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Conical-cylindrical shells are common geometries in launch-vehicle structures as stage adapters and payload adapters, and they are susceptible to buckling due to their large radius-to-thickness ratios. Buckling design guidance is available but it is limited for conical and cylindrical shells. There is no available buckling design guidance for conical-cylindrical shells. This paper presents the validation of two finite element models used to successfully predict the buckling behavior of a composite conical-cylindrical shell with and without reinforcement tested in two separate campaigns. The laminate design for the first test campaign consisted of a quasi-isotropic layup. For the second test campaign, additional composite plies were applied to reinforce the transition region of the original laminate. The work presented demonstrates the ability to predict the buckling behavior of a composite conical-cylindrical shells with two different designs, which may aid in creating buckling design guidance for conical-cylindrical shells. Additionally, this paper shows that there is no appreciable benefit to adding reinforcement to the transition region if the intent is to increase the buckling load, due to the fact reinforcement brings increased buckling imperfection sensitivity to the shell. [ABSTRACT FROM AUTHOR]

This paper proposes a study on the thermal buckling of Variable Angle Tow (VAT) composite plates using high-order theories. Here, the governing equations are derived via the principle of virtual work. Under the assumption of linear pre-buckling, the stability problem is reduced to a linear eigenvalue analysis considering proportional geometric stiffness. In contrast, a constant thermal load is assumed to be known along the plate thickness, and the uncoupled thermo-mechanical formulation is used, where the thermal effects are described as external loads. The plate is discretized using the Finite Element Method (FEM) and high-order theories are developed using the Carrera Unified Formulation (CUF). Using the CUF, the equations are expressed as an invariant of the plate theory approximation order. Therefore, Equivalent Single Layer (ESL) and Layer-Wise (LW) models can be easily implemented. Several geometries and lamination cases are considered for verification purposes, including different side-to-thickness ratios and fiber orientations, which result in various anisotropy effects. In addition, the effect of changing constraints and materials is evaluated. Particular attention is paid to the effect of the structural theory approximation on the evaluation of the thermal buckling load. It is shown that the correct evaluation is highly dependent on the edge-to-thickness ratio and on the anisotropy given by both the fiber orientation and the material properties. As a final remark, sensitivity analysis and best fiber angle solutions are discussed to highlight the importance of the LW modeling approach. [ABSTRACT FROM AUTHOR]

Hybrid columns of FGM/FML type with inhomogeneous transverse structure perpendicular to their length are discussed. After that, laminated columns with different layups of laminate plies are discussed, with focus put on the effect exerted by many coupling of the stiffness submatrix on the lowest eigenvalue load. All columns were simply supported The study uses three methods for determining the lowest eigenvalues. The first two are analytical beam methods (i.e. 1D modelling approaches) based on the use of the Euler-Bernoulli theory. The proposed 1D methods are a generalisation of the well-known approach of determining the lowest eigenloads of isotropic columns. The first approach is to solve the eigenproblem directly from the differential equation of the deflection line. The second approach assumes that the curvature of the beam depends on the susceptibility of the beam. This is a fundamental assumption in the bending theory of beams and thin plates. The third method is the FEM (3D shell approach) which is used for the verification of the previous calculations. A comparison of the obtained results showed that the proposed 1D (one-dimensional) approach based on the full susceptibility matrix, which is the inverse stiffness matrix was as accurate as the 3D (three-dimensional) FEM shell model. The relative difference does not exceed 3%. Second 1D approach based on the stiffness matrix yields many times unacceptable differences relative to the reference results obtained by the FEM method. This comparison clearly demonstrates that an approach based on the assumption that curvature is directly proportional to susceptibility in flexural composite structures produces accurate results for all types of coupling. The existing literature extensively explores the impacts of stiffness matrix elements on both the linear and non-linear stability of laminate columns. However, there is a notable absence of studies focusing on the influence of susceptibility. This crucial aspect has been overlooked in prior studies. The present paper endeavors to fill this gap by shedding light on the influence of susceptibility, thereby emphasizing its significance in the analysis of laminate column stability. [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]

Abstract This paper aims to highlight the effect of SiO 2 substrate on the buckling behavior of Zinc Oxide (ZnO) nanotube. ZnO nanotube is modeled in various length and diameter to show the effect of size on buckling loads. Silicon Dioxide (SiO 2) is the material on which Zinc Oxide (ZnO) is grown and used as gas/chemical sensor. In present paper, SiO 2 substrate is modeled as two parameters elastic layer. In order to consider the elastic substrate, Winkler and Pasternak foundation models are used. Different values of elastic foundation parameters are taken into consideration to see the effect of these parameters on buckling loads of Zinc Oxide (ZnO) nanowire. Additionally, to take the size effect into consideration on calculating buckling loads, nonlocal elasticity, surface elasticity, modified couple stress, modified strain gradient theories are used. Some benchmark results have been depicted. Some detailed results are also given and compared in figures and tables. [ABSTRACT FROM AUTHOR]

