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• The elastic instability phenomenon in hyperelastic layered materials with the phases exhibiting stiffening behavior is studied • A closed-form expression for the critical stretch of macroscopic instability is derived • An analytical prediction based on Bloch-Floquet analysis for the microscopic instability is exhibited • The critical parameters and transition of instability modes are found to be highly tunable with phase stiffening This paper investigates the elastic instability behavior in soft periodic laminates subjected to finite strains, with a focus on both macroscopic and microscopic instabilities. Considering the deformation-induced phase stiffening, the Gent model with a high bulk-to-shear modulus ratio describes the behavior of incompressible phases. This non-Gaussian statistics-based model captures the non-linear constitutive results from the limited extensibility of polymeric molecular chains. This paper derives an analytical prediction for the onset of macroscopic (or longwave) instability and microscopic instability as functions of material parameters. Moreover, a numerical Bloch-Floquet analysis is imposed on identifying the instability behavior under compression. We consider a wide range of phase combinations and find that the relatively rapid stiffening of the matrix compared to the stiff layer increases the stability of laminates by decreasing the critical stretch ratio. Essentially, properly manipulating the stiffening parameters can produce an absolutely stable region without observed instability. This paper also systematically illustrates the changes in instability and the transition between macro and micro instability in fully Gent laminates, which show higher stability than fully neo-Hookean laminates with larger critical stretch ratios. The critical characteristics of instabilities, such as critical stretch ratios and critical wavenumbers, can be controlled by the choice of stiffening parameters and other material properties, enlarging the tuning of soft laminates for desired buckling patterns in practical applications. [ABSTRACT FROM AUTHOR]

A novel meshfree local method is developed in the context of Trefftz approaches to solve eigenvalue problems related to buckling and free vibration of arbitrarily shaped thin plates, potentially having complicated cutouts. The formulation is based on Kirchhoff's assumptions for thin plates with C 1 continuity of the solution function. The mesh grid is replaced by a set of nodal points containing the degrees of freedom, located over the domain and its boundaries, thus removing the need for heavy mesh generation process. A sub-domain (cloud) centered at each node and containing several adjacent nodes is considered, in which the approximation functions are defined. The bases are made from Exponential Basis Functions (EBFs), so as to automatically satisfy part of the governing PDE and thus, removing the numerical integration procedure and increasing the solution accuracy. Due to the existence of indefinite values as the critical buckling load or the free vibration frequency, Trefftz approaches have difficulties to directly apply for eigenvalue problems. To resolve this, first the homogeneous eigenvalue problem converts into a non-homogeneous problem by moving the parts with indefinite eigenvalues to the right hand side of the equality and keeping the rest on the left. The solution to the whole eigenvalue problem is approximated using a series of EBFs. Then the solution to the homogeneous part is interpolated using another series of EBFs capable of exactly satisfying the homogeneous part of the newly defined PDE, while the particular solution is approximated using the eigenvalue solution series defined at the first step. Numerical results reveal that the proposed method can efficiently produce results with high accuracy. [ABSTRACT FROM AUTHOR]

• Using the FG-X graphene pattern in channel section struts boosts the critical buckling temperature by 12 % for clamped and 9 % for simply-supported struts, compared to the FGO pattern. • For a shape factor of b f / b w = 0.2 , changing graphene in the flanges minimally affects strut buckling temperature. However, altering the web's graphene pattern, with consistent flange reinforcement, can alter the temperature by up to 12 %. • The study on thermal pre- and post-buckling vibrations in struts with various graphene patterns reveals FGX configurations yield the highest frequencies through the pre-buckling state, though this trend shifts in the post-buckling. • Integrating an asymmetric graphene pattern (FGV) or embedding geometric imperfections sustain the primary natural frequencies of FG-GRC channel section struts above zero as they approach the critical buckling temperature. This study explores the effect of local buckling on the compressive performance of slender structural elements, particularly those with thin-walled sections. The phenomenon of local buckling significantly reduces the axial compressive stiffness, leading to a notable decrease in the load-bearing capacity of these elements. The main goal of this research is to examine how the post-buckling characteristics of polymeric composite channel section struts can be improved under thermal loading by incorporating multi-layer graphene reinforcements. The solution methodology incorporates the von Karman geometrical nonlinearity and is based on the layerwise third-order shear deformation theory (LW-TSDT). To ascertain the precision and computational performance of the results derived from LW-TSDT, a three-dimensional (3D) finite element model is created in ABAQUS for comparative evaluation. An extensive analysis of nonlinear thermal instability in perfect and geometrically imperfect FG-GRC laminated channel section struts is undertaken to discern the graphene distribution patterns that are most and least effective in elevating the critical buckling temperature and natural frequencies through pre- and post-buckling conditions. The comparative analysis indicates that employing the FG-X graphene distribution pattern across the thickness of the web and flanges in channel section struts leads to a projected increase of 12 % in the critical buckling temperature for clamped channel section struts, in contrast to those that adopt the FGO graphene distribution pattern. For cases with simply-supported boundary conditions, this increase is noted to be approximately 9 %. Moreover, findings confirm that incorporating an asymmetric graphene distribution pattern (FGV) or introducing geometrical imperfections in the flanges and web that generate a bending moment within the structure from the beginning of thermal loading effectively prevents the primary natural frequencies of FG-GRC channel section struts from declining to zero close to the critical buckling temperature. This is significantly different from scenarios involving perfectly structured and symmetrically reinforced graphene distribution patterns such as FGX. [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]

