the load carrying performance of the sandwich hemispherical structure. The optimal thickness ratio range of out and inner metal sheets are proposed. The methods can help improve the design of sandwich hemispherical structures to obtain better load carrying capacity with reasonable configuration. [ABSTRACT FROM AUTHOR]

• Constructal Design is effective to improve the perforated composite plate's mechanical behavior. • The best mechanical behavior of cross-ply lamination includes angles of 45°. • The maximum buckling load for each volume fraction occurs when the elliptical geometry is longer on y-axis. Thin plates when subjected to compressive loads can present a structural instability phenomenon known as buckling, causing displacements out of the plane of the plate. In addition, it is known that the use of composite materials in naval engineering can bring many benefits in the medium and long term, like the major corrosion resistance, when compared with steel structures. Moreover, for specific applications perforated plates are necessary, like passage of cables and pipes, inspection windows, among others. Therefore, to find the optimal geometry of a composite plate with a centered elliptical hole the Constructal Design (CD) was applied in association with the Exhaustive Search (ES) technique and Finite Element Method (FEM). The CD allows the evaluation of the geometry that provides the optimal distribution of imperfections, leading to the maximum value of the performance parameter used for the analysis of solids mechanics problems. Applying different laminations, it was observed an increase in the critical buckling load for a composite plate without perforations of up to 10.47%. In its turn, despite suffering a reduction in the critical load value if compared to the plate without holes, an improvement of 16.89% was observed when optimal and worst geometries for the perforated plates are compared. [ABSTRACT FROM AUTHOR]

This paper presents a method for the determination of the buckling loads of symmetrically laminated composite plates under uniaxial compressive load with explicit consideration of bending–twisting-coupling (BTC). The plates under consideration are assumed to be thin and balanced with a symmetric stacking sequence and consist of layers with ply orientations of {0°/±45°/90°}, but otherwise arbitrary lamination schemes. The characteristic laminate quantities are described in a non-dimensional notation in order to capture all combinations of material and stacking sequences that are physically possible. Plates with rectangular planforms in the framework of Classical Laminate Theory (CLT) under several different sets of boundary conditions are considered, and the buckling problem of such composite laminated plates is solved in an approximate manner by using the classical Rayleigh–Ritz method. Several combinations of the boundary conditions ‘simply supported’ and ‘clamped’ are analyzed, and the obtained results are compared with finite-element simulations for verification purposes. Based on the computed data, two different design equations for sufficiently long plates are developed which allow for a rapid and closed-form analytical assessment of the buckling behavior of symmetrically layered composite plates under explicit consideration of bending–twisting coupling. It is found that the closed-form analytical analysis equations are simple in their application and yet still work with very satisfying accuracy which makes them very suitable for use in practical engineering work. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, static and dynamic buckling of an FGM beam subjected to uniform temperature rise loading and uniform compression are studied. Material properties of the beam are assumed to be graded across the thickness. Each thermo-mechanical property of the beam is assumed to be temperature dependent. Initial imperfection of the beam is also taken into account. The beam is resting over a three-parameter elastic foundation with hardening/softening cubic nonlinearity which acts in tension as well as in compression. Nonlinear governing equations are obtained based on the static version of virtual displacements and are solved via the multi-term Galerkin method. Dynamic buckling load levels are estimated based on the well-known Hoff-Simitses criterion. Results reveal that for sufficiently stiff softening elastic foundation, post-buckling equilibrium path becomes unstable. Furthermore, when the thermal post-buckling equilibrium path is stable, no dynamic buckling occurs according to this criterion. [Copyright &y& Elsevier]

Abstract The ability to steer carbon fibre tapes, varying the tow angle, can widen the designs possibilities of cylindrical shells that are one of the main components of aerospace structures. This research presents experimental and numerical investigation of two carbon fibre reinforced plastic cylindrical shells – a cylinder with conventional layup made of unidirectional prepreg and a variable-stiffness cylinder manufactured by applying fibre placement technology. The shells were tested in compression until buckling and later subjected to a vibration analysis. Load-shortening curves and buckling shapes were acquired during the compression tests, while the natural frequencies and the mode shapes were measured during the vibration tests. Both tests provide a useful data set of the mechanical response of the cylinders which can be applied for further validation of models. The acquired experimental results were compared to a simple, approximated numerical model of the variable-stiffness cylinder showing good correlation with the test results. [ABSTRACT FROM AUTHOR]

Abstract: Solution of the buckling problem for a uniformly compressed rectangular composite sandwich plate having two parallel edges simply supported, one edge clamped and the remaining edge free (the SSCF sandwich plate) is presented in the paper. A variational buckling equation is derived based on the Lagrange principle and first-order shear deformation theory (FSDT). The Kantorovich procedure is applied to reduce the original equation to a one-dimensional form. Subsequent application of the generalised Galerkin method leads to an analytical formula for the critical load which is verified by using finite-element analysis. Efficiency of the analytical formula derived is demonstrated for design cases in which constraints are imposed on the value of critical load. [Copyright &y& Elsevier]

