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Welded omega-stiffened panels made of thermoplastic carbon composite with initial damage in the conduction welded joint are analysed and tested to investigate the damage tolerance in post-buckling. Finite element analyses are performed, using the virtual crack closure technique to investigate skin-stringer separation for both the pristine welded joint and joints with initial damage. A sensitivity study is executed for the initial damage size and location with different geometrical imperfections. Four omega-stiffened panels are tested, of which three have initial damage consisting of a foil at the welded skin-stringer interface. During the test, digital image correlation is used to measure the panels' deformation to determine the evolution of the buckling shape and the interaction with the initial damage. A high-speed camera is placed on the stringer side of the panel to capture the final failure. The panels fail in post-buckling when skin-stringer separation occurs, starting from the initial damage. The finite element analysis is able to predict the overall structural behaviour well, with conservative failure load predictions for panels with initial damage in the middle stringer. Although the initial buckling shape is predicted well, the buckling shape evolution at higher loads is difficult to predict. [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]

Kresling origami, a representative variant of origami, exhibits several distinctive features such as multistable states, changeable stiffness, and compression-torsion coupling deformation. The first focus of this study involves examining the mechanical properties of origami structures, specifically, the equivalent modulus and critical buckling stress during the deployment process are evaluated. Subsequently, the collapsibility of the Kresling origami structure is explicated with regard to energy and strain. In the folding process, when the Kresling angle is 0.0135 rad, the maximum torque is 959 Nmm, and the structure will occur snap-through instability, which is the nonlinear critical buckling load of the failure. After that, the torque decreases rapidly, and then gradually increases slowly. The mechanical model is developed and subsequently evaluated in terms of its flexibility and adjustment of stiffness. The present study investigates the buckling modes and vibration properties of Kresling origami structures, as well as their combination structures. For the buckling of Kresling origami structure, the critical buckling load of Euler buckling is 0.023 N and that of local buckling is 0.67 N. In short, the critical buckling load of the column shell is greater than that of the Kresling origami structure, which is due to the small local stiffness of structure. [ABSTRACT FROM AUTHOR]

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

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]

This study encompasses experimental and theoretical research on the stability of tensegrity-inspired structures in view of additive manufacturing technology. The aim of the research is to produce a qualitative and quantitative estimation of the post-critical behavior of struts in 3D-printed tensegrity-inspired modules. Presented results of compression tests performed on modules and single struts show that the bars work in the post-critical state before they reach their load bearing capacity. Comparison of theoretical solutions with experimental tests allowed us to conclude that the struts can carry axial loads significantly higher than the limits resulting from the classical Euler theory. [Display omitted] • Experimental and theoretical study on 3D-printed tensegrity-inspired structures. • Study of the post-critical behavior of additively manufactured struts. • The post-critical state is reached before the load bearing capacity is achieved. • The limit load of the struts is higher than the value predicted by the Euler theory. [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]

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]

The study aimed to analyse the stability and load-carrying capacity of compressed thin-walled composite columns subjected to axial compression. The subject of the survey was composite columns with closed square cross-sections made of carbon-epoxy composite. Different lay-ups of the composite material characterised the test specimens - several cases of lay-ups were considered. The application of the subject of the research is closely related to the use of these elements as load-carrying elements of aerospace and building structures. The requirements for such structures are closely related to the provision of a large reserve of load-carrying capacity after buckling. Experimental testing was carried out using a universal testing machine and other testing techniques, where acoustic emission, an optical deformation measurement system, and a digital microscope, among others, were used. Numerical simulations using the finite element method were carried out parallel to the experimental studies. In the case of FEA simulations, original numerical models were developed considering known failure models of the composite material. For both empirical studies and FEM simulations, an in-depth analysis of the buckling and post-buckling states was carried out, considering the failure phase of the composite material. The novelty of the present work was the development of original FEM models, allowing faithful reproduction of experimental studies conducted on physical models, as well as the use of research methods to determine the load-carrying capacity of composite structures. [ABSTRACT FROM AUTHOR]