Thin-walled prismatic metallic members as well as structures made of laminated composite materials are routinely employed in engineering branches such as civil engineering or lightweight construction and design. Due to their thin-walled nature, such structures exhibit a number of specific characteristics that need to be taken into account during analysis and design. One of these special features is the tendency to exhibit an interaction of local, global and distortional deformation patterns which has a major impact on the structural response in the framework of first-order analysis, but also concerning the buckling, postbuckling and vibration behavior of such structures. One analysis method that takes such effects into account in a natural and straightforward way is the so-called Generalized Beam Theory (GBT), and this paper aims at providing an overview of the state of the art in this specific field. In all, 460 references are cited. • Presents a state-of-the-art survey of the Generalized Beam Theory for the analysis of thin-walled structures. • Presents an encompassing literature survey sorted by working groups around the world. • Enables researchers to find their own starting point in research in this specific field. • Includes 460 references. [ABSTRACT FROM AUTHOR]

• Higher order FEMs are proposed for bio-inspired laminated composites plates using a quasi-3D theory for the first time. • Three different FEMs are derived based on non-conforming elements with different number of nodes and degree of freedom. • No shear locking phenomenon was observed in the analyses conducted using these FEMs. • Effects of lamination scheme, orthotropy ratio and aspect ratio on the mechanical response of the bio-inspired helicoidal composite plates are examined. A comprehensive study is carried out by employing various finite element models (FEMs) for the bending, buckling stability and free vibration analyses of bio-inspired helicoidal composite plates with various lamination schemes. A higher order quasi-3D kinematic plate theory is developed to include a shear deformation effect. The variational formulation of the problem is exploited to derive the equations of motion, element stiffness, geometrical stiffness, and mass matrices based on a non-conforming rectangular element. Three different finite elements models are derived based on non-conforming elements with different number of nodes and degree of freedom. The developed finite element model has been validated with those found in the open literature. The effects of boundary condition, lamination scheme, orthotropy ratio and aspect ratio on the mechanical response of the bio-inspired helicoidal composite plates are examined. Notably, for the lamination schemes investigated in this study, no shear locking phenomenon was observed in the analyses conducted using these FEMs. Dimensionless centre deflections, critical buckling loads and fundamental frequencies of bio-inspired helicoidal composite plates vary depending on the type of lamination scheme, boundary condition and aspect ratio. The new orientation schemes can replace the traditional ones to overcome the shear singularity and overcome the delamination defects. [ABSTRACT FROM AUTHOR]

The mechanics of laminates made up of elastic alternating stiff/soft layers is dominated by bending and membrane actions in the stiff layers, while transverse shear deformations concentrate in the soft interlayers producing significant zigzag warping effects. Additionally, curved geometry and large deformations can induce an interlayer thickness strain affecting the overall response of the laminate. This work presents a rotation-free Total Lagrangian large deformation curved shell model to accurately capture such a structural response. Each stiff layer is modeled as a Kirchhoff–Love shell. Without additional DOFs, each soft interlayer is modeled as a solid-shell by expressing, in finite kinematics, the displacement of top and bottom interfaces as a function of the mid-surface displacement of the upper and lower stiff layers it couples. The model is characterized by a sparse stiffness matrix compared to high-order theories and requires a small number of DOFs (3 per stiff layer) to reproduce the 3D solution. A NURBS discretization meets the high continuity of the weak form with a patch-wise reduced quadrature to avoid locking and enhance efficiency. All thickness integrals are pre-computed just once. • A nonlinear shell model is developed for stiff/soft laminates. • It is reliable for curved laminates and large deformations. • The stiff layers are isogeometric Kirchhoff–Love shells. • The soft layers are solid-shells without independent DOFs. • Warping and thickness change are captured with minimal DOFs. [ABSTRACT FROM AUTHOR]

• A novel multiscale analysis is developed to assess the buckling behavior of MWCNT-reinforced laminated composites. • Integration of microstructural factors like MWCNT clustering, alignment, and curvature in evaluating composite material performance. • Comprehensive assessment of the influence of moisture and temperature on the buckling performance of MWCNT composites. • Results successfully compared and validated with existing experimental and theoretical data. • Offers significant insights for the design and optimization of MWCNT-reinforced composites. This study introduces a detailed method for analyzing the buckling behavior of laminated composite structures strengthened with multi-walled carbon nanotubes (MWCNTs). We propose a multi-scale analysis that combines analytical and computational techniques to assess the mechanical performance of MWCNT-reinforced composites under combined moisture, temperature, and mechanical stress conditions. The Halpin-Tsai equations are used to calculate the overall stiffness properties of the nano-enhanced matrix, considering factors like MWCNT clustering, alignment, and curvature. Additionally, we incorporate the nanoscopic, size-dependent features of MWCNTs into our model. The Chamis micromechanical formulas are applied to determine the individual elastic properties of the nanocomposite layers, considering the impacts of temperature and moisture. We then explore how variables such as MWCNT content and size, along with temperature and moisture levels, influence the critical buckling load of MWCNT-based laminated composite beams and plates using our multi-scale model. Our results are successfully compared with existing experimental and theoretical data to validate our approach. The developed method offers significant insights for the design and optimization of MWCNT-reinforced composites, potentially benefiting various engineering fields, including aerospace and automotive industries. [ABSTRACT FROM AUTHOR]

• A sequential permutation search (SPS) optimization algorithm is presented for stacking sequence design of composite plates. • SPS is a mechanics-driven algorithm utilizing convexity of lamination parameter and stiffness sensitivity. • Buckling load of composite rectangular plates with various boundaries and load conditions are optimized by SPS algorithm. • The sign optimization algorithm (SOA) is coupled in the SPS to regulate the bending-twisting coupling effects. • Comparisons are performed among SPS, LOA, and GA, demonstrating higher efficiency and robustness of SPS. Buckling problem of composite plates is of importance since it is commonly encountered in thin-walled structural components in engineering. Buckling resistance design of composite plates involves the design of laminate stacking sequence exhibiting high dimensional discrete variables owing to the combination and permutation of ply orientations of layers. In this work, a sequential permutation search (SPS) optimization algorithm is presented for the stacking sequence design of composite rectangular plates accounting for the inherent physical-mechanical behavior of composite laminates. Owing to that the governing equation for buckling of composite rectangular plates is a linear homogeneous equation on bending stiffness parameters, the convexity of flexural lamination parameters and sensitivity of bending stiffness are utilized to construct sensitive detection techniques and linear search procedures. Moreover, to increase the robustness of SPS, a sign optimization algorithm (SOA) is coupled in SPS to regulate bending-twisting coupling effects. The SPS algorithm is applied to the buckling resistance design of composite rectangular plates exhibiting various boundaries under axial compression, where the Rayleigh-Ritz method is developed to perform the buckling analysis. Optimal results of SPS are compared against layerwise optimization approach (LOA) and genetic algorithm (GA), illustrating its reliability and efficiency. [ABSTRACT FROM AUTHOR]

