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Abstract The vibration correlation technique (VCT) is one of the most important nondestructive methods to calculate the buckling load of imperfection sensitivity in thin-walled structures. VCT is widely used for beam and plate structures, but the technique is still under development for thin-walled shells. In this paper, an experimental and numerical validation of VCT approach was presented and discussed for the prediction of the buckling load of the grid-stiffened composite cylindrical shells loaded in compression. From the experimental point of view, three specimens were fabricated using a new silicone rubber mold, and specially-designed filament winding setup. The modal behavior of the grid-stiffened composite cylindrical shells was investigated by exciting the structures using modal hammer method in different applied compression load. Then, the variation of the first natural frequency of vibration with the applied compressive load was measured up to buckling during testing. Furthermore, a series of Finite Element Models (FEMs), including nonlinear effects such as geometric and thickness imperfection, are carried out in order to characterize the variation of the natural frequencies of vibration with the applied load and also compare it with the experimental results. Finally, the buckling test was performed to validate the experimental and numerical results of VCT approach. The results showed that the difference between the predicted buckling load using the VCT approach on the experimental results and numerical results with an experimental buckling load is 3.1% and 5.0%, respectively. Also, the current VCT approach has a very good correlation for grid-stiffened composite cylindrical shells when the maximum applied load is higher than 68% of the experimental buckling load. [ABSTRACT FROM AUTHOR]

Two curved thermoplastic composite multi-stringer panels with roller boundary conditions are analysed and tested to investigate the buckling and failure behaviour. The panels are made of AS4D/PEKK-FC thermoplastic composite, have five stringers with an angled cap on the side and are joined to the skin with the short-fibre reinforced butt-joint technique. The panels have a roller attached to each loading edge, approximating simply-supported boundary conditions to apply compression and bending. One panel has an initial damage representing a barely visible impact damage in one of the stringer butt-joints, and one panel is in pristine condition. Finite element analyses are performed to predict the structural behaviour, and different approximations of the roller boundary conditions are compared. The analyses include material damage initiation and evolution. The out-of-plane displacement of the panels is measured by digital image correlation, and failure is captured with high-speed cameras. The panels fail in a sudden manner when the cap separates from the web, followed by web failure and skin–stringer separation in the butt-joint. The numerical analysis predicts the overall structural behaviour but cannot capture well the sudden panel collapse due to material damage. [Display omitted] [ABSTRACT FROM AUTHOR]

The paper investigates the validity and reliability of the blind-bolt repair method for repairing delaminated composite aircraft panels. The delaminated specimens are prepared by inserting Teflon films during the manufacturing process to simulate interlayer damage. Subsequently, these specimens are repaired using the blind-bolt method. Modal and uniaxial compression tests are conducted to quantitatively evaluate the natural frequency, mode shape and load-bearing strength of both delaminated and bolt-repaired specimens. Digital image correlation and ultrasonic phased array techniques are employed to characterize buckling instability and damage evolution of specimens. The results reveal that the natural frequency and compressive buckling strength of delaminated specimens significantly decrease. The mode shape also changes nonlinearly with the stiffness reduction. This variation is proportional to the size and the quantity of delaminations. The blind-bolt repair method effectively restores the vibration and mechanical properties of the delaminated composite structure by reconnecting separated sub-laminates. A repair tolerance of 20 mm–60 mm is recommended for a single blind-bolt. When the delamination length is 35 mm, the repair efficiency for the critical buckling load and the ultimate load is the highest, at 58.3% and 64.4%, respectively. [Display omitted] [ABSTRACT FROM AUTHOR]

Abstract: The local and global compressive buckling behavior of stability-critical, high-aspect ratio, cantilevered composite IsoTruss® grid structure columns was examined. The influence of local bay length and number of carbon fiber tows in the longitudinal and helical members on the compressive strength of IsoTruss® columns was examined. Four 3-m (118.0in.) long IsoTruss® specimens were fabricated and tested in axial compression with fixed-free boundary conditions. The test results exhibit the same trend as the finite element predictions, although the error is higher for shorter bay lengths. Local buckling depends on bay length, with higher buckling loads observed for shorter bay lengths. Global buckling, on the other hand, is independent of bay length; although increasing the bay length reduces the weight and thus increases the overall efficiency of an IsoTruss® structure. The Euler column buckling prediction only considers the overall diameter and the axial stiffness of the longitudinal members; therefore, Euler buckling predictions are accurate only for IsoTruss® configurations that fail in global buckling. [Copyright &y& Elsevier]

Abstract: Experimental and numerical investigations were conducted into the damage growth and collapse behaviour of composite blade-stiffened structures. Four panel types were tested, consisting of two secondary-bonded skin–stiffener designs in both undamaged and pre-damaged configurations. The pre-damaged configurations were manufactured by replacing the skin–stiffener adhesive with a centrally located, full-width Teflon strip. All panels were loaded in compression to collapse, which was characterised by complex post-buckling deformation patterns and ply damage, particularly in the stiffener. For the pre-damaged panels, significant crack growth was seen in the skin–stiffener interface prior to collapse, which caused a reduction in load-carrying capacity. In the numerical analysis of the undamaged panels, collapse was predicted using a ply failure degradation model, and a global–local approach that monitored a strength-based criterion in the skin–stiffener interface. The pre-damaged models were analysed with ply degradation and a method for capturing interlaminar crack growth based on multi-point constraints controlled using the Virtual Crack Closure Technique. The numerical approach gave close correlation with experimental results, and allowed for an in-depth analysis of the damage growth and failure mechanisms contributing to panel collapse. The successful prediction of collapse under the combination of deep post-buckling deformations and several composite damage mechanisms has application for the next generation of composite aircraft designs. [Copyright &y& Elsevier]