Abstract: A geometrically nonlinear finite element model of a composite curved beam is presented, accounting for moderately large rotations of the cross-sections, moderately large shear strains, small axial strains, and different elastic response of the material in tension and compression (bimodular behavior). A path following procedure in displacement control is employed to compute the stability points and the post-buckling response of the given model. Several comparisons are established with different numerical approaches available in the literature, showing the accuracy of the proposed finite element scheme in the unimodular case. Some original results on the in-plane and out-of-plane buckling of bimodular arches highlight that the post-buckling response of such structures is strongly influenced by the ratios between tensile and compressive moduli. [Copyright &y& Elsevier]

• The functionalized MWCNTs/HDPE based functionally graded nanocomposites are fabricated using 3D printing. • The micrographs of 3D printed FGNC samples reveal the seamless bonding between each layer of different compositions. • The highest P cr is noted for H5 and FGNC-2 among the 3D printed NC and FGNC samples, respectively. • The natural frequency of the NCs and FGNCs increases with increased MWCNTs % while decreases with increasing compressive load. • The numerical and experimental results are noted to be in good agreement. The experimental and numerical investigations are carried out for buckling and vibration of 3D printed functionalized MWCNTs/HDPE based nanocomposite (NC) and their functionally graded nanocomposite (FGNC) variants. P cr (critical buckling load) is computed through MBC (modified budiansky criteria) and DTM (double tangent method) techniques. It is observed that P cr of the 3D printed NCs and FGNCs increases with the functionalized MWCNTs content. The P cr values for the NCs (H0.5-H5) computed using DTM and MBC increased in the range of 16–79%, while for FGNC-1 (H0.5-H1-H3) and FGNC-2 (H1-H3-H5), the P cr increased from 54 to 91% compared to HDPE. Further, it is observed that the natural frequency of the NCs and FGNCs increases with the functionalized MWCNTs loading while decreases with rise in compression. The natural frequency of the NCs (H0.5-H5) and FGNCs increased up to 41% than HDPE. The highest P cr and the natural frequency is noted for H5 and FGNC-2 prints. The experimental and numerical results showed good agreement. [ABSTRACT FROM AUTHOR]

This work developed a comprehensive finite element model and numerical studies to illustrate the effect of porosity parameter on critical buckling responses of functionally graded power-based and sigmoid plates and spherical caps subjected to various types of edge compression loads, for the first time. The model, which follows the kinematics of the first-order-shear deformation theory (FSDT) in many aspects, accounts for a quadratic variation of the transverse shear strains and satisfy the zero condition of the transverse shear stresses at the upper and bottom surfaces of the structure without using shear correction factors. Due to lack of investigations on buckling analysis of porous FGM structures and notably for spherical cap shells, we provide new buckling results for porous FGM structures with evenly and unevenly porosity distributions. The influences of functionally graded index, porosity coefficient, porosity patterns, geometrical design parameters and boundary conditions are investigated and presented in a new graphic manner. The recommended model is helpful for predicting and controlling of the buckling behavior of porous FGM structures used in nuclear and aeronautical sectors where the safety of the engines is a crucial criterion. [ABSTRACT FROM AUTHOR]

Abstract: The main key performance factors of honeycombs are represented by the ability to withstand through-thickness compression and to absorb energy by plastic deformation of the cell walls. The knowledge of the constituent material properties, including the sensitivity of these structures to material defects, and of the folding mechanism occurring during the crushing mode represents a basic step to perform reliable finite element analyses able to accurately reproduce the behavior of such structures. The present paper reports a comprehensive study of the compressive response of hexagonal honeycomb structures made of phenolic resin-impregnated aramid paper (Nomex®); the compressive response is numerically investigated and compared with experimental results. A shell model of a representative single cell made of expanded Nomex has been created using the implicit ABAQUS finite element solver. Imperfections due to the manufacturing process are taken into account including material imperfections (elastic modulus variability) and geometrical defects (thickness variability). Imperfections are included in the model by defining different material and thickness properties for each element according to a pre-defined statistical distribution. The effects of imperfections on the honeycomb structure behavior are investigated. The predicted structural response, numerically obtained using different sets of imperfections, shows a good correlation with experimental results. [Copyright &y& Elsevier]

Thin-walled cylindrical CFRP shells tend to buckle under compressive loads. The experimental buckling load is significantly lower than the theoretical one. The reason for this are various kinds of imperfections which are partially caused by the manufacturing process and the test conditions. A major challenge in the design of these shells is the lack of experimental data. Additionally, the quality of test results is rarely critically reviewed in the validation of design approaches. In this paper, the influence of two different manufacturing processes on the geometric imperfections and the influence of three different test rigs on the buckling load are investigated in an experimental campaign with 12 cylindrical CFRP shells. Furthermore, the influence of varying the test rig boundary conditions is analysed. [ABSTRACT FROM AUTHOR]