• A simulation of multiple transverse ply cracking in laminates is presented. • Many phase-field variables are used, each one describes the crack of the layer. • Some interesting phenomenons when the cracks appear at different layers of the structure are shown out. The phase-field theory is a well-known mathematical model for solving interface problems, including crack problems in fracture mechanics. In this study, the formula is derived by variational approaches based on the Reissner-Mindlin plate kinematics and the multi-phase-field theory for simulation of the buckling phenomenon in cracked laminates. Phase-field parameters are defined independently in different plies of laminate to capture the crack behavior of each ply. Simulation is carried out to numerically investigate the stiffness reduction and buckling behavior of transverse cracked laminated composite plates. This paper focuses on the consideration of laminated composite plates, which have a crack in each layer. Therefore, this work is more complicated than the case of the plate has one crack throughout the plate thickness. The significant advancement of the phase-field approach for laminated composite plates with complex crack geometries is demonstrated. [ABSTRACT FROM AUTHOR]

• Altering the distribution patterns of graphene reinforcement across the flanges and web, while keeping the geometrical parameters constant, can enhance the critical buckling end-shortening and load-bearing capacity by approximately 80% and 25%, respectively. • The study revealed that the suggested approach (LW-TSDT) accelerates the running time by about 31% compared to the FEM. • In cases where web buckling is predominant, variation in graphene distribution across the flanges has negligible influence on the web's stability response. • Disregarding the specific graphene distribution patterns, the point of highest membrane stress occurs at the junction of the flange and web. The role of local buckling on the behavior of slender members under compression has received considerable attention in structural engineering. For thin-walled sections, in particular, there is a noticeable decrease in the axial compressive stiffness, resulting in a substantial reduction in their load-bearing capacity due to the occurrence of local buckling. The principal purpose of this article is to explore the potential improvements in the postbuckling characteristics of polymeric composite channel section struts subjected to a progressive end-shortening by employing multi-layer graphene sheets reinforcements. The solution methodology incorporates the von Karman geometrical nonlinearity and is based on the layerwise third-order shear deformation theory (LW-TSDT). To verify the accuracy of the results obtained based on LW-TSDT and to evaluate its computational efficiency, a three-dimensional (3D) finite element model is also developed using ABAQUS for the comparative analysis. A thorough examination of nonlinear instability is conducted on composite laminated channel section struts, featuring distinctive graphene distribution patterns through the thickness directions of the flanges and webs to identify the most effective material distribution with the objective of a significant increase in critical end-shortening and axial compressive stiffness. The influence of the geometrical parameters on the critical end-shortening, postbuckling equilibrium paths, and load-bearing capacity of functionally graded graphene reinforced composite (FG-GRC) laminated channel section struts are elicited. The conducted parametric analyses emphasize that altering the distribution patterns of graphene reinforcement across the flanges and web can enhance the critical end-shortening and load-bearing capacity by 80% and 25%, respectively. [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]

Delamination is one of the most serious failure modes in carbon fiber reinforced composite laminates, because it can reduce the overall stiffness, which further leads to premature structural buckling and failure at loads below the design level. Arbitrary elliptical delamination is the most representative case in engineering practice, and the delamination propagation and failure behaviors are much complicated. To completely evaluate the compressive failure behaviors of composite laminate with arbitrary elliptical delaminations, an extended analytical model was established based on the first order shear deformation theory and brittle fracture mechanics. The analytical model innovatively incorporated the failure evaluation, and especially the delamination propagation path into buckling analysis of composite laminate containing an arbitrary elliptical delamination. The predicted results are highly consistent with the outcomes of uniaxial compression tests, thus validating the applicability and accuracy of the analytical model as a highly efficient tool in engineering practices for the most representative arbitrary elliptical delamination problems. It is found that the propagation of the elliptical deamination in composites was fast and unstable, which led to catastrophic failures. The delamination propagation tends to initiate from the delamination boundary points with the maximum transverse coordinates and propagate transversely to the loading direction. [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 work provides an assessment of Equivalent Single Layer (ESL) and Layerwise finite element models, aimed for panel flutter and buckling analysis of supersonic variable stiffness composites, exploring variable-order shear deformation theories and Lagrange z -expansions. Numerical applications focus on simply supported panels with curvilinear fibre composite layers, including a cross-ply configuration for comparison purposes, and various side-to-thickness ratios. The accurate prediction of transverse shear and bending–twisting coupling is highlighted, as rather necessary for proper tailoring and analysis of supersonic curvilinear composites, especially when including in-plane loads. This is attainable through high-order ESL descriptions, in thin panels, even without thickness stretching. • Refined models for aeroelastic stability analysis of variable stiffness composites. • Variable-order ELS and LW descriptions assessed for flutter and buckling response. • Proper modelling of curvilinear fibre composites in pre-stressed supersonic panels. [ABSTRACT FROM AUTHOR]