Abstract The result of an experimental programme investigating a novel technique to strengthen web plates against breathing fatigue is presented in this paper; the programme was divided into five phases, including: (1) the development of a novel preformed corrugated FRP panel for strengthening thin-walled steel plate girder webs against buckling, (2) selecting the adequate adhesive and epoxy using double-lap shear and tension specimens, (3) producing the FRP panel, and (4, 5) testing its performance in two main experimental series; the initial (static) series and the final (cyclic) series. Only the initial series which involved tests on 13 steel plates strengthened with the proposed preformed corrugated FRP panel and subjected to in-plane shear will be reported in this paper. This series investigated the performance of different forms of strengthening under static load, in preparation for a subsequent series of cyclic tests to investigate their fatigue performance. Test results showed the efficiency of the technique at increasing the stiffness of the strengthened specimens in comparison to the unstrengthened ones and reducing the critical stresses which will serve as a precursor for the anticipated increase in the fatigue life of the girders. [ABSTRACT FROM AUTHOR]

Composite materials have been widely used in the field of pressure shells for underwater vehicles due to their great potential. This paper presents an experimental study of composite cylindrical shells with and without the circular hole subjected to external hydrostatic pressure. The mechanical response of the composite cylindrical shells under external hydrostatic pressure is recorded by the strain acquisition system, and the buckling deformation process of the shells is also captured by the high-speed camera system. According to the experimental results, the entire compression process of the shell can be divided into three stages based on variations in strain. Based on the findings that buckling starts very early and accounts for about 35 % of the entire process, the concept of initial buckling pressure is proposed to distinguish the critical point of the shell transition from a stable state to an unstable state. It is found that the damage positions of the three shells all correspond to the troughs in the buckling waveform, and the final fiber breakage of the perforated shells with the reinforcements both occur near the reinforcement component. Finally, a comparative analysis of the strain response of the shell with the hole and the complete shell is carried out to explore their similarities and differences. The experimental results in this paper provide valuable information for the design of perforated composite pressure shells for underwater vehicles. [ABSTRACT FROM AUTHOR]

In this paper, an equivalent damage model was proposed to predict the compressive behavior of three T-stiffened composite panels subjected to low velocity stiffener impact. A softening inclusion model combined with the reduction of material properties was used to describe the impacted stiffener damage. The progressive damage of the impacted stiffener and the failure of the panels under compression were simulated within the finite element software package ABAQUS. Compression-After-Impact (CAI) numerical results show that the compressive buckling modes of the stiffened panels are influenced by the damage degree of the impacted stiffener, and the fracture of the impacted stiffener triggers the global buckling of the panel. The buckling and failure loads of the panels predicted by this paper are in good agreement with the experimental results, which proves the validity of the model. [ABSTRACT FROM AUTHOR]

In this paper, the Dual Mesh Control Domain Method (DMCDM) is used to carry out the free vibration and buckling analysis of two-constituent Functionally Graded Beams (FGBs) with through-thickness material variation. The material composition (modulus and density) is varied continuously through the beam thickness according to a power-law. The Euler-Bernoulli beam model consisting of the displacements and bending moment as the primary nodal degrees of freedom (i.e., mixed model) and the Timoshenko beam model with the displacement degrees of freedom (i.e., displacement model) are formulated as eigenvalue problems using the DMCDM. The numerical examples presented consider typical beam boundary conditions and various power-law exponents and slenderness ratios. The accuracy of this method is demonstrated by comparing the numerical results with those available in the literature. [ABSTRACT FROM AUTHOR]

Buckling resistance of variable stiffness composite (VSC) plates can be significantly improved by designing fiber orientation distributions, which affect structural stiffness and stress distribution. In this paper, a meshless model of VSC plates is developed using a radial basis point interpolation method (RPIM) based on the naturally stabilized nodal integration (NSNI) scheme, and the buckling behavior of the VSC plates with elliptical cutouts is investigated. In this model, a set of nodes is used to discretize the problem domain, which makes the loading response of the VSC plates can be calculated by its exact fiber angle. And the mechanical behavior of the VSC plates with various complex geometries and cutouts can be accurately simulated. This meshless method is verified by comparing with the finite element method (FEM) and semi-analytical solutions. And compared with the traditional RPIM based on the Gaussian integration (GI), NSNI-based RPIM achieves considerable enhancement in computational efficiency while maintaining high accuracy. Employing this efficient meshless method, the buckling behavior of the VSC plates with elliptical cutouts for different boundary conditions is studied. And the effects of size and location of the cutout on the buckling response of the VSC plates are analyzed. The research on the VSC plates with cutouts in this paper has practical implications for the design of cutouts for VSC plates and provides a new method for the numerical research of VSC plates. [ABSTRACT FROM AUTHOR]