Truss core sandwich panels have been widely investigated due to their superior mechanical performances. However, local defects or damages during preparation and service may reduce the strength significantly. The objective of this paper is to examine the imperfection sensitive of this kind of structures under in-plane compression. The elastic and plastic buckling behaviour of pyramidal truss core sandwich panels with local damages under in-plane compression are studied experimentally and numerically. Local damages including unbound nodes between lattice truss and the facesheet, missing lattice cells and holes in the facesheet are considered. In-plane compression tests of truss core sandwich panels with prefabricated local damages are conducted, and then a finite element model in conjunction with random number is developed to simulate the buckling behaviour of the panel with randomly distributed damages in a specific region. Experimental and numerical results show that, besides the damage extent, the location of unbound nodes and missing lattice cells have significant effect on the buckling strength of the pyramidal truss core sandwich panel. In addition, the local damage sensitiveness of sandwich panel with round holes in the facesheet is lower than that with square holes. [ABSTRACT FROM AUTHOR]

Current paper is the second part of Kolakowski Z, Mania RJ paper entitled: “ Influence of the coupling matrix B on the interactive buckling of FML-FGM columns with closed cross-section under axial compression ”, Composite Structures, in press. The problem of non-linear multi-mode buckling of thin-walled columns with open cross-sections made of Functionally Graded Materials ( FGMs ) and Fibre Metal Laminate ( FML ) was discussed. FGM layers are a thermal barrier, whereas the FML composite provides rigidity and strength. This new hybrid thin-walled structure is very interesting but there are no interactive buckling solutions. The non-linear problem of buckling was solved with the analytical-numerical method ( ANM ) based on Koiter’s theory. An interaction of global buckling mode with many different local buckling modes was discussed. A plate model and the classical laminate theory are used to define government relations. The differential equilibrium equations were obtained with a variational method. Each column was made of an FML sublayer, a single AL-TiC-type FGM layer and/or a TiC ceramic layer. The FML sublayer consisted of two outer aluminium layers and even carbon-epoxy prepreg interlayers. The layup configuration of the FML/FGM composite is non-symmetric, so the coupling matrix B is non-trivial. Simply supported columns are under mechanical compression only. [ABSTRACT FROM AUTHOR]

• VAM is extended to establish the 2D-EPM of CHSP-NPR, and verified by comparing with 3D-FEM. • The DOFs of 2D-EPM is greatly reduced, resulting in high calculation efficiency. • The linearized buckling and post-buckling behavior of CHSP-NPR are studied using 2D-EPM. • The effects of material and geometric parameters on buckling loads and mode shapes are analyzed. • CHSP-NPR has better buckling resistance than regular CHSP under the same conditions. In present work, the variational asymptotic method is extended to study the bucking of composite honeycomb sandwich plate with negative Poisson's ratio (CHSP-NPR), which is easily buckle under compressive loads or bending moments and may lead to catastrophic failure. For global bucking with small local rotations, the 3D geometrical nonlinear problem is decoupled into linear constitutive modeling using unit cell and geometrical nonlinear problem defined over the 2D equivalent plate model (2D-EPM). Results using 2D-EPM in global buckling analysis are compared with 3D-FEM results to evaluate the accuracy and efficiency of the present model, and parametric studies are carried out to reveal the relative influence of selective parameters on buckling behavior of CHSP-NPR. The results show the increase of the proportion of honeycomb core and the decrease of fiber volume fraction of face sheet may increase the negative Poisson's ratio and weaken the buckling resistance of CHSP-NPR, but the buckling loads of CHSP-NPR are larger than those of conventional honeycomb sandwich plate under the same conditions. [ABSTRACT FROM AUTHOR]

Tow-placement machines are able to fabricate variable-stiffness composite panels with curvilinear stiffeners. In this paper the buckling performance of curvilinearly grid-stiffened composite panels subjected to in-plane compressive loads under various boundary conditions is addressed. A Python-Abaqus script is developed to perform the buckling analysis of the panels. The skin is modelled using shell elements and the grid stiffeners are idealized by beam elements. Different design tailoring scenarios for grid-stiffened and unstiffened constant-stiffness and variable-stiffness skins are presented to demonstrate the influence of the stiffness variation created simultaneously by both the layout of the curvilinear stiffeners and by the fiber orientation variation of the skin on the buckling capacity. It is shown that the buckling resistance of the grid-stiffened quasi-isotropic skins can significantly be improved using curvilinear stiffeners compared to their straight design counterparts. A much higher degree of improvement can be achieved by concurrently tailoring both the skin and the stiffeners using curvilinear fibers. In order to guarantee the manufacturability of the designs, manufacturing constraints in terms of maximum curvature along the fiber and stiffener paths are imposed. It is demonstrated that imposing these constraints has negative effects on the buckling load improvement obtained for designs without considering manufacturing constraints. [ABSTRACT FROM AUTHOR]