Abstract: Based on a continuum elastic double-shell model in which each tube of a double-walled carbon nanotube is described as an individual elastic shell, involving the van der Waals interaction between the inner and outer nanotubes, the governing equations for the buckling and postbuckling behavior of double-walled carbon nanotubes subjected to torsional load are presented based on the Karman–Donnell-type nonlinear differential equations. Applying the boundary-layer theory of shell and employing singular perturbation technique, accurate solutions are obtained to determine the buckling loads and postbuckling equilibrium paths. Through detailed calculations, main postbuckling characteristics, i.e. connections of the angle of twist, axial end-shortening and transverse deflection with applied torque, are clarified for a range of nanotube geometrics. Results reveal that under the torsional load double-walled carbon nanotube has an unstable postbuckling behavior. And it is confirmed that the postbuckling equilibrium path becomes higher when the nanotube becomes thinner. [Copyright &y& Elsevier]

Abstract: Plane plates subjected to tensile loads are usually not considered to fail due to buckling. However if a plate contains a cut-out, regions of compressive stresses arise under a uniaxial tensile load. In thin-walled orthotropic composite plates these compressive stresses may cause local buckling. In general the stress concentration factors of cut-outs are very high, thus the buckling limits will not be exceeded before fracture. However cut-outs, optimised by a shape optimisation method, run risk to initiate buckling before exceeding the fracture load because the stress concentration factors for these cut-outs are very low. In this paper the influence of the shape of optimised cut-outs on the buckling behaviour is investigated. Besides the critical load the under-critical and post-critical behaviour of geometrical imperfect orthotropic composite plates is analysed. Methods that prevent local buckling under tensile stresses are discussed in order to provide the full advantage of optimised cut-outs. [Copyright &y& Elsevier]

Abstract: Theoretical analysis and numerical simulations are performed to investigate the buckling and postbuckling behaviors of stiff lamellae embedded in a compliant matrix under uniaxial compression. First, the analytical solution is derived for the critical compressive strain and wrinkle wavelength of a stiff layer sandwiched between two different soft layers, in which the effects of interfacial shear stresses and matrix thicknesses have been taken into account. During postbuckling, the system may keep the sinusoidal buckling shape or bifurcate into period-doubling morphology. A phase diagram is established, which enables us to easily predict the morphological evolution from the geometric and material parameters of the system. Then the above analysis is extended to two or more parallel stiff lamellae within a compliant matrix. Different buckling modes are found in such multilayer systems, i.e., short-wave mode, long-wave mode, and hierarchical mode. This study not only sheds light on the stability and morphological evolution of lamella composites and structures but also helps understand the morphogenesis of some biological tissues. [Copyright &y& Elsevier]

Abstract: The present study is concerned with the thermal buckling analysis of cross-ply laminated beams subjected to different sets of boundary conditions. The analysis is based on a three-degree-of-freedom shear deformable beam theory. The requirement of the continuity conditions between layers for symmetric cross-ply laminated beams is satisfied by the use of the shape function incorporated into the theory which also unifies the one dimensional shear deformable beam theories developed previously. The governing equations are obtained by means of minimum energy principle. Three different combinations of clamped and hinged edge boundary conditions are considered. The critical thermal buckling temperatures are obtained by applying the Ritz method where the three displacement components are expressed in a series of simple algebraic polynomials. The numerical results obtained for different length-to-thickness ratios and lay-ups are presented and compared with the ones available in the literature. It is interesting to note that some cross-ply beams buckle upon cooling instead of heating and some of them do not buckle irrespective of whether they are heated or cooled. [Copyright &y& Elsevier]

Abstract: The effect of a single circular delamination around the circular hole on the critical buckling load of woven fabric laminated composite plates has been investigated experimentally and numerically. The determination of the critical delamination diameter for laminated composite plates has been intended by using three dimensional buckling analysis. For the experiments, cross-ply laminated composite plates with delamination and without delamination have been produced. The experimental critical buckling loads of plates have been found by clamping from the two edges and then these results have been compared with the results obtained from the numerical analyses. For the numerical analyses, ANSYS 6.1 FEA program has been used. It has been seen that the results obtained the numerical buckling analyses are very close to the experimental results. In the light of this harmony, the numerical analyses for different delamination diameters and fiber orientations have been done and from these analyses, it has been seen that the important decreases occur in the critical buckling loads after a certain value of the delamination diameter and the different fiber orientations also affect to these loads. [Copyright &y& Elsevier]

Abstract: Due to the level of complexity of the governing equations for curved composite panels, few solutions, allowing the critical buckling loads and postbuckling behaviour of such structures to be determined, exist. Those that do are for basic problems based on single load types and simple boundary conditions. For other cases, such behaviour can only be determined by either grossly simplifying both the load and boundary conditions to those which can be predicted using these simplified equations (which may lead to overestimations in buckling load, and thereby premature failure or collapse), or by using alternative tools such as finite strip techniques or finite element analyses. This paper details a series of tests carried out to determine the behaviour of a number of optimised fibre composite panels of differing radii of curvature and aspect ratio, simply supported along two edges and built in along the other two, subject to a varying combination of shear and in-plane bending, for which no theoretical solution exists, and assesses the suitability of finite strip techniques and finite element analysis to predict this behaviour. [Copyright &y& Elsevier]