The composite honeycomb sandwich with auxetic reentrant honeycomb (CSP-ARH) is a typical negative Poisson's ratio structure, which has better mechanical properties than composite structure with positive Poisson's ratio. In this study, a 2D asymptotic equivalent model (AEM) based on the variational asymptotic method (VAM) is proposed and used to analyze the vibration and buckling problems of CSP-ARH incorporating CFRP facesheets and an aluminum honeycomb core. After validation with 3D finite element results, a particle swarm optimization (PSO) algorithm is applied to optimize the mesoscopic size of composite facesheets and honeycomb core. The primary objectives of the optimization process involve maximizing the buckling load and natural frequency, minimizing the mass while satisfying specific mechanical properties requirements. Moreover, a few additional optimization iterations are performed to find the optimal shape coefficients of the curved fibers in the CFRP facesheets for variable stiffness composite sandwich panels. The shape of the curved fiber is defined using a cubic polynomial function f (x , y) and is described by a 20 × 20 grid of discrete elements. The results indicate that CSP-ARH with optimal curved fibers shapes exhibit superior performance compared to those with straight fibers, with buckling load and natural frequency increased by 8.18% and 7.09%, respectively. • VAM is extended to establish 2D-AEM of CSP-ARH, and verified by the 3D-FEM. • 2D-AEM reduces the DOFs of the CSP-ARH and improves calculation efficiency. • The PSO algorithm is applied to optimize the structural parameters of CSP-ARH. • The buckling and free vibration behaviors of CSP-ARH and CSP-ARH-CLF are studied. • Optimizing curved fiber direction improves the mechanical properties of CSP-ARH-CLF. [ABSTRACT FROM AUTHOR]

• Axial compression behaviour of BFRP tubes with three different cross-sections was studied. • The stress–strain curves of the BFRP tubes was classified into three stages of elastic, elastic–plastic, and plastic. • Three types of compressive failure modes were observed in the BFRP tubes. • Two design-oriented three-stage theoretical models were proposed for BFRP tubes with different cross-sections. • A stability equation was derived for predicting the compressive strength of slender BFRP tubes. This study analyzed mechanical properties and stability of pultruded basalt fiber-reinforced polymer (BFRP) tubes under compressive axial loading for large-span space and truss structures applications. This study assessed the compressive strength of BFRP tubes with three different cross-sectional shapes and investigated the failure modes under compression with slenderness ratios ranging from 20 to 150. The results demonstrated that short BFRP tubes can achieve a compressive strength of up to 122.36 MPa with a compressive elastic modulus of 40.39 GPa. Three types of compressive failure modes were observed in the BFRP tubes, including local material, critical, and overall buckling failures. Furthermore, based on the analysis of experiment results, two design-oriented three-stage theoretical models were proposed for BFRP tubes with three different cross-sectional shapes. The proposed models were able to predict both the stress–strain and load-lateral deflection curves by taking into account the post-peak softening behavior of the stress–strain curve. In addition, a stability equation was also derived for predicting the compressive strength of slender BFRP tubes and was validated by experiments. The predictions derived from proposed models were consistent with experiment results. [ABSTRACT FROM AUTHOR]

A variable stiffness optimization (VSO) algorithm is presented for optimizing variable-stiffness composite (VSC) plates with linear fiber path functions. A new definition of lamination parameters characterizing the distances between stacking configurations of VSC plates is presented. Using the inherent sensitivity of bending stiffness of composite laminates, the concept of "through thickness design" is introduced. The first step is to determine a good initial point for the VSC plates using three-dimensional sampling optimization (3DSO). The fiber angle design variables are then categorized into three groups. By optimizing the three groups' design variables sequentially and iteratively, the stiffness of the VSC plates is stiffened part by part until an optimum is reached. Lastly, the obtained optimum is redesigned accounting for the curvature constraint. The finite element method (FEM) is developed for the buckling analysis of VSC plates, and both Q4 and Q8 elements are employed to verify the accuracy and convergence of the FEM. Under a variety of boundary conditions and loading cases, FEM and VSO algorithm are used to maximize the buckling load of square and rectangular symmetrical VSC plates. Optimal results are compared with those available in the literature, demonstrating the effectiveness, robustness, and efficiency of the VSO algorithm. [ABSTRACT FROM AUTHOR]

