Search

Abstract In this study, stress analysis of laminated composite beams is carried out by using Refined Zigzag Theory (RZT) and Peridynamic Differential Operator (PDDO). The PDDO replaces local differentiation with nonlocal integration. This makes the PDDO capable of solving the local differential equations accurately. RZT is suitable for both thin and thick beams eliminating the use of the shear correction factors. Also, RZT ensures a constant number of kinematic variables regardless of the number of layers in the beam. The governing equations of the RZT beam and the boundary conditions were derived by employing the principle of virtual work. The capability of the present approach was assessed by considering various beams for different boundary conditions and aspect ratios. It provides robust and accurate predictions for the displacement and stress components in the analysis of highly heterogeneous laminates. [ABSTRACT FROM AUTHOR]

Abstract This paper presents test results of fifteen reinforced engineered cementitious composite (ECC)-concrete beams. The main parameters investigated were the amount and type of reinforcement, and ECC thickness. All reinforced ECC-concrete composite beams tested were classified into four groups according to the amount and type of main longitudinal reinforcement used; three groups were reinforced with FRP, steel and hybrid FRP/steel bars, respectively, having similar tensile capacity, whereas the fourth group had a larger amount of only FRP reinforcement. In each group, four height replacement ratios of ECC to concrete were studied. The test results showed that the moment capacity and stiffness of concrete beams are improved and the crack width can be well controlled when a concrete layer in the tension zone is replaced with an ECC layer of the same thickness. However, the improvement level of ECC-concrete composite beams was controlled by the type and amount of reinforcement used. Based on the simplified constitutive relationships of materials and plane section assumption, three failure modes and their discriminate formulas are developed. Furthermore, simplified formulas for moment capacity calculations are proposed, predicting good agreement with experimental results. [ABSTRACT FROM AUTHOR]

Abstract In this paper, a Finite-Element (FE) numerical investigation on timber-to-timber joints and composite beams with inclined self-tapping screws (STSs) is presented. Based on past experimental data and numerical literature efforts, full 3D solid FE models of selected geometrical and mechanical configurations of technical interest are implemented in ABAQUS software package and analysed under static loading conditions. The typical push-out samples include GL24h timber members with several types (WT-T-8.2, 190 mm and 220 mm their length), layouts (2 + 2, 4 + 4, 2 + 2 X-shaped) and inclination of screws (up to ±45°). For the full-scale beam samples in bending (8 m their span), composite systems consisting of GL24h timber beam, wooden plank, spruce floorboards and STSs are investigated. There, the STS joints take the form of two-rows or X-shaped connections, respectively (45° or 90° their inclination), including four screw types and different spacing. In both the push-out and full-scale cases, simple modelling approaches are taken from the ABAQUS library and adapted to the timber-to-timber structural system under investigation, so as to explore their structural performance in the elastic and post-damage phases, up to failure. A key role in the typical FE models is assigned to input material properties and mechanical contacts, including damage constitutive laws so as to reproduce possible local failure phenomena in the timber or steel components, as well as cohesive damage interactions for the joints. The presented FE models are calibrated in accordance with past research studies, and validated – for the examined structural typology – against experimental results available in literature. Comparative calculations are hence presented, based on the collected numerical, experimental and analytical estimations for the selected samples. As shown, the examined modelling approach can reasonably capture the expected performance of timber-to-timber joints and composite systems. [ABSTRACT FROM AUTHOR]

Dynamic instability analysis of doubly-tapered cantilever composite beams rotating with periodic rotational velocity is conducted in the present work for out-of-plane bending (flap), in-plane bending (lag) and axial vibrations. Rayleigh-Ritz method and classical lamination theory are used along with an energy formulation. Bolotin’s method is applied to obtain the instability regions. To verify the dynamic instability analysis results, time responses are investigated at different locations of the instability region by using the Runge-Kutta method. A comprehensive parametric study is conducted in order to understand the effects of taper configurations and various system parameters including mean rotational velocity, hub radius, double-tapering angles and stacking sequences, on the dynamic instability characteristics of the composite beam. The composite material considered in the present work in numerical results is NCT-301 graphite-epoxy prepreg. [ABSTRACT FROM AUTHOR]