Unstiffened cylindrical shells are very sensitive to geometric imperfections such as production-related deviations from the ideal geometry (conventional imperfections) as well as imperfect boundary conditions, material and wall thickness imperfections (non-conventional imperfections). The load carrying capability of unstiffened shells is reduced significantly by those imperfections. The NASA SP-8007 design guideline from 1968 is currently used for shell design. This guideline provides knock-down factors for the buckling loads and is based on experimental data of isotropic and orthotropic test specimen. Therefore the structural behavior of composite material is not considered adequately. Based on the single-perturbation load approach (SPLA), this paper introduces a new physical based approach, to determine a lower bound for the buckling load of unstiffened composite cylindrical shells with respect to conventional and non-conventional imperfections, the constant single-buckle imperfection (CSBI) principle. The CSBI principle is based on the theory of the metastability of the geometric imperfect cylindrical shell which is introduced within this paper. The results indicate that the CSBI principle has the potential to provide an improved shell design in order to reduce weight and cost of thin-walled shells. [ABSTRACT FROM AUTHOR]

The design of glass fibre reinforced polymer (GFRP) pultruded members is often governed by deformability and buckling phenomena, preventing the full exploitation of the material potential. Hybridization – the partial replacement of the glass reinforcement with (stiffer) carbon fibres – is a possible approach to improve the performance of GFRP thin-walled profiles. This paper presents an experimental study on the structural behaviour of I-section hybrid fibre reinforced polymer (FRP) pultruded columns made of glass and carbon fibres (GF and CF) embedded in a polyester resin. A bare GFRP reference profile and four series of hybrid C-GFRP profiles, with different types and architectures of CF reinforcement, were designed, manufactured and tested under compression in three different lengths – short, intermediate and long. Particular attention was given to the buckling behaviour of the columns and to the delamination at the interface between GFRP and CFRP layers. In terms of serviceability performance, results obtained confirm the hybridization’s effectiveness in increasing the axial stiffness of GFRP compressive members. In terms of ultimate limit states behaviour, hybridization increased the load carrying capacity of the long columns, which exhibited global buckling. In opposition, for the short and intermediate columns, which failed respectively due to local buckling and a combination of global and local buckling, the load carrying capacity of the hybrid columns was lower than that of the reference profile; such worse performance seems to have been caused by the delamination of the CF layers, owing to the relatively high axial strains that developed in those columns. In a companion paper (Part 2), the experimental data presented and discussed herein is compared with predictions from numerical models and analytical formulae, which also provide further information about the delamination and progressive failure of the hybrid columns. [ABSTRACT FROM AUTHOR]

The structural behaviour of hybrid fibre reinforced polymer (FRP) pultruded members under concentric compression is studied in this paper (Part 2) through the use of numerical models – the experimental characterisation was presented in preceding paper (Part 1, Nunes et al., 2015). The hybridization of glass-FRP (GFRP) profiles is made through the partial replacement of the glass reinforcement with (stiffer) carbon fibres. First, a brief literature review shows the absence of available finite element (FE) models that take into account all the nonlinearities (material and geometrical) that influence the FRP column behaviour, and indicates the need to develop reliable and consistent models. Then, the FE model developed in this paper is described in detail. The elastic buckling behaviour of the columns tested in Part 1, with similar I-section shape but different configurations of carbon fibre reinforcement and different lengths, is evaluated. Three failure criteria for composite materials (Maximum Stress, Tsai–Hill and Hashin) are presented, implemented and their differences discussed. Using the Hashin criterion associated with a material damage model, progressive failure analyses were performed to simulate the nonlinear behaviour and failure of the hybrid columns. The numerical results comprise load – displacement curves, ultimate loads, stress – strain curves and failure modes, which are validated by comparison with the experimental results. Finally, the available design procedures for FRP columns are critically reviewed and applied to evaluate the columns’ ultimate loads. In this regard, it is shown that buckling prevails over material strength and that existing standards do not predict accurately the ultimate load of short columns or laterally braced columns. [ABSTRACT FROM AUTHOR]

This paper presents a comprehensive review of the various methods employed to study the static, dynamic and stability behavior of Functionally Graded Material (FGM) plates. Both analytical and numerical methods are considered. The review is carried out with an emphasis to present stress, vibration and buckling characteristics of FGM plates predicted using different theories proposed by several researchers without considering the detailed mathematical implication of various methodologies. The effect of variation of material properties through the thickness, type of load case, boundary conditions, edge ratio, side-to-thickness ratio and the effect of nonlinearity on the behavior of FGM plates are discussed. The main objective of this paper is to serve the interests of researchers and engineers already involved in the analysis and design of FGM structures. [ABSTRACT FROM AUTHOR]