• CFRP reinforcement increases the stiffness and buckling strength of conical shells. • Increase in buckling strength of cones reinforced with CFRP depends on the cone slenderness ratio. • Modifications were made on analytical models to predict the buckling strength of reinforced cones. This paper presents an experimental study into the behaviour of steel conical shells reinforced by carbon fibre reinforced polymer (CFRP) laminates subjected to uniform external pressure. The tests were conducted on nine conical shells with different slenderness ratios, which utilised different number of CFRP layers. It was concluded that the CFRP laminates increased the stiffness and buckling strength of conical shells, with the increase depending on the conical shell slenderness ratio. Additionally, existing analytical models for predicting the buckling strength of the unreinforced conical shells were visited and modifications were proposed for predicting the buckling strength of reinforced conical shells by CFRP laminates. Comparable predilections between the modified analytical models and the experiments were observed. [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 The present work focuses on the damage assessment of carbon fiber reinforced polymer (CFRP) panels subjected to in-plane shear loading undergoing large deformation. Experimental investigations are carried out to understand the buckling, post-buckling and collapse behavior of quasi-isotropic CFRP panels with and without cut-out under the shear loading. A special picture frame fixture is designed and fabricated in-house for applying shear load over the CFRP test panels with clamped plate boundary conditions. In this work, the presence of a circular cut-out and its counter effects on the structural performance, associated damage mechanisms are monitored by an integrated use of digital image correlation (DIC) and acoustic emission (AE) techniques. The whole-field displacement and strain data over the test panels are monitored in-situ using the DIC technique, and later they are used for predicting the buckling and post-buckling response. Further, the surface strain data obtained from DIC are used to study the damage initiation and propagation zones in the test panels. AE technique is employed to identify the initiation and propagation of various damage mechanisms including classification in the buckling and post-buckling regime. A detailed micrographic study is also carried out on the fractured panels to support the damage assessments done by the AE technique. Additionally, finite element modeling is done to study the post-buckling behavior of CFRP panels with and without cut-out under shear loading conditions. The finite element results are compared with the experimental observations, and the accuracy of the numerical model is validated. This study gives a better understanding of the collapse mechanism of CFRP panels under shear loading and assists in designing damage tolerant composite 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 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]

Highlights • A new FE model developed by authors is used to study biaxial and shear buckling analysis of laminated elliptic paraboloids. • There is no result of the buckling analysis of laminated composite elliptic paraboloids with cutouts and concentrated mass. • The parabolic variation of transverse shear strain is considered hence no shear correction factor is required. • A C° FE coding in FORTRAN is developed to generate many new results for different parameters. • Many new results are presented in this paper which may be useful for further research. Abstract The buckling of laminated elliptic paraboloids with cutouts and concentrated mass subjected to the in-plane bi-axial and the shear load is investigated for various boundary conditions using present mathematical model. Transverse shear stresses are represented by a parabolic function across the thickness and the cross curvature effect is also included via strain relations. The transverse shear stresses free condition at the shell top and bottom surfaces are also satisfied. In this mathematical model having a realistic parabolic distribution of transverse shear strains across the thickness of shell requires unknown parameters only at the reference plane. For generality in the present analysis, nine node curved isoparametric element is used. So far, no solution exists in the literature for dual axis buckling problem of laminated composite elliptic paraboloids with cutouts and concentrated mass. As no result is available for the present problem, the present model is compared with suitable published results and then it is extended to analyze bi-axial and shear buckling of laminated composite elliptic paraboloids. A C° finite element (FE) coding in FORTRAN is developed to generate many new results for different boundary conditions, lamination schemes etc. [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]

This work deals with the problem of the least-weight design of a composite stiffened panel subject to constraints of different nature (mechanical, geometrical and manufacturability requirements). To face this problem, a multi-scale two-level (MS2L) design methodology is proposed. This approach aims at optimising simultaneously both geometrical and mechanical parameters for skin and stiffeners at each characteristic scale (mesoscopic and macroscopic ones). In this background, at the first level (macroscopic scale) the goal is to find the optimum value of geometric and mechanical design variables of the panel minimising its mass and meeting the set of imposed constraints. The second-level problem focuses on the laminate mesoscopic scale and aims at finding at least one stacking sequence (for each laminate composing the panel) meeting the geometrical and mechanical parameters provided by the first-level problem. The MS2L optimisation approach is based on the polar formalism to describe the macroscopic behaviour of the composites and on a special genetic algorithm to perform optimisation calculations. The quality of the optimum configurations is investigated, a posteriori, through a refined finite element model of the stiffened panel making use of elements with different kinematics and accuracy in the framework of the Carrera’s Unified Formulation (CUF). [ABSTRACT FROM AUTHOR]

The aim of the work was to assess the compressive strength of Fibre Metal Laminates after impact. The main objective of the evaluation of the compression after impact assessment of FMLs was the deep analysis of damage growth range, size and mechanisms during load from various initial damage states and final post-impact strength. The glass fibre/titanium and carbon fibre/titanium Fibre Metal Laminates were tested and analysed. Laminates previously subjected to impact energies ranging from 5 to 35 J were tested. Based on the research, three load bearing states of fibre-metal laminates were identified and characterized on the basis of an analysis of force reduction characteristics. In addition, it was found that the strength reduction of FMLs in relation to impact energy does not decrease significantly. One of the most crucial grounds for the above is the protective role of the elastic–plastic metal layers against rapid local buckling of the strength-carrying composite component. [ABSTRACT FROM AUTHOR]