Abstract: The article discusses the buckling analysis of composite orthotropic truncated conical shells under a combined axial compression and external pressure and resting on a Pasternak foundation. The governing equations have been obtained for the orthotropic truncated conical shell resting on a Pasternak foundation and solved by applying the Superposition and Galerkin methods. The novelty of present work is to achieve closed-form solutions for critical combined loads. Finally, the effects of the Winkler and Pasternak elastic foundations, shell characteristics and material orthotropy on the values of critical combined loads have been studied. Comparison of results with those available in the literature has been presented. [Copyright &y& Elsevier]

The present paper deals with the buckling and post-buckling behaviour of plates made of coupling laminates (the so-called general laminates). Such laminates consist of a number of layers arranged in an arbitrarily way. Thus, the sequences of laminated layers are non-symmetric. In this case, the coupling between tension, flexure, shearing and twisting takes place. The behaviour of general laminates substantially differs from that of laminates with a symmetric layup or isotropic materials. Therefore, they undergo out-of-plane deformation (i.e., warping, bending and/or twisting) when exposed to in-plane loads. Due to a wide range of application possibilities for general laminates, it is worth focusing on their advantages. The analytical-numerical method (ANM) based on Koiter’s theory was used to determine the static buckling loads and post-buckling equilibrium behaviour. In order to obtain the equations of equilibrium for plates, the classic laminate theory was used. The plate displacements were considered within the nonlinear geometrical relations. For special laminates (i.e., regular anti-symmetric angle-ply laminates), there are closed-form solutions of the equilibrium equations of the plate when displacements are slight. Those results were the same as the results produced with the presented methods. The differences in buckling stresses are very low, amounting to less than 5%. [ABSTRACT FROM AUTHOR]

Thin-walled cylindrical shells are nowadays widely used for principal structures in the aerospace field. Despite the capacity to sustain high levels of axial compressive loads they are also easily prone to fall into buckling. One of the methods currently studied to increase the value of the critical load associated with this phenomenon consists in the use of curvilinear fibers, through which it is possible to continuously change the stiffness, and consequently the local behavior of the structure. The paper describes an optimization methodology developed for the buckling optimization of thin-walled variable stiffness cylindrical shells subjected to axial load, together with a general fibers path formulation. The framework proposed involves a synergic work between the finite element method and artificial intelligence techniques. The optimal configuration shows an increase of the buckling load of about 4 % together with an increase of the pre-buckling stiffness of about 6 %. [ABSTRACT FROM AUTHOR]

A non-destructive method for prediction of the buckling load of a pressurized unstiffened cylinder was studied. Using vibration correlation technique(VCT), it is possible to predict the buckling load of an imperfection-sensitive cylindrical shell using correlation of loaded natural frequency with axial compressive load. An aluminum can was used as a metallic cylinder and carbon/epoxy unidirectional prepreg was used to fabricate a composite cylinder. Buckling and vibration test were performed and the loaded natural frequency of an unstiffened cylinder under internal pressure and compressive load was measured. Buckling stability was compared with internal pressure and quantitatively calculated geometric imperfection and buckling load was predicted non-destructively using VCT. The loaded natural frequency was calculated using a finite element model with measured geometric imperfection and calculated result was used for verification of the numerical VCT. The effect of internal pressure, buckling stability and geometric imperfection on the accuracy of VCT estimation was examined experimentally and numerically. It was possible to predict the buckling load within allowed tolerance of the actual buckling load. [ABSTRACT FROM AUTHOR]

The design of light aircraft sandwich structures is driven by a local buckling phenomenon named "wrinkling" which can be the primary cause of failure of such structures. Structural tests using the VERTEX methodology were performed to access the wrinkling behaviour of 558x536 mm2 technological sandwich specimens representative of the design used in light aviation. The operating principle of the VERTEX machine is the use of four hydraulic actuators to load a rectangular box structure, the upper part of the central box being closed by the sandwich under test. Thus, sandwich specimens were tested under compressive and shear loading. A wrinkling scenario was identified thanks to Stereo Digital Image Correlation and a high-speed camera. Wrinkling localisation is driven by mechanical and geometrical aspects. Experiments on wrinkling in sandwich panels remain rare in the literature at this level of the test pyramid for certification of aeronautical structures. This upper scale presents some advantages as it allows multiaxial loading and boundary conditions consistent with a lightweight aeronautical structure. Technological elements can also be added to study their influence on the structure. The result will lead to interesting future investigations on the dialogue between experiments and models in a forthcoming paper. [ABSTRACT FROM AUTHOR]