In this paper, we develop a new and efficient finite element for the linear static analysis of composite beams with deformable shear connection. We adopt a 3-field mixed approach, based on the Hu-Washizu principle, combined with the enhanced strain concept. Our proposal includes the possibility of systematically choosing interpolating functions of increasing order for certain generalized stresses and for the enhanced strains. Another distinctive feature of our approach is the fact that only three generalized stresses are directly approximated. As in many mixed formulations, the degrees of freedom associated with the approximation of generalized stresses and enhanced strains can be condensed out at the element level at negligible cost, leading to discrete systems involving only the displacement degrees of freedom. For benchmarking purposes, a conventional displacement-based conforming finite element is also briefly derived. Several illustrative examples demonstrate the mixed element’s ability to perform very well on the coarsest of meshes – often consisting of a single finite element –, even when the material data exhibits a jump discontinuity in its interior, in sharp contrast with the displacement-based conforming element. This is particularly true when it comes to the estimation of generalized stresses, often the variables of most interest to designers. [ABSTRACT FROM AUTHOR]

The Refined Zigzag Theory (RZT), developed by Tessler/Di Sciuva/Gherlone is among the most promising approaches for analyzing shear-elastic composite structures today. Since its appearance many contributions have been published dealing with finite elements for laminated structures based on the efficient kinematic of RZT. For composite beam-columns C 0 -elements of different orders as well as p-type approximations are formulated and assessed. In this work a different approach is given. After establishing the governing equations in a first order differential equation system, the transfer matrix is obtained by a matrix series solution and by similarity transformation. The transfer matrix approach, in principle suited for 1D-structural elements such as beams, disks, circular plates and rotational shells, has been successfully applied in the past. Sometimes this approach exhibits numerical instabilities. The well-known relations between the transfer- and stiffness matrix are invoked to circumvent this drawback. The dynamic stiffness matrix and the load vector are obtained by reordering and partially inverting the submatrices of the transfer matrix. The results, which are obtained by one finite element only, are in agreement with available analytical and numerical solutions. [ABSTRACT FROM AUTHOR]

In this paper, based on Von Kármán’s nonlinear theory and the classical lamination theory, a closed form expression is derived for the tangent stiffness matrix of a laminated composite beam element undergoing large deformation and rotation under mechanical and hygrothermal loads. Stretching, bending and torsion have been considered. A co-rotational element reference frame is used as the Updated Lagrangian (UL) formulation. The model has been verified in different problems by comparison with the results of Nastran and ANSYS composite laminate tools, and the difference in the resulting large deformations is less than 5%. The major advantage of the proposed approach is that the composite structure is modeled using 1D beam elements rather than 2D shell or 3D solid elements as in the case of Nastran and ANSYS where laminates are defined over surfaces or 3D solids. The availability of an explicit expression for the tangent stiffness matrix makes the proposed model highly efficient specially when dealing with large composite space frame structures. The saving in computational time could reach 93% compared to regular FE software packages. The developed model is very useful for modeling and designing flexible composites used in new applications such as morphing aerospace structures and flexible robots. [ABSTRACT FROM AUTHOR]

An attempt has been made here for the isogeometric static analysis of the laminated composite plane beams by using refined zigzag theory. In this study; instead of the standart finite elements, which use polynomial shape functions, an isogeometric refined zigzag finite element (IGRZF) has been developed, that gives the opportunity to get the exact beam geometries directly from a computer aided design (CAD) software, Rhinoceros. To provide less computational effort, the refined zigzag theory has been introduced, that make IGRZF independent from the number of layers considered. The aforementioned finite element has been implemented in an in-house Mathematica code, which can handle both thin and thick beams without the problem of shear locking and does not require shear correction factors. Using this approach, various sandwich beams have been analyzed and the obtained results are compared with other reliable published results for various aspect ratios and support types. [ABSTRACT FROM AUTHOR]

An exact analytical model based on a higher-order beam theory (HBT) is developed for an accurate prediction of the flexural response of two layered composite beams with partial shear interactions. This is achieved by taking a third order variation of the longitudinal displacement over the beam depth for the two layers separately. The deformable shear connectors joining the two different material layers are modelled as distributed shear springs along the beam length at their interface. The principle of virtual work is used to derive the governing equations which are solved analytically using a Navier type solution technique. To assess the performance of the proposed model, numerical examples of composite beams are solved using the model. The results predicted by the model are compared with published results and the numerical results produced by a one dimensional finite element model based on HBT as well as a detailed two-dimensional finite element modelling of composite beams. [ABSTRACT FROM AUTHOR]