Abstract: The present study is concerned with the buckling analysis of cross-ply laminated beams subjected to different sets of boundary conditions. The analysis is based on a three-degree-of-freedom shear deformable beam theory. The requirement of the continuity conditions between layers for symmetric cross-ply laminated beams are satisfied by the use of the shape function incorporated into the theory which also unifies the one-dimensional shear deformable beam theories developed previously. The governing equations are obtained by means of Minimum Energy Principle. Three different combinations of free, clamped and simply supported edge boundary conditions are considered. The critical buckling loads are obtained by applying the Ritz method where the three displacement components are expressed in a series of simple algebraic polynomials. The numerical results were obtained for different length-to-thickness ratios and lay-ups are presented and compared with the ones available in the literature. [Copyright &y& Elsevier]

Abstract: Design rules based on theoretical solutions, which allow the prediction and understanding of the buckling and post-buckling behaviour of homogenous thin plates, exist for only a limited number of simple loading and boundary conditions due to the complexity of the equilibrium equations that describe the problem. When considering fibre composite plates, this issue is exacerbated by the inherent coupling between bending and extensional strains due to unsymmetric lamination, which results in three eighth order coupled partial differential equilibrium equations. This paper details a series of tests carried out to investigate the behaviour of a number of optimised fibre composite plates of differing geometry, simply supported along two edges and built in along the other two, subject to a varying combination of shear and in-plane bending, for which no theoretical solution exists, and assesses the suitability of analytical techniques and finite element analysis to predict this behaviour. [Copyright &y& Elsevier]

Abstract Global buckling failure should be avoided when designing a structure with the requirement of crashworthiness performance. This study characterises the quasi-static in-plane crushing of CF/EP composite sandwich panels by tailoring their bevel angles. A finite element model was developed describing the interlaminar and intralaminar damage of a composite sandwich panel; this model was validated by in-plane compression experiments. A numerical analysis and compression experiments were then performed to determine the responses and failure modes in the CF/EP composite sandwich panels with various bevel angles. The results showed that the global buckling-to-progressive failure transition under compression occurred in the composite sandwich panels when the bevel angle reached a critical value. A microscopic analysis showed that the composite sandwich panels with buckling failure behaviours exhibited an apparently classical post-buckling transverse shearing mode, while those with progressive failure presented individual lamina bending with inward and outward fronds. This study provides some useful data for the design of the crashworthiness of a sandwich composite panel by introducing a progressive failure mode. [ABSTRACT FROM AUTHOR]

Abstract: Buckling of defective single-walled and double-walled carbon nanotubes (SWCNTs and DWCNTs, respectively) due to axial compressive loads has been studied by molecular dynamics simulations, and results compared with those of the perfect structures. It is found that single vacancy defect greatly weakens the carrying capacity of SWCNTs and DWCNTs, though it does slight harm to the effective elastic modulus of the tubes. The influence of defects on the buckling properties of nanotubes is related to the density of the defects, and the relative position of defects also plays an important role in buckling of DWCNTs. The van der Waals force among atoms in the inner and the outer tubes of short defective DWCNTs makes the critical buckling strain of DWCNTs greater than that of the inner tube. [Copyright &y& Elsevier]

Abstract: Thermal buckling analysis of symmetric and antisymmetric cross-ply laminated hybrid composite plates with an inclined crack subjected to a uniform temperature rise are presented in this paper. The first-order shear deformation theory in conjunction with variational energy method is employed in the mathematical formulation. The eight-node Lagrangian finite element technique is used for obtaining the thermal buckling temperatures of hybrid composite laminates. The effects of crack size and lay-up sequences on the thermal buckling temperatures for symmetric and antisymmetric plates are investigated. The results are shown in graphical form for various boundary conditions. [Copyright &y& Elsevier]

Abstract: This article considers the problems of free vibrations, buckling, and static deflections of functionally graded plates in which material properties vary through the thickness. It is shown that, all other parameters remaining the same, the natural frequencies of functionally graded plates are always proportional to those of homogeneous isotropic plates and that the proportionality constant can be easily be predicted. Similar results are obtained for buckling and static deflection cases. Therefore, one can predict the behavior of functionally graded plates knowing that of similar homogeneous plates. Extensive results available in the literature can be used as well as solutions and software developed for isotropic materials, thereby greatly reducing the need for a direct analysis of such problems for functionally graded plates. [Copyright &y& Elsevier]

Abstract: In this article, we present recent progress in selected areas of carbon nanotube mechanics. First, we present the authors’ experimental work on shell buckling mechanics of multi-walled carbon nanotubes using nanoindentation. A comparison with existing elastic theories showed that the shell theories under-predict the buckling loads by as much as 50%. We then present an investigation of electromechanical coupling in carbon nanotubes by focusing on phonon frequency shifts as a result of charge injection. Raman spectroscopic measurements of the electromechanical couplings under varied but controlled charge injection conditions are analyzed, and the close agreement between the model results and the measured Raman peak shifts suggests that geometrical changes of charged carbon nanotubes previously observed or speculated in different experiments can indeed originate from the simple quantum effects described herein. [Copyright &y& Elsevier]

Abstract: In this paper, thermal buckling analysis of symmetric and antisymmetric laminated hybrid composite plates with a hole subjected to a uniform temperature rise for different boundary conditions is presented. The first-order shear deformation theory in conjunction with variational energy method is employed in mathematical formulation. The eight-node Lagrangian finite element technique is used for obtaining the thermal buckling temperatures of glass–epoxy/boron–epoxy hybrid laminates. The effects of hole size, lay-up sequences and boundary conditions on thermal buckling temperatures are investigated. The results are shown in graphical form for various boundary conditions. [Copyright &y& Elsevier]