The design of light aircraft sandwich structures is driven by a local buckling phenomenon named "wrinkling" which can be the primary cause of failure of such structures. Structural tests using the VERTEX methodology were performed to access the wrinkling behaviour of 558x536 mm2 technological sandwich specimens representative of the design used in light aviation. The operating principle of the VERTEX machine is the use of four hydraulic actuators to load a rectangular box structure, the upper part of the central box being closed by the sandwich under test. Thus, sandwich specimens were tested under compressive and shear loading. A wrinkling scenario was identified thanks to Stereo Digital Image Correlation and a high-speed camera. Wrinkling localisation is driven by mechanical and geometrical aspects. Experiments on wrinkling in sandwich panels remain rare in the literature at this level of the test pyramid for certification of aeronautical structures. This upper scale presents some advantages as it allows multiaxial loading and boundary conditions consistent with a lightweight aeronautical structure. Technological elements can also be added to study their influence on the structure. The result will lead to interesting future investigations on the dialogue between experiments and models in a forthcoming paper. [ABSTRACT FROM AUTHOR]

In this paper we will investigate the impact of in-plane negative Poisson's ratio (NPR) on the post-buckling responses of graphene-reinforced metal matrix composite (GRMMC) laminated plates under uni- and bi-axial in-plane compressive loads. The effects of temperature variation and foundation support on the post-buckling responses of GRMMC laminated plates are also taken into consideration. The graphene volume fractions in each layer of a GRMMC plate may vary along the plate thickness direction to achieve a functionally graded (FG) arrangement. The GRMMC layers have temperature-dependent material properties that can be modeled by the extended Halpin–Tsai model. Employing the Reddy's third order shear deformation plate theory, the governing equations containing both thermal and foundation effects for the post-buckling problem of FG-GRMMC plates are formulated. The von Kármán geometrical nonlinearity is also considered. The post-buckling responses of the FG-GRMMC laminated plates are obtained by solving the governing equations using a two-step perturbation approach. The results have revealed that in-plane NPR has a substantial impact on the post-buckling responses of GRMMC laminated plates. [ABSTRACT FROM AUTHOR]

The advanced Automated Fibre Placement (AFP) manufacturing technologies make the synthesis of Variable Angle Tow (VAT) composites, which enable the design of lightweight sandwich structures to possess variable stiffness facesheets. However, both global and local instability phenomena of VAT sandwich plates under in-plane compressive loads are rarely explored till now. The objective of this article is to fill this gap by developing a Rayleigh–Ritz procedure based on a modified extended high-order sandwich plate theory (EHSAPT). The original two-dimensional EHSAPT proposed by Phan et al. (2012) is extended to a three-dimensional case with a minor modification that the first-order shear deformation theory instead of the classical Kirchhoff–Love hypothesis is adopted for each facesheet, which brings several merits such as the conciseness in derivation process and the easiness in program implementation. The Rayleigh–Ritz approach combined with the principle of minimum potential energy is employed to derive the eigenvalue equation that governs the instability problem of VAT sandwich plates under in-plane compressive loads. Both global buckling and wrinkling patterns of VAT sandwich plates can be captured under this proposed analytical model framework. Before instability analysis, the nonuniform prebuckling stresses over the entire sandwich plate are determined under the assumption of membrane prebuckling state. The usage of Lagrange multiplier method in the prebuckling regime removes the restrictions inherent in conventional Rayleigh–Ritz formulation and thus provides a general way to model in-plane boundary conditions. The accuracy and effectiveness of the developed Rayleigh–Ritz procedure are validated by comparing with previously published results and FE solutions given by ABAQUS. Effects of core thickness, core orthotropy, and fibre orientation angle of the facesheets on the instability behaviour of VAT sandwich plates are investigated. Finally, the mechanism of steering the fibre trajectory over the facesheets to improve the buckling resistance for the sandwich plate is studied and discussed. [ABSTRACT FROM AUTHOR]

Traditional lay-ups in laminated composite structural parts have largely focused on using quasi-isotropic laminates made of permutations of 0 ° , 90 ° and ± 45 ° laminae. These laminates are referred to as legacy quad laminates (LQL). In this study, three different lay-ups of symmetric laminates to compute critical buckling loads under uniaxial in-plane compressive loads is first investigated. An optimization problem is solved to determine the lay-ups that maximize the buckling performance. The resulting laminates are compared against a new class of laminates, referred to as double-double (DD), which have distinctive advantages for thickness tapering and therefore manufacturability. Both, symmetric and unsymmetric DD laminates are studied, while in the latter case, a thermal cure cycle followed by the application of in-plane loads is used to determine the structural performance in compression. To further verify the versatility of DD laminates, biaxial buckling loads are computed for quad, DD and optimized lay-ups. It is concluded that DD laminates, because of their manufacturability advantages, are promising candidates for several aerostructural applications. [ABSTRACT FROM AUTHOR]