Abstract: This is the first paper of a two-paper series describing design, implementation and validation of a strain and damage monitoring system for CFRP fuselage stiffened panels based on fiber optic Bragg grating sensors. The monitoring system was developed and tested on the basis of three load-scenarios: compression to failure of the undamaged panel, compression to failure of the impacted panel and compression to failure of the impacted and fatigued panel. This paper focuses on the design of the fuselage panel, the design of the monitoring system, the embedment of fiber sensors in the panel during manufacturing and the impact testing. The network of the sensors was designed based on a numerical buckling analysis from which the strain field of the panel was computed as a function of the applied compressive load. Embedment of fiber sensors in the panel was done so as to minimize risk of fiber breaking during manufacturing and impact testing and to effectively capture strains that are representative of damage developed in the panel due to compressive load. Barely visible and visible low velocity impact damage sites were created at different locations of the panel using a drop-weight impactor. The panels were inspected using C-scan just after manufacturing, to check quality of the material, and just after impact testing to detect impact damage at each location. [Copyright &y& Elsevier]

Abstract: This is the second paper of a two-paper series describing design, implementation and validation of a strain and damage monitoring system for CFRP fuselage stiffened panels based on Fiber Optic Bragg Grating (FOBG) sensors. The system was developed and tested on the basis of compression after impact response of the panel. The first paper describes the system design, the embedment of fiber sensors in the panel during manufacturing and the impact testing. In the present paper, mechanical testing of the panels and validation of the proposed monitoring system are described. The mechanical tests comprised three load-scenarios: compression to failure of undamaged panel, compression to failure of impacted panel and compression to failure of impacted and fatigued panel. In all cases the panel failed due to buckling. In order to monitor the panels’ behavior during testing and be able to validate the accuracy of the measurements of the FOBGs, a network of strain gauges were used. Impact damage and fatigue damage decreased the failure load and displacement at failure of the panel. The measurements taken from the FOBGs captured all changes in the buckling modes of the panel. Moreover, they showed a good correlation with the measurements taken from strain gauges. These findings validate the proposed monitoring system. [Copyright &y& Elsevier]

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]

Abstract: In this paper the dynamic and buckling features of slender structures with curved axis are addressed. A survey on the literature concerning mechanics of beams constructed with non-homogeneous materials or with functionally graded materials reveals only a few papers devoted to the dynamics and buckling of curved beams constructed with such materials. This problem was tackled mainly through 2D or 3D numerical formulations, but comprehensive beam theories on the matter are scarce. In the present paper a model of non-homogeneous and/or FGM curved beams is developed. The model is deduced by adopting a consistent displacement field which incorporates second order rotational terms based on the semi-tangential rule. The model also incorporates the shear flexibility due to bending and warping due to twisting effects. Arbitrary initial stresses and initial off-axis loads are taken into account in the linearized principle of virtual works. The finite element method is employed to discretize the motion equations with the objective to solve problems of dynamics, statics and buckling. The model contains, as particular cases, several straight beam theories as well as curved beam theories. Some comparisons with the available experimental data of the open literature are performed in order to illustrate the predictive features of the model, and comparisons with 2D and 3D finite element approaches are also performed. [Copyright &y& Elsevier]

The subject of the paper is a rectangular plate with symmetrically varying mechanical properties in the thickness direction. The nonlinear hypothesis of deformation of the straight line normal to the plate neutral surface is assumed. The field of displacements of the plate is formulated assuming this hypothesis. Based on the Hamilton's principle three differential equations of motion are obtained. The system of equations is analytically solved. The critical loads and fundamental natural frequencies for exemplary plates are derived. Moreover, the FEM model of the plate in the ABAQUS system is developed, and analogical calculations for exemplary plates are carried out. The calculation results of these two methods are compared. [ABSTRACT FROM AUTHOR]

Launch-vehicle primary structures like cylindrical shells are increasingly being built as monolithic composite and sandwich composite shells. These imperfection sensitive shells are subjected to axial compression due to the weight of the upper structural elements and tend to buckle under axial compression. In the case of composite shells the buckling load and imperfection sensitivity depend on the laminate stacking sequence. Within this paper multi-objective optimizations for the laminate stacking sequence of composite cylinder under axial compression are performed. The optimization is based on different geometric imperfection types and a brute force approach for three different ply angles. Decision tree-based machine learning is applied to derive general design recommendations which lead to maximum buckling load and a minimum imperfection sensitivity. The design recommendation are based on the relative membrane, bending, in-plane shear and twisting stiffnesses. Several optimal laminate stacking sequences are generated and compared with similar laminate configurations from literature. The results show that the design recommendations of this article lead to high-performance cylinders which outperform comparable composite shells considerably. The results of this article may be the basis for future lightweight design of sandwich and monolithic composite cylinders of modern launch-vehicle primary structures. [ABSTRACT FROM AUTHOR]