Taking a biomimetic approach, this study introduces the use of a Voronoi diagram as an indicator of stiffener arrangement in stiffened composite panels. The locations of generator points that determine the shape of the Voronoi diagram are optimized for buckling problems under compression and shear load. An original optimization algorithm that combines the genetic algorithm and the finite element method is developed and implemented. The Voronoi diagram can also be used as an indicator for conventional, periodical stiffener shapes such as grid, lattice, honeycomb, and isogrid. We conducted parametric studies for periodical stiffener shapes, and demonstrated that these shapes can be designed using Voronoi diagrams. The results revealed that the optimized panel has a higher buckling load than that of conventional panels, and this methodology is effective for designing biomimetic stiffened CFRP panel structures. [ABSTRACT FROM AUTHOR]

In contrast to continuous-fiber-reinforced polymer (cFRP), the random distribution of fibers in short-fiber-reinforced polymer (sFRP), which depends on the manufacturing process, has a significant impact on the mechanical properties of sFRP components. In this study, an automatic joint injection-buckling analysis framework was developed that can simulate the injection process and predict the mechanical performance in sequence. This automatic analysis framework can be directly utilized to optimize the manufacturing process to improve mechanical properties. Based on this method, it is demonstrated that an sFRP plate (consisting of carbon fiber-reinforced polyphenylene sulfide) has better buckling resistance than an aluminum alloy plate with the same design weight. The buckling resistance can be further improved by manipulating the gate location in the injection molds. The optimization scheme was verified using the conventional analysis framework. Moreover, the optimization method was improved by utilizing a tensor-similarity-based algorithm, which can substantially decrease the time required to locate the optimal solution. [ABSTRACT FROM AUTHOR]

This article reports on the manufacturing, experimental testing, and finite element analysis of very thick and long carbon-fiber-reinforced polymers (CFRP) tubes under uniaxial compression (radius-to-thickness ratio ∼ 10 and length-to-radius ratio ∼ 21). Herein, long and hollow axisymmetric composite cylinders were produced through bladder molding. The CFRP tubes have two oppositely located cutouts in the middle of the structures. Three test specimens with different cutout diameters (5, 10, and 15 mm) were experimentally tested until failure. The experimental testing campaign was supported by digital image correlation, acoustic emission, and infrared thermographic measurements to investigate the damage propagation and failure analysis. The CFRP tubes failed at the cutout location due to fiber fracture. Linear static and geometrically non-linear analyses were performed using ABAQUS to analyze the CFPR tubes under axial compression. In general, numerical and experimental results are in good agreement if the maximum stress or Hashin criteria are applied. [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 work, a laminated sandwich plate model with external piezoelectric layers is extended for buckling and dynamic stability analysis. In-plane harmonic uniformly distributed loads are considered in the dynamic stability problem, and the Mathieu-type equilibrium equations are solved using Bolotin's method to obtain the regions of dynamic instability. The model is validated to begin with, using available results in the literature for static and dynamic buckling of laminated soft core sandwich panels. Ultimately, the model is used to simulate the behaviour of laminated composite and sandwich plates with piezoelectric patches, controlled using a closed loop law with proportional and derivative gains, for buckling and dynamic stability analysis. This control system is used to postpone buckling, increase fundamental frequencies and reshape the regions of dynamic instability. • Dynamic buckling of soft core sandwich plates with piezoelectric patches. • Finite element model developed for active soft core sandwich plates. • Proportional and derivative control used to reshape the dynamic instability regions. [ABSTRACT FROM AUTHOR]