Abstract: The flatwise compressive behaviour of tetrachiral and hexachiral honeycombs is analysed, using analytical and Finite Element simulations, both with explicit and implicit formulations. The tetrachiral and hexachiral cells are composed by cylinders connected by four and six tangent ligaments respectively. The ligaments act as mixed stiffeners-elastic foundations during flatwise compressive loading, providing different buckling mode shapes during deformation. The models are compared with experimental results obtained using RP-based honeycombs tested according to ASTM C 393-00 and ASTM C365-00. [Copyright &y& Elsevier]

Abstract: This paper is concerned with the buckling of thick sandwich panels with orthotropic elastic face sheets bonded to a linear elastic orthotropic core. When such panels are analyzed for axial load carrying capacity, it is now commonplace to adopt the finite element method to carry out computations. The accuracy of the numerical results will depend not only on roundoff and algorithmic errors, but additionally on the approximations made in computing the incremental (second order) work associated in computing the change of configuration from the unbuckled to the buckled state. Here we show that, particularly for orthotropic thick sandwich structures, large errors can be incurred in computing buckling loads with available commercial software, unless the proper work conjugate measures of stress and strain with their stress-dependent tangential moduli are used in the buckling formulation. [Copyright &y& Elsevier]

Abstract: This work reports on an experimental and finite element method (FEM) parametric study of adhesively-bonded single and double-strap repairs on carbon-epoxy structures under buckling unrestrained compression. The influence of the overlap length and patch thickness was evaluated. This loading gains a particular significance from the additional characteristic mechanisms of structures under compression, such as fibres microbuckling, for buckling restrained structures, or global buckling of the assembly, if no transverse restriction exists. The FEM analysis is based on the use of cohesive elements including mixed-mode criteria to simulate a cohesive fracture of the adhesive layer. Trapezoidal laws in pure modes I and II were used to account for the ductility of most structural adhesives. These laws were estimated for the adhesive used from double cantilever beam (DCB) and end-notched flexure (ENF) tests, respectively, using an inverse technique. The pure mode III cohesive law was equalled to the pure mode II one. Compression failure in the laminates was predicted using a stress-based criterion. The accurate FEM predictions open a good prospect for the reduction of the extensive experimentation in the design of carbon-epoxy repairs. Design principles were also established for these repairs under buckling. [Copyright &y& Elsevier]

Abstract: We demonstrate effects of nanotubes buckling and debonding in octadecylamine (ODA) derivatized single wall carbon nanotubes (SWCNT)/epoxy nanocomposites under mechanical and thermal loads uniquely detected by means of Raman spectroscopy and documented by TEM imaging. It is shown that ODA functionalization of SWCNTs provides weak sidewall interactions between the nanotubes and epoxy matrix, which make axially compressed ODA-SWCNTs susceptible to buckling. The feasibility of ODA-SWCNTs buckling in epoxy matrix is also supported by the structural mechanics calculations. [Copyright &y& Elsevier]

Abstract: The creep-buckling of hexagonal honeycombs with non-uniform cell-edge thickness is analyzed. Here, the non-uniform cross-section of cell edges is taken to be a plateau border and the solid making up the cell edges is assumed to follow power law creep. Theoretical expressions for describing the elastic buckling strength and the failure time for the onset of creep-buckling of hexagonal honeycombs with plateau borders are thus derived. The results indicate that the elastic buckling strength and the failure time for creep-buckling are significantly affected by the solid distribution in cell edges. Meanwhile, creep-buckling is more likely to occur when the applied compressive stress is close to the elastic buckling strength. However, creep-bending of cell edges becomes dominant if the applied compressive stress is much smaller than the elastic buckling strength. The transition from creep-buckling to creep-bending for hexagonal honeycombs with plateau borders depends on their relative density, the solid distribution in cell edges and the creep parameters of solid cell edges. [Copyright &y& Elsevier]

Abstract: This paper studies the thermal effect on axially compressed buckling of a multi-walled carbon nanotube. The effects of temperature change, surrounding elastic medium and van der Waals forces between the inner and outer nanotubes are taken into account. Using continuum mechanics, an elastic multi-shell model with thermal effect is presented for axially compressed buckling of a multi-walled carbon nanotube embedded in an elastic matrix under thermal environment. Based on the model, numerical results for the general case are obtained for the thermal effect on axially compressed buckling of a multi-walled carbon nanotube. It is shown that the axial buckling load of multi-walled carbon nanotube under thermal loads is dependent on the wave number of axially buckling modes. And a conclusion is drawn that at low and room temperature the critical load for infinitesimal buckling of a multi-walled carbon nanotube increase as the value of temperature change increases, while at high temperature the critical load for infinitesimal buckling of a multi-walled carbon nanotube decrease as the value of temperature change increases. [Copyright &y& Elsevier]

Abstract: In this paper the buckling and post-buckling behaviour of unidirectional and cross-ply composite laminated plates with multiple delaminations has been studied. Finite elements analyses have been performed, using a linear buckling model, based on the solution of the eigenvalues problem, and a non-linear one, based on an incremental-iterative method. With non-linear method large displacements have been taken into account and also contact constraints between sublaminates have been added to avoid their interpenetration. It has been found that both delamination length and position and stacking sequence of the plies influence the critical load of the plate; furthermore, linear and non-linear buckling models are not always in perfect agreement. [Copyright &y& Elsevier]

Abstract: The material properties of functionally graded materials (FGMs) possess inherent randomness due to their complicated fabrication process, in which the total control of various design parameters is often impossible. The present work investigates the effect of this randomness on the elastic buckling of FGM rectangular plates which are resting on an elastic foundation and subjected to uniform in-plane edge compressions. The interaction between the plate and foundation is included in the formulation with a two-parameter Pasternak model. The elastic material properties (including the Young’s modulus and Poisson’s ratio of each constituent material) and the foundation stiffness parameters are modeled as independent random variables. First-order shear deformation plate theory and a mean-centered first-order perturbation procedure are used to examine the stochastic characteristics of the buckling load. Typical results are presented for plates with aluminum/zirconia two-phase functionally graded material to show the influence of variation in material constants and foundation stiffness parameters, volume fraction index, edge in-plane forces, side-to-thickness ratio, and plate aspect ratio on the second-order statistics of buckling loads. [Copyright &y& Elsevier]