Abstract This paper presents a comprehensive study on structural failure of a trailing edge section cut from a composite wind turbine blade. The focus is placed on understanding progressive failure behavior of the trailing edge section in subcomponent testing during its entire failure sequence. Digital Image Correlation (DIC) is used to capture buckling deformation and strain distributions of the specimen. Detailed post-test inspection is performed to identify failure modes and failure characteristics. A nonlinear Finite Element (FE) model that accounts for all observed failure modes is developed based on continuum damage mechanics and progressive failure analysis techniques. Multiple structural nonlinearities due to buckling, contact and material failures are included in the model to predict the failure process. The study shows that in addition to the buckling-driven failure phenomenon, the surface contact of sandwich panels contributes to the failure process of the trailing edge section. Foam materials start to fail before the ultimate load-carrying capacity of the specimen is reached, while both composite materials and adhesive materials fail in the post-peak regime. The matrix-dominant failure and delamination develop before the fiber-dominant failure in composite laminates. The proposed FE model captures the progressive failure process of the trailing edge section reasonably well. [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]

Abstract This paper is dedicated to study the elastic buckling behavior of isotropic, laminated composite and sandwich beams subjected to various axially varying in-plane loads and boundary conditions (BCs). The formulation of the problem is derived by using the Ritz method with the displacement field based on a shear and normal deformable beam theory (SNDBT). Polynomial functions are employed to present the displacement field. The convergence studies are performed and then obtained results are compared with those of reported works. Results from extensive analysis are presented for different BCs, aspect ratios, orthotropy ratios, fiber angles and loading conditions. It is observed that the type of the axially variable in-plane load significantly affects the critical buckling loads and mode shapes of the beams depending on the BCs. The normal deformation effect depends on not only the aspect ratio but also BCs and the fiber orientation angles. [ABSTRACT FROM AUTHOR]

Abstract This paper was dealt with buckling and post-buckling behavior of short thin-walled Z-columns made of a carbon-epoxy laminate, subjected to eccentric compressive load. The buckling mode and the buckling load of real structures versus load eccentricity were discussed. The study involved both experimental tests were carried out on real laminated structures and numerical simulations by the finite element method. The buckling load of real structures was determined by approximation methods on the basis of experimental and numerical post-buckling equilibrium paths of the structure. Additionally, in numerical simulations, the bifurcation load value was determined by solving an eigen problem. In all cases, experimental findings and numerical results show high agreement. The study determined the quantitative influence of the direction and value of compressive load eccentricity on the buckling load and rigidity of the structure in the post-buckling state. [ABSTRACT FROM AUTHOR]

Abstract Damage tolerance is of critical importance to laminated composite structures. In this paper, we present a new semi-analytical method for predicting the strain at which delamination propagation will initiate following sublaminate buckling. The method uses a numerical strip model to determine the thin-film buckling strain of an anisotropic sub-laminate created by delamination, before evaluating the strain energy release rate for delamination propagation. The formulation assumes that all energy is available for propagation in a peeling mode (Mode I); avoiding an approximate mixed-mode criterion. Results are compared with twelve experimentally obtained propagations strains, covering a variety of laminates each containing a circular PTFE delamination. Comparison shows agreement to within 12% for balanced sublaminate tests in which delamination propagation occurred before intra-ply cracking. The method can be used to significantly improve the damage tolerance of laminates, opening up new opportunities for structural efficiency using elastic tailoring, non-standard ply angles and material optimisation. [ABSTRACT FROM AUTHOR]

Abstract Pultruded glass fiber reinforced polymer (GFRP) sections face a critical issue of premature web crippling failure when loaded in the transverse direction. However, limited research on the web crippling behavior of asymmetric sections like channel section was reported in the literature. In addition, the effect of specimen length on the web crippling behavior has not been explicitly investigated. This paper presents an experimental study on the web crippling behavior of pultruded GFRP channel sections under transverse bearing load. Four channel sections with various dimensions were tested under two transverse loading conditions, i.e. interior-two-flange (ITF) and exterior-two-flange (ETF). For each section, two specimen lengths were adopted to study the effect of specimen length on the web crippling behavior. Therefore, three variables including sectional dimensions, specimen length and loading conditions were considered in the experimental program. Two failure modes, namely web-flange junction failure and web buckling failure, were observed. The load-displacement curves and web crippling capacities of all specimens were reported and compared. Finally, design equations were proposed considering the failure mechanisms. The predicted web crippling capacities generally agreed well with the experimental results. [ABSTRACT FROM AUTHOR]

Abstract Natural fiber reinforced composites may have a great potential applications in the automotive and aerospace industries. Hydrothermal ageing in natural fiber reinforced composites leads to significantly degradation of their mechanical properties. This paper proposes a theoretical model for predicting the mechanical responses of bidirectional natural fiber reinforced composites under hydrothermal loading. Nine elastic coefficients of orthotropic composites after hydrothermal reaction and moisture absorption are obtained. Based on the present model, closed-form solutions for buckling load and frequency of a simply supported composite plate are derived. It is found that the elastic module and buckling load decrease monotonously with time, and approaches to a certain value with time. However, the frequency decreases with time firstly, and then increases with time, finally approaches to a certain value with time. In addition, the degradation of elastic modulus, buckling load and frequency for the composites with high fiber content are larger than those with low fiber content. This research may be helpful for designing natural fiber reinforced composites for applications in humid environments. [ABSTRACT FROM AUTHOR]