This study is devoted to illustrate the mechanical buckling and free vibration analyses of double-porous functionally graded (FG) nanoplates embedded in an elastic foundation. A new quasi-3D refined plate theory is presented to model the displacement field. This theory contains only five unknown functions and considers the shear strain as well as thickness stretching. Based on the modified Mooney-type exponential relation, a new exponential law is presented to govern the materials variation and porosities distribution through the thickness of the nanoplates. The two porous nanoplates are bonded together by a set of parallel elastic springs and surrounded by Pasternak medium. The nonlocal strain gradient theory containing the nonlocal parameter and gradient coefficient is utilized to study the size-dependent effects. Based on Hamilton's principle, the equations of motion are drawn including the material parameters, elastic foundation reaction and biaxial compressive forces. An analytical approach for simply-supported and clamped bilayer porous FG nanoplates is implemented. The obtained results are compared with those available in the literature. Additional numerical calculations are introduced to show the influences of the material length scale parameters, inhomogeneity parameter, porosity factor and other parameters on the critical buckling and frequencies of the double-porous FG nanoplates. [ABSTRACT FROM AUTHOR]

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 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 A finite element method and phase-field model used by authors have been firstly extended to the buckling analysis of stiffened functionally graded (FG) plate with cracks. The finite formulation of the plate is based on the first order shear deformation theory (FSDT). The material properties of the FG plate change from the bottom surface to the top one by a power-law function, the stiffener is full of the material, which is the same as the bottom surface, where the stiffeners are attached to. Firstly this work studies on the accuracy of our results with reference solutions available in the literature. Then, the exploration of the interaction between the stiffeners and cracks under compressive buckling is investigated. The numerical results show much useful information for readers, scientists, designers, especially the smallest of the stiffener depth needs to add to the cracked FG plate to have a cracked one with stiffeners, which has the same buckling strength as the uncracked FG plate with no stiffeners. [ABSTRACT FROM AUTHOR]

Abstract A novel strengthening method using prestressed (PS) carbon fiber reinforced polymer (CFRP) strips was proposed. This method can be used for repairing existing steel columns or constructing new columns for high-rise buildings, power transmission towers and other buildings. Specifically, a prestressing system (PS system) can be used to prestress CFRP strips without using a hydraulic jack. A steel column, PS CFRP strips and the PS system comprise a self-balanced system that offers much greater stiffness against overall buckling than a pure steel column. To verify this strengthening method, axial compression tests are conducted. The results show that the buckling load of the PS-strengthened specimen is 2.5 times greater than that of an unstrengthened specimen, and the failure mode ranges between the first order symmetric and the second order asymmetric overall buckling mode. In addition, finite element analysis (FEA) was adopted to obtain the optimal prestress value, which can also be used as a guide in design. Finally, a simple calculation method of axial bearing capacity was proposed. [ABSTRACT FROM AUTHOR]

Abstract The buckling load parameters of the graded nanotube sandwich structure reported in this article under the influence of uniform thermal loading. The corresponding properties of the graded nanotube sandwich evaluated via the extended rule of mixture including temperature dependent properties of each constituent. The nanotube structural model derived mathematically using a higher-order polynomial displacement to maintain the required shear stress continuity and thermal distortion via Green-Lagrange strain. Further, the variational technique is adopted to obtain the governing equilibrium equation of the sandwich structural panel and the subsequent algebraic form achieved using the isoparametric displacement finite element steps. The computational buckling load parameter predicted using the own MATLAB code with the help of the current mathematical model. The model accuracy and the consistency are established through simultaneous convergence and validity study with available published results. Finally, the detail applicability of the current higher-order model is highlighted through a series of numerical examples and corresponding inferences. [ABSTRACT FROM AUTHOR]