Solid-shell models are developed for the geometrically nonlinear analysis of multi-layered composite structures made of alternating layers with large difference in material properties. Exemplificative applications are presented for laminated glass, in which a number of stiff plies of glass are permanently shear-coupled by soft interlayers. The sectional warping due to significant transverse shear strains in the soft layers makes theories of laminated plates based on the plane-section hypothesis unreliable. The proposed approach is based on a geometrically exact solid-shell finite element model with one element per layer in the thickness direction, as alternative to solid discretization. The element approximation is based on the displacement nodal values at the top and bottom surfaces of the layers, with a natural C 0 continuity. An alternative solid-shell model with fewer parameters is derived imposing the equal finite rotation of the stiff layers at each surface point by a local rotation-free re-parametrization of the nodal displacements and enforcing the plane stress condition. The approach permits an easy coupling with a fully solid discretization, e.g. to model connections, and is based on a simple strain measure quadratic in the displacement unknowns and suitable for finite strains. Extensive numerical examples for laminated glass plates and curved shells susceptible to large deflections and buckling are provided, comparing the results with those from a fully solid approach. • Solid-shell models are proposed for laminates with alternating stiff/soft layers. • A first model uses a linear solid-shell element for each layer. • A second model reduces the DOFs imposing equal rotation of all the stiff layers. • Both the models use displacements variables and are tested for laminated glass. • The second model is as accurate as the first one even for large deformations. [ABSTRACT FROM AUTHOR]

The non-linear response of a sandwich panel with the core that consists of a functionally graded material (FGM) undergoing in-plane loading is investigated. The panel consists of two face sheets, metallic or composite laminated, and an FGM core that is a medium whose mechanical properties change through the depth facilitating a desirable response of the structure. The effect of the FGM core is introduced through the constitutive relations that affect conventional and high-order stress resultants and stress couples in the panel. The formulation employs the Extended High-Order Sandwich Panel Theory (EHSAPT) to assess the effect of the FGM material of the core. A variational approach is adopted to derive the linear and non-linear governing equations with a prescribed FGM distribution through the depth of the core. The wrinkling study of FGM panels includes two loading scenarios where in-plane loads are applied through a rigid edge beam connected to the core only and where the loads are applied through a rigid edge structure attached to both the face sheets and core causing uniform end shortening. The post-wrinkling behavior is also considered to prove that the initial pattern of wrinkles is not affected. [ABSTRACT FROM AUTHOR]

This study implements key mechanisms and parameters observed from the previous compression after impact (CAI) experimental studies into finite element models, to study their effects parametrically on residual compression strength. The mechanisms and parameters include: impact damage area, the role of intact interfaces within the overall damaged region (identified here as the “undamaged cone”), interlaminar toughness, and the extent of permanent out-of-plane deformation. The findings highlight that within the limits observed experimentally, in addition to the size of the damaged area, interlaminar toughness and the extent of permanent out-of-plane deformation strongly affect CAI strength (by up to ∼100% for a given damage area), with toughness playing a more significant role than permanent out-of-plane deformation. For the first time, and contrary to much of the literature, the significant role of the undamaged cone is evidenced and quantified. [ABSTRACT FROM AUTHOR]

This study proposes a method for repairing delaminated composite plates using micro-bolts. We first conducted a test to examine the effect of the hole size on the tensile strength of composite laminates. The test results showed that, among laminates with the same total area of holes, those with multiple small holes had a higher tensile strength than those with only a single large hole. Based on this result, brass bolts with a 0.6 mm diameter were used to repair the delaminated composite plates. Buckling tests and analysis were conducted for an intact laminate without delamination, an unrepaired laminate with delamination, a repaired laminate using one bolt, three bolts with two types of layout, and nine bolts. The test results indicate that the unrepaired specimen demonstrates local buckling at 68% of the buckling load of an intact specimen. In contrast, the buckling load was recovered to 82% of that of an intact specimen when only a single brass bolt was fastened. When nine bolts were used, the buckling load recovery rate increased to 90%. Finite element analysis produced the same results as the test, and predicted that the use of nine steel bolts will increase the buckling load to 93%. [ABSTRACT FROM AUTHOR]

A high-dimensional variable design space in optimization problems for tapered composite structures presupposes a development of efficient computational techniques to improve the design efficiency and flexibility. In this work, a mathematical model for optimization of tapered composite structures with buckling and manufacturing constraints is developed, then a ply-drop-based global blending model (GBM) is suggested to address the layers’ addition/deletion and blending problems. Within the framework proposed in Part I of this work (Compos Struct, 2016, 154: 106-128), by incorporating the global blending model, operations of add-layer, exchange-blend and sequence-adjustment are revised and enhanced. The GBM can not only characterize the global blending property, but also guide the maximum blending design. Accordingly, the design framework is simplified, and its computational cost is reduced significantly since there is no iteration of shape prediction and stacking-sequence optimization procedure. An 18-panel benchmark problem is adopted to verify the enhanced design framework, as compared with previous design results, the obtained better solution with higher efficiency implies its feasibility and potential for effective design of tapered composite structures. [ABSTRACT FROM AUTHOR]

Buckling analyses of laminated truncated conical shells subjected to external hydrostatic compression are carried out by employing the Abaqus finite element program. The critical buckling loads of these truncated conical shells with a given material system are maximized with respect to fiber orientations by using the golden section method. Through parametric studies, the influences of the end condition, shell thickness, shell length, shell radius ratio and cutout size on the optimal buckling loads, the associated optimal fiber orientations and the associated buckling modes are demonstrated and discussed. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to present optimal designs for variable stiffness laminated composite truncated cones under lateral external pressure. The objective is to maximize the failure load which is defined as the minimum of the buckling load and the first-ply failure ( FPF ) load. The numerical results are obtained using a semi-analytical degenerated shell element based on a refined first-order shear deformable shell theory and the influences of the pressure stiffness ( PS ) and the thickness/radius ratio are taken into account. A 2D degenerated shell element is also used for verification purposes. Results are presented for the related verification problems solved and the semi-analytical shell element is validated. Optimal designs, where FPF and buckling are imposed as design constraints, are presented for laminated composite thin and relatively thick cones having variable thickness and ply-angle. A simple graphical optimization technique and a modified Micro-Genetic Algorithm are employed. It is shown that, FPF constraint may be active for thicker cones having lower cone angles, PS slightly decreases the buckling pressures, and the stacking sequence has considerable influence on the failure load. The numerical results presented show that restraining the large end against rotation significantly increases the failure load. [ABSTRACT FROM AUTHOR]