Abstract This paper investigates the in-plane instability of functionally graded multilayer composite shallow arches reinforced with a low content of graphene platelets (GPLs) under a central point load. The GPL weight fraction, which is a constant within each individual GPL reinforced composite (GPLRC) layer, follows a layer-wise variation along the thickness direction. The effective Young' modulus of the GPLRC is estimated by modified Halpin-Tsai micromechanics model. The virtual work principle is used to establish the nonlinear equilibrium equations for the FG-GPLRC arch fixed or pinned at both ends which are then solved analytically. A parametric study is conducted to examine the effects of distribution pattern, weight fraction, and size of GPL nanofillers and the geometrical parameters of the FG-GPLRC arch on its buckling and postbuckling behaviors. The conditions for multiple limit point buckling to occur in an FG-GPLRC pinned arch are also discussed. It is found that GPL nanofillers have a remarkable reinforcing effect on buckling and postbuckling performances of nanocomposite shallow arches. [ABSTRACT FROM AUTHOR]

Abstract Wind turbine blades present different types of failure mechanisms and modes which are associated with specific loading conditions. Trailing edge failure mode has been documented in full-scale blade tests as one of the failure types observed in blades on service. Trailing edge failure is characterized by failure of the trailing edge adhesive joint and the buckling of the trailing edge sandwich panels. This failure is governed by the contribution of edgewise, flapwise and torsion moments, with edgewise moments being the main driver. This paper describes a blade sub-component test setup suitable for studying trailing edge failure on static and fatigue load conditions, which is an improvement in the experimental verification of a trailing edge blade design. The test setup and design drivers are described and studied via FE models. Static and fatigue test results are reported for a full-scale blade section sub-component obtained from a 34 [m] wind turbine blade. Moreover, experimental results are discussed and compared with FE models to describe and study the trailing edge failure mechanism. [ABSTRACT FROM AUTHOR]

Abstract The present paper deals with the description of the stability loss and postbuckling for multilayered composite structures. Both, the experimental results and theoretical predictions are presented and discussed. The wide literature review is also pointed out considering the issue of both experimental and theoretical buckling analyses for composite rectangular plates and shells. A special attention is focused on the buckling and postbuckling behaviour od structures with cutouts and reinforcement. [ABSTRACT FROM AUTHOR]

Abstract: The available plate theories have been generally calibrated using linear strain–displacement expressions. Furthermore, many of them do not consider the transverse normal stress continuity and the transverse flexibility of the sandwich plates. Majority of the investigations performed so far in the buckling analysis of the sandwich plates, have been restricted to linear buckling analysis of the perfect sandwich plates based on theories that either violate the continuity condition of the transverse stresses at the layer interfaces or do not satisfy the mentioned condition when nonlinear strain–displacement expressions are used. Therefore, their results may be unreliable for nonlinear stress and buckling (especially in the postbuckling region) analyses. In the present paper, nonlinear strain–displacement expressions are employed for imperfect sandwich plates subjected to thermo-mechanical loads to propose an accurate global–local theory that satisfies the continuity of all of the transverse stress components. The theory is presented in a compact matrix form. Compatible Hermitian elements with C1 continuity are employed to enhance the results. Buckling and wrinkling loads are detected employing a criterion previously published by the author. Comparisons made in the paper with results reported by well-known references, confirm the accuracy and the efficiency of the proposed theory and the relevant solution algorithm. [Copyright &y& Elsevier]

Abstract: The buckling behavior of several simple tri-axial woven composite structures is studied. These structures include basic tri-axial structure, modified tri-axial structure and enlarged tri-axial structure. The structure is subjected to bi-directional loading. Approximate analytical method using equivalent anisotropic plate theory is presented in this paper. Its confirmation is obtained by non-linear finite element solution. Approximate analytical method provides a simpler way to obtain the buckling load, while the non-linear finite element method gives the numerical results and detailed analysis of buckling behavior of the tri-axial structures. The non-linear finite element analysis results reveal that the structures investigated in the paper approximately have the same buckling behavior, but with different values of buckling load. When more X-crossovers are involved in the tri-axial structures, their buckling loads increase and tend to approach a certain value. The results show that techniques used for approximate analytical solution can be used to obtain the buckling load of a real life tri-axial structure. The sensitivity of the buckling behavior of the basic tri-axial structure to the change in the boundary conditions and to the imperfection due to initial configuration is investigated. [Copyright &y& Elsevier]