Abstract Repair of a composite laminate with delamination using micro-bolts is studied parametrically. The effects on compressive buckling load of delamination crack length, bolt material, bolt diameter and arrangement, and bolt–laminate clearance are considered. For 45- and 65-mm crack lengths, buckling load recovery rates using brass bolts are 90% and 73%, respectively. Using steel increases the rate by 6.6% compared to the intact specimen. Tests are performed fixing the number of steel bolts for bolt diameters of 0.6, 1.0, and 1.2 mm. The buckling load recovery rate using 1.2- versus 0.6-mm bolts increases by 6.8%. Finite element analysis confirms the effect of the bolt–laminate gap: 27% larger buckling load for no clearance than for a 0.1-mm gap. 18% higher buckling load, which is 97% of intact-specimen buckling load, is obtained for a 1.2-mm-diameter bolt repair by gluing bolts and holes and then tightening them compared with using bolts alone. [ABSTRACT FROM AUTHOR]

Abstract The study investigated thin carbon/epoxy composite plate elements with a central cut-out of regular shape, under uniform compression. The aim of the study was to investigate the possibility of using these elements as elastic elements whose stiffness depends on tailoring the cut-out geometry and laminate ply orientation. To ensure stable operation of the structure in the postbuckling range, the plate was assigned the properties of an unsymmetrical lay-up with extension-twisting and extension-bending couplings. The structure was analysed numerically by the finite element method. The scope of numerical simulations included linear analysis of an eigen problem using procedures for geometrically nonlinear analysis and the commercial simulation software ABAQUS®. The aim of the analysis was to determine a laminate ply orientation generating the lowest buckling mode (flexural-torsional) in order to ensure stable operation of the structure in the postbuckling range. [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 The study investigates the effect of eccentric load on the stability and postcritical states of thin-walled CFRP channel section columns under compression. Test specimens are subjected to compression on a testing machine provided with a fixture for applying eccentric compressive loads. Loading forces, deflection and strains of the column walls and web are measured. The experiments also involve examination of the operating performance of a structure undergoing buckling and determination of its postcritical equilibrium paths describing the relationship between load and deflection. Based on experimental results, numerical models of composite structures are designed and verified by the FEM. The scope of the numerical analysis involves performing a linear analysis of stability, which allows for determining the buckling mode depending on the amplitude of compressive load eccentricity and corresponding critical loads. The next stage of the analysis involves performing a nonlinear analysis of the structures with implemented geometric imperfections reflecting the lowest buckling modes. Based on obtained results, postcritical equilibrium paths of the developed FEM models are determined. Obtained equilibrium paths are then compared with experimental characteristics of real structures. The numerical results and experimental findings show a satisfactory agreement. [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 The composite materials used at sea are today nearly all based on thermoset resins (polyester, epoxy). However, there is an increasing number of thermoplastic matrix polymers available on the market (PP, PA, PPS, PEEK...), which offer possibilities for forming by local heating, attractive mechanical properties and the potential for end of life recycling. The aim of this study was to design, manufacture and test thermoplastic composite pressure vessels for 4500 m depth, in order to establish a technical, economic and ecological assessment of the use of these materials to replace traditional composites underwater. First, finite element calculations have been carried out to optimize the stacking sequence with respect to the external pressure and buckling resistance. Thick thermoplastic cylinders were then manufactured and tested until implosion, their behaviour showed a good agreement with calculations. Overall, the results show that it is possible to use Carbon/Polyamide 6 (C/PA6) thermoplastic composite cylinders for deep sea applications, as implosion pressures higher than 600 bar (6000 m depth) were achieved. [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 The ability to steer carbon fibre tapes, varying the tow angle, can widen the designs possibilities of cylindrical shells that are one of the main components of aerospace structures. This research presents experimental and numerical investigation of two carbon fibre reinforced plastic cylindrical shells – a cylinder with conventional layup made of unidirectional prepreg and a variable-stiffness cylinder manufactured by applying fibre placement technology. The shells were tested in compression until buckling and later subjected to a vibration analysis. Load-shortening curves and buckling shapes were acquired during the compression tests, while the natural frequencies and the mode shapes were measured during the vibration tests. Both tests provide a useful data set of the mechanical response of the cylinders which can be applied for further validation of models. The acquired experimental results were compared to a simple, approximated numerical model of the variable-stiffness cylinder showing good correlation with the test results. [ABSTRACT FROM AUTHOR]