The progressive damage and fracture behaviour of Glare® fibre-metal laminates (FMLs) was investigated experimentally for the buckling and postbuckling regimes of laminates containing internal ‘splice’ and ‘doubler’ joints. Specimens were either ‘pristine’ or contained artificial delaminations in the form of strips of release film to represent manufacturing defects. Each was tested under in-plane compression. Tests were monitored using Digital Image Correlation (DIC) for visualisation of three-dimensional full-field displacements whilst acoustic emission (AE) monitoring – combined with the novel Delta-T location algorithm – was used for the first time to detect and locate damage events in these FML structures. Results were validated using Scanning Electron Microscopy (SEM) to determine the damage mechanisms present. Large numbers of AE events were recorded at the splice and doubler locations during initial loading and throughout the postbuckling regime, suggesting that the novel AE location algorithm used is suitable for the monitoring of delaminations and matrix cracks in internal features in Glare® laminates. Moreover, AE events located away from internal features correlated well with buckling and postbuckling deformation as identified by the full-field DIC data. Finally, good correlation was observed between the onset of buckling and a rapid increase in cumulative AE energy, demonstrating that as well as locating damage, AE monitoring is able to indicate quite clearly when the buckling load has been reached. [ABSTRACT FROM AUTHOR]

A 3D finite element model using cohesive elements and continuum (bulk) material damage models was developed to examine the progressive damage and failure behaviour of Glare® Fibre Metal Laminate (FML) specimens subjected to in-plane compressive loading. The specimens contained internal ‘splice’ and ‘doubler’ features and were either pristine or contained simulated manufacturing defects in the form of artificial delaminations. The initiation and growth of delaminations at the inter-laminar interfaces, damage in the glass fibre reinforced polymer (GFRP) plies, ductile damage in the resin pockets (FM94 epoxy) and the onset of plasticity in the metal layers were examined. Geometric imperfections and load eccentricity were incorporated in an explicit dynamic nonlinear analysis implemented in the software Abaqus/Explicit. A series of buckling tests on specimens with and without artificial delaminations were conducted for validation, which are described in detail in a companion paper. Tests were monitored using Digital Image Correlation (DIC) for visualisation of full-field displacements and strains whilst Acoustic Emission (AE) monitoring enabled detection and localisation of the onset and progression of damage. Results for ‘Glare 4B’ specimens incorporating longitudinal and transverse delaminations into both splice and doubler geometries are presented. These results revealed that in order for the finite element analyses to be validated, all the damage and plasticity mechanisms described above need to be accounted for, as well as load eccentricity and geometry imperfections. [ABSTRACT FROM AUTHOR]

Laminated composite and sandwich structures are lightweight structures that can be found in many diverse applications especially civil, mechanical and aerospace engineering. The rapid increase in the industrial use of these structures has necessitated the development of new theories that suitable for the bending, buckling and vibration analysis of composite structures. Many review articles are reported in the literature on laminated composite plates and shells in the last few decades. But, in the whole variety of literature very few review articles are available exclusively on laminated composite and sandwich beams. In this article, a critical review of literature on bending, buckling and free vibration analysis of shear deformable isotropic, laminated composite and sandwich beams based on equivalent single layer theories, layerwise theories, zig-zag theories and exact elasticity solution is presented. In addition to this, literature on finite element modeling of laminated and sandwich beams based on classical and refined theories is also reviewed. Finally, displacement fields of various equivalent single layer and layerwise theories are summarized in the present study for the reference of researchers in this area. This article cites 515 references and highlights, the possible scope for the future research on laminated composite and sandwich beams. [ABSTRACT FROM AUTHOR]

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

In this study, buckling, post-buckling and progressive failure of composite laminated plates have been investigated numerically and experimentally. Buckling load, load-displacement relations for post buckling and maximum out-of-plane displacements of the plates are determined. Furthermore, the numerical results are compared with experimental findings for two different laminates made of woven fabric and uni-directional tapes. The comparisons show that there is a good agreement between numerical and experimental results obtained for buckling load and post-buckling behavior especially for the laminates with uni-directional tapes. [ABSTRACT FROM AUTHOR]

In this paper, The Isogeometric approach (IGA) and Carrera's Unified Formulation (CUF) are employed for free vibration and linearized buckling analysis of laminated composite plates. The non-uniform rational B-spline (NURBS) basis functions utilized in IGA, are employed as higher order smooth functions to approximate field solution leading to enhance precision of analysis. CUF presents an effective formulation to employ any order of Taylor expansion to analyze two-dimensional plate models. Higher order NURBS basis functions attenuate the shear locking properly and higher order theories supposed by CUF are free from Poisson locking phenomenon and they do not need the use of any shear correction factor. Therefore, combining IGA and CUF ends in a suitable methodology to analyze laminated plates. [ABSTRACT FROM AUTHOR]

In this work a multi-scale two-level (MS2L) optimisation strategy for optimising VAT composites is presented. In the framework of the MS2L methodology, the design problem is split and solved into two steps. At the first step the goal is to determine the optimum distribution of the laminate stiffness properties over the structure (macroscopic scale), while the second step aims at retrieving the optimum fibres-path in each layer meeting all the requirements provided by the problem at hand (mesoscopic scale). The MS2L strategy has been improved in order to integrate all types of requirements (mechanical, manufacturability, geometric, etc.) within the first-level problem. The proposed approach relies on: (a) the polar formalism for describing the behaviour of the VAT laminate, (b) the iso-geometric surfaces for describing the spatial variation of both the laminate stiffness properties (macro-scale) and the layers fibres-path (meso-scale) and (c) an hybrid optimisation tool (genetic and gradient-based algorithms) to perform the solution search. The effectiveness of the MS2L strategy is proven through a numerical example on the maximisation of the first buckling factor of a VAT plate subject to both mechanical and manufacturability constraints. [ABSTRACT FROM AUTHOR]