Abstract: The axial compressive strength and failure time of IM7/977-2 quasi-isotropic viscoelastoplastic laminates are investigated. Effects of non-linear shear behaviour and fibre misalignment are emphasized because they are important strength-limiting factor in those strongly anisotropic composites which fail by local buckling in the shear mode of deformation. We first describe the basic model of Budiansky [Budiansky B, Fleck NA. Compressive failure of fibre composites. J Mech Phys Solids 1991; 41(1): 183–211], the model of Schapery [Schapery RA. Compressive strength and failure time based on local buckling in viscoelastic composites. Appl Mech Rev 1993; 46(2): S221–8] neglecting non-linear effects in the quasi-elastic solution and finally we adapt the model of Slaughter and Fleck [Slaughter WS, Fleck NA. Viscoelastic micro-buckling of fibre composites. J Appl Mech 1993; 60: 802–6] to predict creep compressive strength for any multi angle laminate. The analysis is formulated in terms of general non-linear viscoelastic viscoplastic behaviour within the kink band. Failure is due to the attainment of a critical failure strain or a critical angle ϕ r in the kink band. [Copyright &y& Elsevier]

Abstract: A closed form expression to determine the effective flexural modulus of a laminated composite beam is developed and presented in this contribution. This effective flexural modulus is applied to the bending, buckling and free vibration response of generally laminated composite beams with various boundary supports. The expression was developed using the combination of the Euler–Bernoulli beam and classical lamination theory. In addition the results of an extensive finite element analysis are used to validate the analytical model. The comparison of the analytical results, the finite element results and the experimental results showed good correlation. It is also observed that coupling response is an important variable that must be included in the computation of the effective flexural stiffness of generally laminated beam. [Copyright &y& Elsevier]

Abstract: Carbon nanotube reinforced copper matrix (CNT/Cu) composites with high strength and good damping have been developed using acid treatment, sintering processes and consolidation techniques. Strengthening of the composites as a result of nanotube buckling has been demonstrated by experimental nanoindentation tests and molecular dynamics (MD) simulations. The experimental results show that the buckling behavior of additional CNTs in the CNT/Cu composites varies with the slenderness ratio of CNTs. Specifically, this study shows that the significant buckling behavior of CNTs in the CNT/Cu composites where the shorter CNTs (with a smaller slenderness ratio) give rise to a global buckling and the slender CNTs (with a larger slenderness ratio) induce local buckling. The MD simulation results reveal that the buckling behavior of the CNTs plays a key role in increasing the mechanical strength of CNT/Cu composites by acting as a “buffer” in releasing excess strain in the Cu matrix. [Copyright &y& Elsevier]

Abstract: Unlike widely used carbon nanotubes, boron nitride nanotubes (BNNTs) have shown to possess stable semiconducting behavior and strong piezoelectricity. Such properties along with their outstanding mechanical properties and thermal conductivity, make BNNTs promising candidate reinforcement materials for a verity of applications especially nanoelectronic and nanophotonic devices. Motivated by these abilities, we aim to study the buckling behavior of BNNT-reinforced piezoelectric polymeric composites when subjected to combined electro-thermo-mechanical loadings. For this, the multi-walled structure of BNNT is considered as elastic media and a set of concentric cylindrical shells with van der Waals interaction between them. Using three-dimensional equilibrium equations, Donnell shell theory is utilized to show that the axially compressive resistance of BNNT varies with applying thermal and electrical loads. Also, a new equivalent spring constant model of piezoelectric matrix under electro-thermo-mechanical loadings is developed according to the concept of Whitney–Riley model. Results indicate that the support of piezoelectric matrix significantly enhances the buckling resistance of BNNT. Alternatively, the effect of BNNT piezoelectric property on the buckling behavior of composites is demonstrated. Furthermore, it is demonstrated that the supporting effect of elastic medium depends on the direction of applied voltage and thermal flow. More specifically, it is shown that applying direct and reverse voltages to BNNT changes the buckling loads for any axial and circumferential wavenumbers. Such capability could be uniquely utilized when designing BNNT-reinforced composites for structural vibration control applications. [Copyright &y& Elsevier]

Abstract: The influence of winding pattern on the mechanical response of filament wound glass/epoxy cylinders exposed to external pressure is studied by testing cylindrical specimens having stacked layers with coincident patterns in a hyperbaric testing chamber. Different analytical models are evaluated to predict buckling pressure and modes of thin wall cylinders (diameter to thickness ratio d/h of 25) and satisfactory predictions are obtained which are in the same order of magnitude that those obtained in experimental results. Test results show no evident pattern influence on either strength (implosion pressure) or buckling behavior (buckling modes) of thin wall or thick wall (d/h of 10) cylinders. [Copyright &y& Elsevier]