Abstract 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 The result of an experimental programme investigating a novel technique to strengthen web plates of steel plate girders against breathing fatigue due to shear buckling deformations is presented. An experimental test series is present in which six specimens were manufactured to simulate the end panel of a plate girder; these were strengthened with an optimized FRP retrofit panel that was developed in an earlier phase of the research project, and tested for plate girder web shear buckling deformation mitigation under repeated cyclic loading, as well as ultimate load capacity enhancement. Test results and non-linear finite element modelling demonstrated the efficiency of this technique for stiffening the web against these deformation and thus reducing the critical stresses, consequently increasing the fatigue life of the girders by a factor ranging between three and seven, depending on the applied stress range and the fatigue resistance assessment method. The research demonstrates the applicability of this novel FRP strengthening technique to prolong and extend the fatigue life of existing plate girder bridges. [ABSTRACT FROM AUTHOR]

Abstract The vibration and buckling of the coating-FGM-substrate conical shells (CFGSCSs) with mixed boundary conditions (MBCs) under the hydrostatic pressure are studied. The basic equations of CFGSCSs are displayed based on the Donnell-type linear shell theory and solved using by Galerkin's method. The novelty of current study is to obtain formulas for the critical hydrostatic pressures (CHPs) and the cyclic frequencies (CFs) of CFGSCSs with the MBCs. Finally, the influences of FGM cores and variation of the material gradient index on the CFs and CHPs for CFGSCSs are studied. [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 The increasing need for automatic mesh generation has led to the development of efficient triangulation algorithms that are able to discretize any 2D or 3D domain. Modern finite element formulations based on strain smoothing techniques (SFEM) provide enhanced convergence properties, preventing yet the stiffening behavior of triangular meshes. Recent research has shown that meshless methods based on triangular mapping of the integration domain can be used to produce even better convergence properties than SFEM. The present study explores the Edge-based Smoothed Point Interpolation Method (ES-PIM) as a meshless solution to investigate linear buckling on variable angle tow (VAT) laminates. Such advanced composite structures show a heterogeneous distribution of constitutive properties and thickness, presenting additional challenges to the numerical solution. Important aspects related to the transverse shear correction herein adopted are investigated, leading to interesting conclusions regarding the possibility to use the ES-PIM for conservative estimates of the critical buckling load of VAT laminates. [ABSTRACT FROM AUTHOR]

Abstract The translation of natural (or biological) structures into synthetic materials offers a spectrum of feasible pathways towards enhanced or even unprecedented material properties for a wide range of applications. Inspired by excellent mechanical properties of stomatopod dactyl club, herein we propose a new functionally graded material (FGM) model that can adequately describe the characteristics of hierarchical structures in the stomatopod dactyl club. The proposed FGM model is incorporated into extended finite element method with stabilized discrete shear gap to investigate the mechanical buckling behavior of the plate made of materials similar with that in stomatopod dactyl club. The critical buckling factors for cracked FGM plates are computed and analyzed. Numerical results show that the design motif of bioinspired FGM increases the normalized buckling factor, even higher than that of homogenous plates, which suggests that the stability of plates can be enhanced by the use of bioinpsired FGM. The proposed FGM model opens a broad avenue to explore more fascinating mechanical properties of hierarchical gradient materials inspired by stomatopod dactyl club. [ABSTRACT FROM AUTHOR]

Abstract A Notched Curved Compact Tension (NCCT) and Extended Notched Curved Compact Tension (ENCCT) specimen geometries are presented for the measurement of translaminar critical strain energy release rates in composite laminates with low compressive to tensile strengths. Premature compressive and buckling failure occurred when a conventional Compact Tension (CT) specimen geometry (similar to ASTM E399 (2013)) was utilised for monolithic Non-Crimp Fabric (NCF) S2-Glass/MTM57 epoxy composite and an interlayer fibre hybrid T700 carbon spread tow/NCF S2-glass epoxy composite. The NCCT and ENCCT specimen design methodology and manufacturing routes are presented where premature compressive failure was mitigated through a curvature at the rear of the profile and the introduction of a through-thickness groove that had been pre-cured along the crack growth region. The latter ensured that buckling was eliminated, whilst stable crack growth was achieved. The development involved FE model material validation and optimisation for the novel specimen design. Experimental tests presented both interlayer and intralayer fibre hybrid composites with good repeatability and low scatter within the 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 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]