The main purpose of this study is to give a numerical solution for static buckling problem of circular cylindrical panels, conical panels, conical shells and circular cylindrical shells under axial load. Isotropic, laminated composite, functionally graded material (FGM) and carbon nanotube (CNT) reinforced functionally graded cases are taken into consideration. By using the Donnell’s shell theory and first-order shear deformation (FSDT) shell theory, the related equations have been obtained for buckling phenomena of shells. Then, the method of discrete singular convolution (DSC) based on the Shannon’s kernel is applied for the solution of these equations. Convergence and comparison studies are carried out to check the validity and accuracy of the DSC method. The effects of shell geometric quantities and material properties on buckling are examined and results are presented for isotropic, FGM, CNT reinforced FGM and laminated composite conical and cylindrical shells and panels. Performance and convergence conditions of the method of DSC have also been investigated. [ABSTRACT FROM AUTHOR]

The definitive list of stacking sequences is presented for Bending-Twisting coupled ( A S B 0 D F ) laminates, with up to 21 plies. This class of laminate arises from the ubiquitous balanced and symmetric design rule, but symmetry is shown to be a sufficient rather than a necessary constraint. Each stacking sequence configuration is derived in symbolic form together with dimensionless parameters from which the extensional and bending stiffness terms are readily calculated for any fibre/matrix system and angle-ply orientation. Expressions for ply orientation dependent lamination parameters are also given, together with graphical representations, which demonstrate the extent of the design space. Pseudo Quasi-Homogeneous ( A S B 0 D F ) laminates are introduced as an important laminate sub-set, since such laminates have concomitant orthotropic properties, i.e. matching orthotropic or isotropic stiffnesses in extension and bending, from which the isolated effects of Bending-Twisting coupling can be studied. These coupling effects are quantified for compression buckling of Angle-ply and Quasi-Isotropic laminated plates with simply supported and clamped edges. [ABSTRACT FROM AUTHOR]

On the basis of adequate considering the process constraints and defect control methods of tow curve placement, two types of variable stiffness laminates were designed and manufactured. A comprehensive experiment has been carried out through the 3D digital image correlation system, strain gauges, and displacement meters. The measured results show that the buckling and failure loads of variable stiffness specimens are improved by at least 40% and 70%, respectively. The FEA results of out-of-plane displacement and strain agree well with the experimental results. Furthermore, the reason for the higher buckling and failure loads of the variable stiffness specimens was elucidated by numerical results. [Display omitted] • Minimum curvature radius and process parameters were determined by tests. • Variable stiffness specimens were designed with multiple defect control methods. • Through multiple measurement methods, abundant test data has been obtained. • The variable stiffness laminates can effectively reduce the buckling deformation. • Variable stiffness design can significantly increase buckling and failure loads. [ABSTRACT FROM AUTHOR]

The aim of this paper is to highlight the seminal works and their approximate derivatives that formed the basis of shear buckling design provisions of thin-walled plated structural elements in structural engineering practice. Works on the subject are reviewed mainly from a critical and historical point of view. Approximate shear buckling equations pertaining to orthotropic plates are verified by numerical results computed from rigorous analytical solutions and validated from results from experiments conducted on laminated composite plates subjected to shear forces. As a result of this appraisal, a practical shear buckling equation is proposed for routine uses in the design of pultruded fiber-reinforced polymer composite girder webs and plates. • History of the shear buckling design provisions. • Early studies on the shear buckling of isotropic and orthotropic rectangular plates. • Buckling strength design of Pultruded fiber reinforced polymer composite plated elements. [ABSTRACT FROM AUTHOR]

Helicoidal laminates inspired by mantis shrimp crustacean can sustain higher loads compared to conventional laminated structures. However, there is still a lack of bending studies on the plates inspired by these helicoidal structures. The buckling and free vibration studies have been undertaken in the present work on the laminated composite and sandwich plates inspired by the helicoidal structures of the biological characters. Investigations are carried out using higher-order zigzag theory. For sandwich plates, the top and bottom face sheets are assumed to be made up of helicoidal layup schemes. Different kinds of helicoidal schemes, namely, recursive, exponential, semicircular, Fibonacci, and linear helicoidal are considered during the analysis. The buckling and free vibration behavior of helicoidal-based laminated sandwich plates are compared with the conventional laminated sandwich plates such as uniform distribution and cross-ply configurations. The influence of the number of layers, helicoidal schemes, geometric properties, and end conditions on the buckling and free vibration analysis of bio-inspired helicoidal laminated composite and sandwich plates is carried out in detail. • Free vibration and buckling analysis of helicoidal laminated sandwich plates is carried out. • The kinematics for the model is set within the framework of the higher-order zigzag theory. • The analysis has been carried out for normal and skew plates. • Hamilton's principle and the principle of minimum potential energy are used for solving free vibration and buckling problems. • The model can be used to analyze and design naval, civil, automobile, and aerospace structures, domes, and pressure vessels. [ABSTRACT FROM AUTHOR]

In this paper, the free vibration and uniaxial, biaxial, and shear buckling analyses of a sandwich plate with an auxetic honeycomb core and two laminated three-phase polymer/GNP/fiber face sheets are investigated. The sinusoidal shear deformation theory (SSDT) is utilized to model the plate, Hamilton's principle is hired to derive the governing equations and boundary conditions, and a numerical solution is performed via the differential quadrature method (DQM). The effects of various parameters on the critical buckling loads and the natural frequencies of such a plate are examined such as the geometrical parameters of the auxetic honeycomb core, mass fractions of the GNPs and the fibers, and total thickness of the plate. Numerical results reveal that by increasing the thickness of the auxetic honeycomb core the critical buckling loads decrease and the natural frequencies experience an initial growth followed by a small reduction. It is concluded that the inclined angle in the auxetic honeycomb core has no remarkable effect on the critical buckling load, but affects the natural frequencies in all vibrational modes. • Free vibration and buckling analyses of a sandwich plate with an auxetic honeycomb core are studied. • The auxetic is covered with two laminated three-phase polymer/GNP/fiber face sheets. • The plate is modeled based on the sinusoidal shear deformation theory. [ABSTRACT FROM AUTHOR]