Abstract: A solution is proposed to the buckling problem formulated for a rectangular sandwich plate having all the edges fully clamped (CCCC plate) and subjected to a uniaxial compressive loading. The analysis of the out-of-plane deformation of the buckled plate is based on the equations of the first order shear deformation theory (FSDT). Galerkin method has been employed to solve the problem. Variations of the plate deflection and angles of rotation between the unloaded edges have been approximated using the solution to the bending problem for the shear deformable beam with clamped ends. The approximation of these variables between the loaded edges has been performed using trigonometry series. The solution to the problem is reduced to the calculation of the eigenvector of corresponding homogeneous system of linear equations and determination of its least component. Verification of the solution obtained has been performed using finite-element analysis. [Copyright &y& Elsevier]

Three series of airframe composite panels with T-stiffener, I-stiffener and J-stiffener are designed and optimized to have the same local skin buckling load and weight. All the panels are designed to undergo local skin buckling between Design Limit Load (DLL) and Design Ultimate Load (DUL), approximately at 120% of DLL to utilize the reserve strength in structures. Additionally, identical panels are designed and fabricated from each series to study the effect of various extrinsic parameters such as disbond, delamination, impact damage and repeated loading to identify the best performing series for post-buckling design. All the panels are tested under compression to demonstrate no onset of damage before DUL. The influence of defects such as disbond, delamination and impact damage on the post-buckling behavior is also demonstrated. One pristine panel of each series is repeatedly loaded 1000 times beyond buckling to determine the onset of damage if any. The panels with I-stiffener and J-stiffener found to be the potential design choices for post-buckling design philosophy due to the high margin between skin buckling and collapse load even in the presence of damage. The results from this study would help in moving closer to the post-buckled composite design philosophy for airframe structure. [ABSTRACT FROM AUTHOR]

In this paper a novel concept is proposed for improving the buckling capacity of composite aircraft panels with cutouts. The key idea is to adopt the streamlines of a fluid flow around a given body of arbitrary shape that represents the cutout to define both the fibre and stiffener trajectories. As such, fibres and stiffeners can curve around the cutout in a continuous fashion which may improve the structural performance of panels. The buckling performance of typical aircraft panels with cutouts is addressed. Circular cutouts with various sizes as well as elliptical ones with different sizes and alignments are considered. Unstiffened, longitudinally stiffened and grid-stiffened panels subjected to in-plane uniaxial compressive and shear loads are investigated. The critical buckling loads obtained using curvilinear fibres and stiffeners are compared with those obtained for conventional panels with straight fibres and stiffeners. It is shown that up to 30% improvement in the buckling performance of the unstiffened panels can be achieved. For the stiffened panels, replacing the straight-line format by a streamline format for the fibres and stiffeners yields tremendous improvements in the buckling capacity. The improvements may exceed 150% and 200% for longitudinally stiffened panels and grid-stiffened panels, respectively. [ABSTRACT FROM AUTHOR]

This paper presents an investigation of the dynamic buckling phenomenon in thin-walled Fiber Metal Laminate short columns subjected to axial compressive loading. The numerical analysis is performed with the FEM ANSYS software for three profiles differentiate in the laminate stacking sequence. Two groups of criteria were implemented to assess the structure resistance to dynamic pulse loading: the dynamic buckling criteria and strength failure criteria. Parametric analysis was performed to determine the effect of initial geometric imperfection, laminate stacking sequence, and the pulse load's shape on the dynamic stability. The value of the amplitude of initial geometric imperfection and the shape of pulse load influence the value of critical Dynamic Load Factor strongly. Aluminium yielding was observed as the primary failure source developed in the FML structure subjected to the pulse loading. [ABSTRACT FROM AUTHOR]

Abstract: A numerical investigation was conducted into a perturbation-based analysis approach for assessing the imperfection sensitivity of composite cylindrical shells buckling under compression loading. The Single Perturbation Load Analysis (SPLA) approach was applied, which uses a single lateral load to introduce a realistic, worst-case and stimulating imperfection pattern. Finite element analysis was conducted for cylinders of both monolithic composite laminate and sandwich construction, with and without small and large cutouts. It was found that using a perturbation displacement equal to the shell thickness provides a suitable technique for estimating the reduction in buckling load caused by imperfections. Predictions of buckling knockdown factors using the SPLA approach showed advantages over the use of eigenmodes as the SPLA approach provides a clear design point and does not require experimental data for calibration. The effect of small and large cutouts was analogous to the effect of small and large perturbation loads. The location of the perturbation load influenced the buckling knockdown factors for both small and large cutouts, and worst-case locations were identified for both configurations. [Copyright &y& Elsevier]