This paper presents analytical and numerical evaluations of polymer matrix composite (PMC) infill wall systems, one of which was introduced by the authors [J. Struct. Eng. ASCE 129 (4) (2003) 440]. Used primarily as infill material for seismic retrofitting of steel frames, the basic PMC infill wall system consists of two fiber-reinforced polymer (FRP) laminates surrounding an infill of vinyl sheet foamcore. This paper addresses two issues crucial to an understanding of PMC infill wall systems: (1) a simplified method for predicting the maximum strength and critical design parameters essential for assessing the performance of a PMC infill panel, and (2) two simple compressive sandwich strut models are studied, and the results of one of these is compared to experimental data. Results obtained from simplified analyses have shown strong correlation with experimental data. Numerical simulations and discussions pertaining to various design parameters of PMC infill systems in steel frame structures are also presented in this paper. [Copyright &y& Elsevier]

In this paper experimental tests are described and discussed which illustrate the feasibility of buckling control in composite structural elements using induced strain actuation in a smart technological manner. Compressive tests on simply supported square composite plates which utilise the shape memory effect for buckling control are shown to exhibit substantially reduced post-buckling deflections when under activated control in comparison to those experienced for the uncontrolled case. The alleviation of the post-buckling deflections is shown to result in reduced non-linear stress levels in the post-buckling range and thus it is intimated that the ultimate failure levels of the composite plates can be improved through the application of shape memory control. The influence of temperature, from ohmic heating of the actuated shape memory alloy wires, on the mechanical performance of the composite laminated plates is discussed and the analysis procedures for the determination of the resulting non-uniform stress profiles in the composite plates are duly outlined. It was found that temperature effects could be significant and that these in turn depended to a large extent on laminate lay-up configuration. Particular attention is paid in the paper to tests carried out to ascertain the characteristic behaviour of the Nickel–Titanium shape memory material employed for actuation purposes. The cyclic recovery force capabilities of the actuator wires utilised in the compressive plate tests is highlighted and a detailed account of the determination of the alloys characteristic transformation temperatures is given. The paper discusses, in some detail, the feasibility of the proposed smart structural concept and gives some thought to the implementation of smart advanced composite materials within the marketplace with particular reference to future aerospace applications. [Copyright &y& Elsevier]

The buckling analysis of cracked functionally graded material (FGM) plates resting on an elastic foundation taking into account the effect of the delamination of the elastic foundation is presented in this paper. The plate kinematics are based on the high-order shear deformation theory, the buckling of this cracked plate is computed by mixing the phase-field theory and finite element method (FEM), and material properties are assumed to vary through the thickness direction by a power-law distribution. The cracked FGM plate rests on the two-parameter elastic foundation, in which, the delamination areas are rectangular and circular. The accuracy of the present approach is proved by the comparison with published results. This paper also studies the effect of some parameters on the mechanic buckling behavior of the plate. The numerical results reveal that the delamination area and the crack length have a strong effect on the buckling loads as well as the buckling mode shapes of this plate. [ABSTRACT FROM AUTHOR]

This paper focuses on strengthening carbon fiber hierarchical composite square honeycomb structures (HCSH) by selecting high-modulus hierarchical phase and optimizing its thickness. HCSH have been manufactured from carbon fiber composite foam sandwich structures by a simple snap-fit and bonding method. The measured compressive and shear strengths are shown to be well predicted by micromechanics failure models of HCSH. Compared to the monolithic composite square honeycomb structures (CSH), the measured specific out-of-plane compressive strength of HCSH improves to approximately 330% and the specific shear strength improves to about 180%. Furthermore, the relationships between hierarchical phase modulus and its optimum thickness are developed to design the optimum HCSH. Carbon fiber HCSH are found to exhibit better mechanical properties than other cellular structures, and thus provide new opportunities for light-weight multifunctional sandwich structures. [ABSTRACT FROM AUTHOR]

In this paper, we propose an efficient and accurate approach to investigate the post-buckling behavior of sandwich structures. In this framework, a novel one-dimensional layer-wise model using Euler-Bernoulli beam theory in the skins and higher-order kinematics in the core is proposed. The resulting nonlinear governing equations are then solved by the Asymptotic Numerical Method (ANM) with a bifurcation indicator, which is more reliable and efficient than the classical iterative methods, e.g., Newton-Raphson method, in terms of detecting critical points and computing bifurcated branches. Several numerical tests, i.e., global buckling, local wrinkling and global-local-coupling instability phenomena of sandwich beams, are performed and the results show that the proposed approach is able to efficiently and precisely characterize the critical loads and the post-buckling behaviors of sandwich structures. Finally, the effect of three aspects, i.e., kinematics, strain-displacement relationships and interpolation functions on the computational accuracy of predicting these instability phenomena are investigated. [ABSTRACT FROM AUTHOR]

In this paper insights are provided into the implementation and use of the Ritz method for free vibration and buckling analysis of composite plates. Focus is given on the choice of the trial functions in relation to the degree and the kind of anisotropy exhibited by the plates. The Ritz approximation is applied to models based both on the classical lamination theory and a more advanced variable-kinematic formulation, capable of dealing with several higher order plate theories within an unified framework. A very efficient computation of the Ritz integrals is proposed, which allows to handle hundreds of admissible functions. In this way, accurate upper bound solutions can be obtained even for problems where the convergence rate of the Ritz method is low due to extreme levels of anisotropy. The effect of different forms of elastic couplings, boundary conditions and amount of material anisotropy on the convergence and accuracy of the solution is investigated when different sets of admissible functions – Legendre and Chebyshev polynomials, as well as of trigonometric type – are adopted. Important remarks about the completeness and numerical efficiency of the selected basis are also provided. [ABSTRACT FROM AUTHOR]