The study aimed to analyse the buckling behaviour and damage mechanics of thin, cross-ply CFRP plates after impact by using progressive deformation analysis. Thin-walled CFRP was chosen as the one presenting stability issues and delamination susceptibility due to slender geometry and low out-of-plane strength. The study showed, that the buckling behaviour of laminates during CAI is determined by the initial damage character caused by impact. As the main source of laminate stiffness loss, the characteristic delaminations and fibre cracks were identified. The nature of delamination growth and cracks causes were described and proven. • CAI of thin cross-ply CFRP was made to track their buckling and damage response. • The DIC was used to measure plate deformation during the whole test. • Growth of internal and external damage was measured by non-destructive methods. • The buckling behaviour of plates after 5 J and 10 J LVI differs significantly. • The level of impact energy affects the type of detected damage mode in CFRP plates. [ABSTRACT FROM AUTHOR]

Structural components with variable stiffness can provide better performances with respect to classical ones and offer an enlarged design space for their optimization. They are attractive candidates for advanced lightweight structural applications whose functionalities often impose the presence of cutouts that requires accurate and effective analysis for their design. In the present work, a single-domain Ritz formulation is proposed, implemented and validated for the analysis of buckling and post-buckling behaviour of variable stiffness plates with cutouts. The plate model is based on the first-order shear deformation theory with nonlinear von Karman strain–displacement relationships. The plate generalized displacements are approximated with trial functions built as products of one-dimensional Legendre orthogonal polynomials. The non linear governing equations system is then deduced from the stationarity of the energy functional; the involved matrices are numerically computed by a special integration algorithm based on the implicit description of the cutout via suitable level-set functions. The formulation has been implemented in a computer code which has been used to validate the method through comparison with literature solutions for variable angle tow laminates with circular cutouts. Several investigations on buckling and post-buckling behaviour of variable angle tow composite plates with cutouts having different shapes and dimensions are then presented to illustrate the approach capabilities, provide benchmark results and point out features and design opportunities of the variable stiffness concept for the buckling and post-buckling design of advanced lightweight structures. • Variable stiffness plates with cut-outs are modeled via a single-domain Ritz method • Quadrature rules are based on the description of the cut-out via level set functions • Buckling and post-buckling of variable angle tow composite laminates are investigated [ABSTRACT FROM AUTHOR]

Free vibration characteristics and buckling behaviors of generally laminated composite beams subjected to the concentrated axial force and various classical end conditions are investigated in this paper. The analysis is based on a unified higher-order shear deformation beam theory. The Poisson effect, axial force, extensional deformation, bending deformation, shear deformation, and rotary inertia are all incorporated in the formulation. The dynamic stiffness method is employed to perform the exact vibration and buckling analyses of laminated composite beams. The dynamic stiffness matrix is developed from the complete analytical solutions of the homogeneous governing differential equations. Numerical results for the natural frequencies and buckling loads of particular laminated beams are presented and compared with previously published results. The effects of shear deformation, axial force and end condition on the natural frequencies, buckling loads and/or mode shapes of the laminated beams are thoroughly analyzed. [ABSTRACT FROM AUTHOR]

Grid structures are extensively used in many engineering structures as an orthotropic layer with at most in-plane anisotropy. In this study, the laminated grids structures are considered. These structures are composed of various numbers of thin composite grid layers. This concept yields to numerous laminated grid configurations with disparate coupling effects, which can be used to tailor the stiffness, compare to conventional grids. In the present study, four known grid patterns with equal weight and thickness constitute the laminated grids. The genetic algorithm (GA) is employed to optimize the stacking sequence and pattern composition of the laminated grid. The buckling load is taken as a fitness function and the pattern and orientation of the grid layer are considered as the design variables. The first-order shear deformation and classical laminated plate theories are considered along with Ritz method to obtain the elastic buckling loads. The optimization results are presented for various boundary conditions and aspect ratios. The results show, using the laminated grid considerably improves the axial buckling load of the plates. Moreover, the plate boundary conditions and aspect ratios play an imperative role in the optimum pattern and stacking sequence of the laminated grid plates. [ABSTRACT FROM AUTHOR]

This paper investigates the use and efficiency of structural continuous tapes (laminates), fibre tapes and fibre ropes made of different materials (natural or not) in enhancing the axial strain ductility and stress of confined concrete. All used confining materials are non-impregnated, unbonded to concrete and thus easy to reuse and recycle. Concrete cylinders confined with polypropylene rope reached axial strain as high as 0.15 with no rope fracture. Wrapping of cylinders with ultra-high molecular weight polyethylene (UHMWPE) tape or aramid fibre tapes or basalt fibre tapes may provide concrete significantly enhanced mechanical properties under monotonic or cyclic load. Cylinders wrapped with basalt fiber tape presented gradual fibre fracture and ductile load drop after maximum bearing load. Vinylon fibre ropes and UHMWPE or basalt or aramid fibre tapes show interesting resilience features as they can reach high portion of their confining efficiency even after their fracture initiation. In addition, the study presents the test results of severely damaged reinforced concrete (RC) column, repaired with high strength mortar and externally wrapped with hybrid basalt – polypropylene confinement. The retrofitted column fully restored the original ever-increasing σ-ε behavior, revealing remarkable energy dissipation under cyclic loading. It reached 0.052 axial strain and then it was early terminated for safety reasons, despite having already sustained 0.058 strain during initial loading. [ABSTRACT FROM AUTHOR]