This paper presents an experimental study into the buckling behaviour of glass fabric-reinforced polymer (GFRP) cylindrical shells subjected to axial compression load. The tests were conducted on six cylindrical shells with different height-to-radius ratios. It was concluded that the GFRP cylindrical shells showed the full-buckling strength and had local buckling failure mode. Moreover, the nonlinear numerical analysis and analytical procedure were developed. In general, the results indicated that there is an acceptable adaptation between the experimental, theoretical and numerical results. [ABSTRACT FROM AUTHOR]

Abstract This paper studies buckling and post-buckling behaviours of multi-layered plates under in-plane compression based on Reissner-Mindlin plate theory. The governing equations are derived from a kinematic nonlinearity based on the von-Kármán assumptions and are thereafter discretized by isogeometric analysis (IGA), which utilizes the NURBS basis functions. For the symmetrically laminated plates, stability analysis consists of three steps: pre-buckling, buckling and post-buckling analyses. In fact, the pre-buckling stresses must be first determined in the pre-buckling analysis and become an important factor in accurate estimation of the critical buckling and post-buckling loads. Otherwise, in the imperfect or unsymmetrically stacked plates, there is no buckling bifurcation phenomenon. The Newton-Rapshon method is hence adopted to solve the geometrically nonlinear problem. Numerical examples are supplied to investigate the effect of an initially geometrical imperfection, which is possible imperfection type such as sine-type, global-type or local-type imperfection, on the post-buckling response of the plates. [ABSTRACT FROM AUTHOR]

[Display omitted] • A generic third-order nanoplate theory with significant surface stresses is built. • Coupling of surface stresses with transverse shear deformation is established. • Analytical model is constructed and critical buckling loads are derived. • Numerical solutions are verified with benchmarks and excellent comparison is shown. • Effects of surface stresses on buckling of nanoplates are comprehensively analyzed. In this paper, a general third-order shear deformation plate theory (GTSDPT) is employed to investigate the buckling behaviors of rectangular nanoplates. A new model with non-isotropic surface modulus that depends on in-plane and transverse shear strains, such as that for most crystalline faces, is established to analyze the significance of non-isotropic surface effects on buckling behaviors. The governing equations and the corresponding boundary conditions are established by using the principle of minimum potential energy. The analytical critical buckling load solutions are obtained for nanoplates with different boundary conditions. The proposed model is verified by comparing buckling results against the ones from existing plate theories. Using both Reddy's third order shear deformation plate theory (TSDPT) and GTSDPT, the influence of plate thickness, length-to-thickness ratio, surface modulus, residual surface stress, bulk modulus and boundary conditions on the buckling behavior of nanoplates with surface stress effects is analyzed in detail. It is observed that the buckling results of the nanoplates from TSDPT and GTSDPT exhibit some differences due to the presence of shear stresses on the interface between surface layers and the bulk of the plates. The TSDPT theory may not be able to capture shear stress effect and the GTSDPT theory may need to be employed in this case. Finally, the influence of surface stresses on the buckling behaviors of nanoplates made of gold, nickel, silver and copper and subjected to uni- and bi-axial compressive loads is investigated using the GTSDPT theory. [ABSTRACT FROM AUTHOR]

Pultruded glass fiber reinforced polymer (GFRP) sections are increasingly used as load bearing elements in civil construction. Their low elastic modulus and thin-walled nature make these sections prone to buckling phenomena when loaded in compression. This paper presents a study on the axial compression behavior of the pultruded GFRP channel sections. Two variables were considered including column slenderness ratio and wall width-to-thickness ratio. Therefore, four channel sections with different dimensions were selected. Seven column lengths ranging from 100 mm to 1400 mm were used for each channel section under axial compression. Three failure modes were observed including section crushing, local buckling and global buckling which were highly related to the column slenderness. Load-displacement curves and compression capacities were reported and compared. Finally, existing analytical design equations in the literature were validated using experimental results. Recommendations on compression design of pultruded GFRP channel sections were made based on the results in the current study. [ABSTRACT FROM AUTHOR]

[Display omitted] This article investigates the potential of a large strain morphing skin based on a Zero Poisson's Ratio (ZPR) Fish-Cells metamaterial. A multi-objective genetic algorithm shape optimisation is performed to improve the ZPR characteristics of the Fish-Cells metamaterial. High-fidelity finite element models are developed to assess the performance of the optimised Fish-Cells metamaterial for large non-linear strains. A detailed joint design study is devised to obtain consistent ZPR behaviour over a maximum strain range. Trends of Poisson's ratio, effective elastic modulus and von-mises stress for the different geometries are discussed in detail. Results provide valuable insight into non-linear behaviour of the Fish-Cells ZPR metamaterial. Furthermore, experimental investigations are conducted to verify the enhanced mechanical behaviour of shape optimised ZPR samples. Linear buckling analysis is performed to assess the performance of the optimised metamaterial under compressive loads. Finally, a preliminary study is conducted to evaluate the performance of the shape optimised ZPR metamaterial as a candidate skin for a morphing aircraft wing. [ABSTRACT FROM AUTHOR]