Abstract: A postbuckling analysis is presented for a three-dimensional textile composite cylindrical shell of finite length subjected to axial compression in thermal environments. Based on a micro–macro-mechanical model, a three-dimensional textile composite may be as a cell system and the geometry of each cell is deeply dependent on its position in the cross-section of the cylindrical shell. The material properties of epoxy are expressed as a linear function of temperature. The governing equations are based on a higher order shear deformation shell theory with a von Kármán–Donnell-type of kinematic nonlinearity and including thermal effects. A singular perturbation technique is employed to determine the buckling loads and postbuckling equilibrium paths. The numerical illustrations concern the postbuckling behavior of perfect and imperfect, braided composite cylindrical shells with different values of geometric parameter and of fiber volume fraction in different cases of thermal environmental conditions. The results show that the shell has lower buckling load and postbuckling path when the temperature-dependent properties are taken into account. The results reveal that the temperature changes, the fiber volume fraction, and the shell geometric parameter have a significant effect on the buckling load and postbuckling behavior of textile composite cylindrical shells. [Copyright &y& Elsevier]

A postbuckling analysis is presented for a functionally graded cylindrical thin shell of finite length subjected to compressive axial loads and in thermal environments. Material properties are assumed to be temperature-dependent, and graded in the thickness direction according to a simple power law distribution in terms of the volume fractions of the constituents. The governing equations are based on the classical shell theory with von Ka´rma´n–Donnell-type of kinematic nonlinearity. The nonlinear prebuckling deformations and initial geometric imperfections of the shell are both taken into account. A boundary layer theory of shell buckling, which includes the effects of nonlinear prebuckling deformations, large deflections in the postbuckling range, and initial geometric imperfections of the shell, is extended to the case of functionally graded cylindrical shells. A singular perturbation technique is employed to determine the buckling loads and postbuckling equilibrium paths. The numerical illustrations concern the postbuckling response of axially-loaded, perfect and imperfect, cylindrical thin shells with two constituent materials and under different sets of thermal environments. The effects played by temperature rise, volume fraction distribution, shell geometric parameter, and initial geometric imperfections are studied. [Copyright &y& Elsevier]

A methodology for studying the implications of taking into account manufacturing at early design stages is presented. It is applied to a rectangular laminate made by RTM and compression (RTCM). The plate is designed for injection time, maximum mold pressure, stiffness and buckling. Semi-analytical, numerically inexpensive models of the processes and structure enable a thorough investigation of the couplings between process and structure by comparing four design formulations: in decoupled problems, either the process or the structure is optimized; then, the process is optimized with targetted low or high structural performance. A globalized Nelder–Mead optimization algorithm is used. The rigour of the method and the relative simplicity of the application case provide a clear description of how maximum mold pressures, injection times and final structures properties are traded-off. [Copyright &y& Elsevier]

Abstract: In the present study, the compressive failure mechanism of quasi-isotropic composite laminates with an open hole was experimentally and numerically studied to explain the mechanical meaning of the open hole compression (OHC) strength. In the experiment, we adopted a fixture for the OHC test method proposed by the National Aerospace Laboratory (NAL III). Two types of composite systems were tested to examine the dependence of failure behavior on the material properties such as interlaminar toughness. The damage which appeared first was fiber micro-buckling in the 0° layer. Some accumulation of damage, such as further fiber micro-buckling in the 0° layers and interlaminar delaminations in several interfaces, was observed before the final unstable fracture in the laminate with high interlaminar toughness, while sudden failure occurred in the laminate with low interlaminar toughness. In the numerical study, a full three-dimensional finite element analysis was conducted. At the transverse edge of the hole, not only stress singularity at the interface but also high stress concentration at the 0° layers was obtained. Singular stress at the interfaces decreased quickly to a level much below the interlaminar strength. To consider the effect of micro-buckling on the stress redistribution and further damage accumulation, a damage analysis was conducted by reducing the stiffness components of the corresponding elements to 1/10. When one element was damaged, the maximum stress next to the damaged element became higher than the maximum stress for the intact laminate. The maximum stress decreased with the increase in number of the damaged element in the transverse direction and became lower than that for intact laminate after some extension of the damage area. This result indicates that some unstable damage progress of limited size would be expected just at the first damage occurrence and a stable increase of damage would follow it with further compressive load increase until other damage systems occurred. [Copyright &y& Elsevier]

Abstract: The effective moduli of a multi-scale composite are evaluated by a bottom-up (hierarchical) modeling approach. We focus on a two-scale structure in which the small scale includes a platelet array inside a matrix, and the large scale contains fibers inside a composite matrix. We demonstrate that the principal moduli of the multi-scale composite can be fine-tuned by the platelet arrangement and orientation. As a case study, we consider the phenomenon of fiber micro-buckling within the multi-scale composite. It is found that the compressive micro-buckling strength can be considerably increased for specific platelet orientations. The multi-scale design approach presented here can be used to generate novel families of composite materials with tunable mechanical properties. [Copyright &y& Elsevier]

Abstract: A postbuckling analysis is presented for a functionally graded cylindrical shell with piezoelectric actuators subjected to axial compression combined with electric loads in thermal environments. Heat conduction and temperature-dependent material properties are both taken into account. The temperature field considered is assumed to be a uniform distribution over the shell surface and varied in the thickness direction and the electric field is assumed to be the transverse component E Z only. The material properties of functionally graded materials (FGMs) are assumed to be graded in the thickness direction according to a simple power law distribution in terms of the volume fractions of the constituents, and the material properties of both FGM and piezoelectric layers are assumed to be temperature dependent. The governing equations are based on a higher order shear deformation theory with a von Kármán-Donnell-type of kinematic nonlinearity. A boundary layer theory of shell buckling is extended to the case of FGM hybrid laminated cylindrical shells of finite length. A singular perturbation technique is employed to determine the buckling load and postbuckling equilibrium paths. The numerical illustrations concern the postbuckling behavior of axially loaded, perfect and imperfect, FGM cylindrical shells with fully covered piezoelectric actuators under different sets of thermal and electric loading conditions. The results reveal that temperature dependency, temperature change and volume fraction distribution have a significant effect on the buckling load and postbuckling behavior of FGM hybrid cylindrical shells. In contrast, the control voltage has a very small effect on the buckling load and postbuckling behavior, and it has almost no effect on the imperfection sensitivity of the FGM hybrid cylindrical shells. [Copyright &y& Elsevier]