This paper proposes novel Ritz functions for the size-dependent analysis of micro laminated composite beams with arbitrary lay-ups. Displacement field is based on a higher-order deformation beam theory and size effect is captured by the modified couple stress theory. Lagrange’s equations are used to obtain the governing equations of motion. The present beam model, which can recover the classical one by neglecting the material length scale parameter, is used to predict the size-dependent responses of micro composite beams. The results indicate that the present study is efficient for bending, vibration and buckling problems of micro composite beams. Some new results are given to serve as benchmarks for future studies. [ABSTRACT FROM AUTHOR]

In this paper, a shear deformable beam model for nonlinear stability analysis of frames made of composite materials is presented. Each wall of the cross-section is assumed to be orthotropic in such a way that normal stress does not cause shear strains to occur. The incremental equilibrium equations for a straight thin-walled beam element are derived within the framework of updated Lagrangian formulation and the nonlinear displacement field of cross-sections, which accounts for the restrained warping and the large rotations effects. Timoshenko’s theory for non-uniform bending and modified Vlasov’s theory for non-uniform torsion are applied to include the shear deformation effects. The coupled bending-torsion shear deformation effects occurring at the asymmetric cross-section are also included in the model. To account for the semi-rigid connection behaviour, the hybrid finite element is introduced through the special transformation procedure. Several benchmark examples are demonstrated for verification purposes. The obtained results indicate that the proposed model can be classified as shear locking-free one. [ABSTRACT FROM AUTHOR]

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

This paper aims to explore the behaviour of substandard reinforced concrete (RC) columns confined with Steel-Reinforced Grout (SRG) jackets under monotonically increasing uniaxial compression. A total of 24 specimens of short RC columns of square cross section were designed to fail due to longitudinal reinforcement buckling. Single-layered SRG jackets were applied to 18 of these specimens, whereas the rest served for control without SRG jackets. Parameters of this investigation were the type and density of the steel fabric as well as the corner radius of the cross section. The employed SRG jacketing managed to increase the strength and strain capacity and postpone the buckling of the longitudinal steel bars to occur at higher compressive strain level. Confinement effectiveness with respect to the lateral confining pressure exerted by the used SRG jacketing is discussed along with the observed mode of failure. [ABSTRACT FROM AUTHOR]

This paper presents the results of an experimental program investigating flexural creep and creep buckling behavior of pultruded glass fiber reinforce polymer (pGFRP) plate specimens. In this study (a) short-term material properties were determined; (b) 1000 h flexural creep tests at three load levels were conducted from which Findley power law parameters describing creep strain behavior were obtained; (c) creep buckling tests of slender concentrically loaded specimens were conducted; and (d) results from the buckling tests were compared with the predictions of the Findley power law which is shown to predict results reasonably well. Provided the flexural creep tests have relatively small loads and sufficient duration to pass through the primary creep stage of the material, reliable creep parameters were established. The intent of this study is to demonstrate a framework for establishing creep behavior and creep buckling performance of pGFRP materials. [ABSTRACT FROM AUTHOR]

Several sectors have increased the use of lattice structures due its great capacity to reduce the structural mass with reasonable rigidity loss. However, these structures can present complex mechanical behaviors, impossible to be determined analytically. Surrogate models obtained from design of experiments have been shown to be promising but insufficient. Numerical models using finite elements are computationally expensive when optimization model updating is considered. In order to solve these problems, in this paper a deep learning model is trained in order to predict 16 different structural responses (static, dynamic and stability) of a complex composite isogrid structure tube. All input data were generated from a numerical finite element model. The results demonstrated substantial capacity of the deep learning model to fit the isogrid physical behavior and also predict the structural responses. In addition, it was also to predict the design parameters of the isogrid structure from the desired results, also demonstrating the good performance (R2 > 90 %) of the artificial intelligence model to perform this prediction. [ABSTRACT FROM AUTHOR]

The hygro-thermal effects on vibration and buckling analysis of functionally graded beams are presented in this paper. The present work is based on a higher-order shear deformation theory which accounts for a hyperbolic distribution of transverse shear stress and higher-order variation of in-plane and out-of-plane displacements. Equations of motion are obtained from Lagrange’s equations. Ritz solution method is used to solve problems with different boundary conditions. Numerical results for natural frequencies and critical buckling temperatures of functionally graded beams are compared with those obtained from previous works. Effects of power-law index, span-to-depth ratio, transverse normal strain, temperature and moisture changes on the results are discussed. [ABSTRACT FROM AUTHOR]