We have numerically and experimentally studied the elastic stability and buckling behaviors in a particular kind of bending-dominated periodic lattice (BDPL) composed of curved cell walls. When the BDPL is subjected to certain amount of uniaxial compression load, in-plane or out-of-plane elastic buckling occurs. The two instability mechanisms in such planar structured panels are investigated based on finite element simulations and experiments, and a systematic parametric study has been conducted to study various factors influencing the buckling behavior. The results show that increasing the curvature of lattice struts could lead to a decrease in critical buckling loads for both in-plane and out-of-plane buckling. The spatial ratio of struts and the thickness of the studied panel are found also to play a significant role. The different buckling modes can be observed by altering the microstructure parameters of the BDPL, such as the strut curvature. This study is deemed to be helpful in the design of lattice metamaterials composed of curved struts, which can be useful in energy absorption and mechanical auxeticity. [ABSTRACT FROM AUTHOR]

In this paper, the effect of compressive in-plane load on the equilibrium paths and vibration characteristics of a vertical symmetric laminated plate coupled with fluid is studied theoretically both in the pre- and post-buckling state. The Third-order shear deformation theory and von Karman nonlinear strain displacement relationship are utilized to describe the nonlinear deformation of the plate consists of a number of fiber-reinforced layers. The Hamilton's principle is introduced to formulate the plate-fluid coupled governing equations. A two-step theoretical approach is developed. Firstly, based on the Cylindrical arc-length method, we solve the nonlinear static equations to trace the snap-back behavior and pass the limit points along the complex equilibrium paths obtaining the stable buckling deflection. Then the coupled vibration characteristics are calculated using the tangent stiffness at the stable positions. The present theoretical results are validated by the numerical results. The effects of added mass and hydrostatic load are compared and analyzed. It is noted that, in the post-buckling state, the number of limit points along the static unstable equilibrium path increases with the compressive in-plane load getting larger. The variation trends of the natural frequencies and modes under different in-plane loads in pre- and post-buckling state are investigated. [ABSTRACT FROM AUTHOR]

Elastic boundary conditions play an important role in the buckling analysis of cylinders under compressive loading. These structures are used widely in aerospace applications and are highly sensitive to geometrical, material, loading, and boundary imperfections. In fact, the presence of these imperfections can lead to catastrophic failure. In 1968, NASA reported relations for obtaining the Knockdown Factor (KDF) based on an empirical method that is valid for isotropic and orthotropic materials; however, these relations do not consider the effect of elastic boundaries that can lead to highly conservative values of KDF. In design practice, a universal KDF of 0.65 has been used for recent designs by NASA, which may not be applicable to new types of structural configuration with different loading and boundary conditions. Therefore, there is a need for robust design factors for future designs which reduce the dependency on testing during preliminary design phases and speeds up the product development process. The availability of up-to-date and different KDF expressions for different structural configurations would help engineers to design lighter structures with improved load carrying capacity and reliability. The main objective of this work is to identify the buckling load sensitivity of cylindrical shells due to their boundary conditions and develop KDF relations considering elastic boundaries. To achieve this goal, the effect of axial, radial and tangential support stiffness on a quasi-isotropic cylinder under axial compression is investigated. A data-driven design approach is used to develop new KDF empirical relations for a quasi-isotropic cylinder on different elastic foundations. The accuracy of these relations is within 5% for any elastic foundation considered. [ABSTRACT FROM AUTHOR]

Robust and efficient predictions of buckling-driven delamination propagation, enabled by a novel analytical modelling approach, are presented. The model considers full mechanical coupling (extension-shear, extension-bend, extension-twist/shear-bend and bend-twist), contact and mode-mixity and thus significantly enhances the capabilities of current analytical approaches. A problem description in cylindrical coordinates enables the evaluation of the energy release rate along the delamination boundary. The model uses an energy formalism to determine the post-buckling deformation and a crack-tip element analysis employing force and moment resultants acting on the delamination boundary to determine the energy release rate. Composite panels with circular thin-film delaminations and various multi-directional stacking sequences are investigated for in-plane compressive loading. Predictions of applied strains causing delamination growth, i.e. threshold strain, show good agreement with published experimental data and 3D finite element analysis. A parametric study varying the ratio of delamination size to depth is performed. Based on the findings obtained, governing deformation characteristics of buckling-driven delamination growth are identified and insight into damage tolerant design of composite laminates is obtained, which is of particular interest for compression after impact (CAI) strength of composite structures. [ABSTRACT FROM AUTHOR]