Abstract Buckling of axially functionally graded and nonuniform Timoshenko beams is examined based on the nonlocal Timoshenko beam theory. Small scale effect on the buckling is taken into account via the length scale parameter often referred as the nonlocal parameter. The material properties vary in the axial direction and the nanobeam is modelled as a nonuniform Timoshenko beam which rests on a Winkler-Pasternak foundation. Rayleigh quotients for the buckling load are derived for Euler-Bernoulli and Timoshenko beams. Chebyshev polynomials based on the Rayleigh-Ritz method is used to obtain the numerical solution of the problem for a combination of clamped, simply supported and free boundary conditions. Accuracy of the method is verified by comparing the buckling loads obtained by the present approach with those available in the literature. Numerical results for the problem are given in the form of contour plots to study the effect of nonlocal parameter, cross-sectional non-uniformity, axial grading and the boundary conditions on the buckling loads. [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]

Highlights • A coupled mechanochemical model is proposed for buckling simulation. • The buckling behavior is strongly dependent on SOC & electrochemical process. • Lithiation-soften of active material remarkably reduces the buckling stability of cell system. • Design insights into enhancing the buckling resistance of electrode are provided. Abstract This work has proposed a coupled mechanochemical model to investigate the buckling performance of electrode and thereby enhance the mechanical integrity of lithium-ion batteries. This method based upon finite deformation theory is capable to simulate the state of charge (SOC) and path dependent buckling phenomenon of the layered structure. It is revealed that the buckling behavior of an electrochemical loaded electrode depends not only on the material properties and the electrode geometry but also on the charging/discharging process, SOC as well as the operation current rate. Moreover, with regarding to the lithiation stiffening active material, the results show that increasing the current density in lithiation while decreasing it upon delithiation can increase the relatively critical buckling load, and contribute the electrode to withstand buckling failure. As for the lithiation softening one, it is disclosed that the bucking resistance would be impaired in lithiation and recovered upon full delithiation. In addition, to eliminate the adverse effect of lithiation soften on the electrode buckling resistance, design insights into the current collector have been provided. [ABSTRACT FROM AUTHOR]

Abstract A refined four-unknown quasi-3D zigzag beam theory is developed to model the free vibration and buckling behaviors of multilayered composite beams subjected to axial mechanical loading (e.g., distributed load and terminal force) and uniform temperature variation. Types of the composite beams considered include laminated composite beams, sandwich beams with composite face sheets, and fiber metal laminates. The proposed theory accounts for not only thickness stretching but also interlaminar continuity of transverse shear stresses and displacements. Associated eigenvalue problems for various boundary conditions are derived using the Ritz method. Accuracy and effectiveness of the theoretical predictions are verified by comparison with existing results and present finite element simulations. The theory is employed to quantify the effects of axial distributed load/terminal force and temperature variation on free vibration and buckling for different boundary conditions, geometric parameters and material properties. The present theory could produce sufficiently accurate predictions of natural frequencies and buckling capacities of multilayered beams at a very low computational cost. [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 This study considers the buckling of double nanofibers embedded in an elastic matrix based on an Euler-Bernoulli beam model. A scale dependent doublet mechanics theory is used in modelling of the double nanobeam system. Critical buckling loads are obtained using doublet mechanics and results are compared with the classical elasticity theory. The variation of critical buckling loads with different beam length, doublet separation distance and stiffness of the springs are investigated. Some mode shapes of the double nanobeam system are presented. [ABSTRACT FROM AUTHOR]