A quasi-conforming triangular sandwich plate element with 7 degrees of freedom (DOF) per node is established based on a simplified Zig-Zag model and a transverse shear deformation theory. The accuracy of the proposed element has been validated to be equivalent to the element based on the complete Zig-Zag model (11 DOF per note). The path-following method, proposed by Huang and Atluri, is improved and applied to follow complex postbuckling paths with secondary bifurcation points and progressive failure. A finite element (FE) modeling is completed to study the shear postbuckling behavior and failure of composite sandwich plates, based on the energy criterion of stability and the strength criterion of each layer. The basic characteristics of the shear postbuckling and failure are illustrated. The complexity and computation difficulty caused by secondary bifurcations and multi-paths are discussed. Numerical examples show that the proposed method is efficient in improving the convergence of iterations. [ABSTRACT FROM AUTHOR]

Abstract: The onset of fracture process in a layered composite with coplanar interface cracks under compression along layers is studied within the scope of 3-D theory of stability using the model of piecewise-homogeneous medium. Each layer consists of a matrix reinforced by continuous parallel fibres and is modelled by a compressible, linear elastic, transversely isotropic material. The eigenvalue problem with respect to the controlled parameters, namely, the crack length, the crack spacing and the 0°-plies layer volume fraction is solved for the shear and the extensional modes utilizing the finite element analysis by commercially available FE code. The results are obtained for 0°-plies volume fraction V 0° =0.1…0.9 for the typical dispositions of cracks. The effect of the crack length, the crack spacing and the 0°-plies volume fraction on the critical microbuckling strain in the composite was determined. [Copyright &y& Elsevier]

To get strong, stiff and light cylindrical shell, carbon fiber reinforced hierarchical Isogrid stiffened cylinder (HISC) was designed and fabricated. The cylinder has fractal stiffeners, including the first-order primary Isogrid stiffeners and the self-similar second-order sub-Isogrid stiffeners. The primary Isogrid has thick and high ribs and contains several sub-Isogrid cells whose rib is much thinner and lower. The primary Isogrid improves the bending rigidity of the cylindrical wall to resist the global instability while the sub-Isogrid improves the bending rigidity of the skin enclosed by the primary Isogrid to resist local buckling. The HISC was fabricated by filament winding method based on a silicone rubber mandrel with hierarchical grooves. Axial compression test was performed to reveal the failure mode. With hierarchical stiffeners, the cylinder balances the construction of the skin and the ribs and fails at material failure. Global instability and local buckling are both well restricted by the hierarchical stiffeners. [ABSTRACT FROM AUTHOR]

A theoretical study was carried out to predict the failure load and mode of composite anisogrid lattice sandwich cylinder (LSC) under fundamental loads. Four failure modes were suggested for this structure under axial compression, uniform external pressure and torsion, including global buckling, skin monocell buckling, rib crippling and strength failure. For each failure mode, the load capacity of the composite LSC was predicted theoretically and corrected by finite element method (FEM) with proper correction coefficients. To instruct the design of the LSC, failure mode maps were constructed, showing the dependence of failure mode and load on the geometrical variables of the lattice and skins. The concept of a failure mode map is extended to give a useful design tool for anisogrid sandwich cylinder manufacturers and their customers. [ABSTRACT FROM AUTHOR]

Abstract: This paper reports a multiscale modeling of the compressive behavior of carbon nanotube/polymer composites. The nanotube is modeled at the atomistic scale, and the matrix deformation is analyzed by the continuum finite element method. The nanotube and polymer matrix are assumed to be bonded by van der Waals interactions at the interface. The stress distributions at the nanotube/polymer interface under isostrain and isostress loading conditions have been examined. The buckling forces of nanotube/polymer composites for different nanotube lengths and diameters are computed. The results indicate that continuous nanotubes can most effectively enhance the composite buckling resistance. [Copyright &y& Elsevier]

Abstract: Two-dimensional (2D) hierarchical cellular materials made up of sandwich walls are predicted to have superior mechanical properties compared with solid-wall cellular materials. Equations of the stiffness, the buckling strength, the plastic collapse strength, the brittle failure strength and the fracture toughness were deduced. The enhancement of the mechanical properties of 2nd order hierarchical honeycombs is substantial (even an order of magnitude). The hierarchical honeycomb is much more damage tolerant and insensitive to wavy imperfections of the cell wall. Sandwich struts also enhance the buckling strength of the stretching-dominated 2nd order lattice grid material. Made up of sandwich struts, the hierarchical honeycomb has comparable mechanical properties with the stretching-dominated lattice grid material. [Copyright &y& Elsevier]

To reveal compression failure modes of one-dimensional (1D) lattice truss composite structures (LTCSs), parameterized finite element modeling (FEM) method and theoretical models were developed. LTCS has four failure modes: (a) fracture of the strut; (b) global buckling; (c) shell-like buckling and (d) mono-cell buckling. Changing the bay length and the column length, buckling modes of 8-node LTCS were revealed by FEM. It is found that enough column length could induce global buckling. When the column length decreases, the failure mode will turn to shell-like buckling and mono-cell buckling or strut fracture successively. Bay length greatly influences the buckling mode. Longer bay length could change the buckling mode from global buckling or shell-like buckling directly to mono-cell buckling. Theoretical models were proposed to predict the failure loads of LTCS. Through these models, failure maps were plotted to instruct optimal designing of LTCS. [ABSTRACT FROM AUTHOR]

In this work, the impact of high stress gradients, found in bending of thin unidirectional fiber reinforced shells (~0.1 to 1 mm), on compressive micro-buckling failure, was analyzed. Such thin shells show increased resistance to compressive failure under high curvatures, which may even allow tensile fiber damage to drive ultimate failure for very low thickness (e.g. <0.5 mm). The main scope of this work is to analyze this increased resistance to compressive failure and propose a robust modeling scheme. The mechanical failure response was captured by a shell-buckling experimental campaign. The origins of the increased compressive failure resistance were initially attributed to the reduction of shear stresses acting on the most susceptible domain of a representative wavy fiber. This effect was effectively described by an analytically derived, stress-gradient-dependent parameter. The hypothesis for the establishment of this parameter was corroborated by a numerical micromechanical model adopting the embedded cell approach. This model also revealed important micromechanical interactions which were incorporated by simple stress and strain factors. The derived failure prediction scheme was further extended to include the non-negligible, non-linear elastic material behavior of carbon fibers by means of a numerical algorithm. The validity of the failure prediction model was demonstrated by the successful comparison with results acquired from the shell-buckling experiments on a unidirectional carbon-fiber reinforced epoxy system. To this end, the validity of the initial hypothesis of stress-gradient-dependence on compressive failure was corroborated. Major effect on the overall behavior modeling has carbon fiber's material non-linearity, as well as micromechanical interactions. [Display omitted] [ABSTRACT FROM AUTHOR]

Abstract: A closed form model predicting debond growth in composite flanged joints is presented. This model calculates the non-uniform distribution of strain energy release rate (G) across the crack front. Such a model is useful for assessing the effects of partial debonds in adhesively-bonded joints that are subjected to compressive loads. The model’s accuracy is gauged by comparison of the G profile prediction with finite element analysis (FEA) based virtual crack closure technique (VCCT) calculations. For the woven glass/epoxy joints analyzed, it was found that the closed form model predicted the peak values of G to within 20% of the FEA calculated values when the applied far-field strain ε o was greater than 1.3 times the strain at which the flange first buckles, i.e., the critical buckling strain ε cr. At moderate loads (ε o <1.3ε cr), peak values of G were greatly under-predicted due to the nonlinear FEA predictions of ε cr being lower than the analytical values. Since the amount of strain applied beyond buckling (ε o − ε cr) drives postbuckling deformation, the FEA predictions for G tend to exceed the closed form values. Physical insight into which material and geometric parameters strongly affect this problem is gained due to the analytical model being presented in closed form. Such expressions are useful in conducting trade-off studies for damage tolerant designs and for making decisions related to maintenance and repair. [Copyright &y& Elsevier]

Abstract Kink-band nucleation and propagation has been monitored over time in three dimensions (3D) by time-lapse X-ray computed tomography (CT) in the compressive zone of a blunt notched unidirectional (UD) T800 carbon fibre/epoxy composite under in situ four-point bending (FPB). The kink bands that develop from micro-buckling are classified into two types, namely type 1 and type 2 by analogy with Euler buckling. Type 1 (shear) kink bands accommodate a lateral displacement of the fibres either side of the kink band; whereas type 2 kinks comprise conjugate pairs forming chevrons (accompanied by a tilt if the bands are wedge-shaped). In the central plane of the sample the kink bands lie in the plane of bending, whereas near the side surfaces the lack of lateral constraint means that type 2 kink band pairs protrude out of the surface (normal to the bending plane) from the notch corners down the sides of the sample. Moreover, a comparison of CT scans during loading and after unloading shows that geometries measured post-mortem on cross-sections may not be wholly representative, with the angle of the broken fibre segments within the kink bands reduced by 10–20° and the curvature of buckled fibres almost halved. The novelty of this work relates to the observation of the nucleation and propagation of fibre kink bands in three dimensions and the definition and quantification of kink band variables that could lead to more accurate modelling and simulation of compressive behaviour. [ABSTRACT FROM AUTHOR]

Abstract: An existing procedure based on the combined use of the Virtual Crack Closure Technique and of a fail release approach for the analysis of delamination growth phenomena in composite structures has been enhanced with a front-tracing algorithm and suitable expressions for the evaluation of the Strain Energy Release Rate when dealing with non-smoothed delamination fronts. The enhanced procedure has been implemented into a commercial finite element software by means of user subroutines and applied to the analysis of a composite stiffened panel with an embedded delamination under compressive load. The effectiveness and robustness of the enhanced procedure have been assessed by comparing literature experimental data and numerical results obtained by using different mesh densities in the damaged area (global/local approach). [Copyright &y& Elsevier]

Abstract: A new solid hexahedron element for composite delamination analysis is introduced. The 8-node solid is derived from a 20-node hexahedron element and has three translational and three rotational degrees of freedom. The particularity of this new element is its aptitude to be transformed into two physically independent 4-node shell elements. This separation into two shells is governed by a delamination criterion. Thus, the decrease in mechanical properties due to delamination, i.e., bending stiffness and buckling resistance, is correctly represented independently of the membrane stiffness which, in some cases, might stay intact. This element will be essentially used to model damages on structures like helicopter blades and sine-wave crash absorber beams. The actual classical modelling of such complex structures is onerous. The new element will allow simplifying models and decreasing the calculation time. Experimental tests are carried out on composite structures such as double cantilever beam specimens. The DCB test is modelled using the new element. A delamination criterion based on the virtual crack closure method and beam theory is used to govern the delamination propagation. The numerical simulation correlate well with the experimental results. [Copyright &y& Elsevier]