This paper presents free vibration of composite beams under axial load using a four-unknown shear and normal deformation theory. The constitutive equation is reduced from the 3D stress-strain relations of orthotropic lamina. The governing differential equations of motion are derived using the Hamilton’s principle. A two-node C 1 beam element is developed by using a mixed interpolation with linear and Hermite-cubic polynomials for unknown variables. Numerical results are computed and compared with those available in the literature and commercial finite element software (ANSYS and ABAQUS). The comparison study illustrates the effects of normal strain, lay-ups and Poisson’s ratio on the natural frequencies and load-frequency curves of composite beams. [ABSTRACT FROM AUTHOR]

The Carrera Unified Formulation (CUF) was recently extended to deal with the geometric nonlinear analysis of solid cross-section and thin-walled metallic beams (Pagani and Carrera, 2017). The promising results provided enough confidence for exploring the capabilities of that methodology when dealing with large displacements and post-buckling response of composite laminated beams, which is the subject of the present work. Accordingly, by employing CUF, governing nonlinear equations of low- to higher-order beam theories for laminated beams are expressed in this paper as degenerated cases of the three-dimensional elasticity equilibrium via an appropriate index notation. In detail, although the provided equations are valid for any one-dimensional structural theory in a unified sense, layer-wise kinematics are employed in this paper through the use of Lagrange polynomial expansions of the primary mechanical variables. The principle of virtual work and a finite element approximation are used to formulate the governing equations in a total Lagrangian manner, whereas a Newton–Raphson linearization scheme along with a path-following method based on the arc-length constraint is employed to solve the geometrically nonlinear problem. Several numerical assessments are proposed, including post-buckling of symmetric cross-ply beams and large displacement analysis of asymmetric laminates under flexural and compression loadings. [ABSTRACT FROM AUTHOR]

[Display omitted] • Different impact energies were selected based on the absorption energy of beams under static loading. • The difference in impact performance between reinforced concrete and reinforced concrete composite beams was tested. • The damage assessment method based on the residual deformation under impact loadings was proposed. • The impact performance of the reinforced concrete beams and reinforced concrete composite beams can be treated as the same within the tested impact loadings. Composite (CC) beams are employed more and more extensively because of their advantages in environmentally-friendly and rapid construction. These beams are possibly subjected to impact loadings due to occasional accidents or terrorist attacks during the service. It should be clarified whether the previous research achievements on the impact performance of reinforced concrete (RC) beams can be directly applied to CC beams. Five groups of full-scale CC beams and RC beams were fabricated with the same reinforcement ratios. One group of these specimens was tested under static bending loading, and the other eight specimens were tested under impact loading through the drop hammer test system. The failure modes, deformation, and force response of CC beams and RC beams were compared. The experimental results presented that the failure modes of CC beams are consistent with those of RC beams in the impact energy range of 1.0 E s ∼ 3.5 E s. The increasing impact energy changes the failure mode of CC beams from flexure failure to flexure‐shear failure until shear failure. With the increase of impact energy from 1.0 E s to 3.5 E s , the residual deformation increases first and then decreases, and the impact force of CC beams and RC beams are increased by 55.9% and 78.2%. There is little difference between CC beams and RC beams in peak deformation and residual deformation, a similar trend is found in impact force and support reaction force. Moreover, the beams can perform well impact resistance in the range of 1.0 E s ∼ 2.3 E s. Based on the residual deformation under impact loading and the deformation under static loading, the damage assessment method was proposed to evaluate the damage level of beams subjected to impact loadings. [ABSTRACT FROM AUTHOR]

This paper presents an investigation into the buckling and postbuckling of composite beams in hydrothermal environments. The free expansion due to both temperature variation and moisture absorption has been taken into consideration. In the meantime, the material properties are considered to be temperature- and moisture-dependent. A micromechanics-based model is proposed to consider the effect of the fiber volume fraction, temperature and moisture on the mechanical and hygrothermal material properties. The equilibrium equations are derived from the principle of virtual work where the small strain, moderate rotation assumption has been adopted. The classical Euler–Bernoulli beam (EBB) theory and the higher-order shear-deformation Reddy beam (RB) theory are presented. The critical buckling loads and the postbuckling amplitude are calculated at varying temperature, moisture, and fiber volume fraction. The model has been validated versus results published in the literature. The temperature variation has been found to significantly reduce the buckling load and increase the postbuckling amplitude. However, the contribution of the moisture concentration on the critical buckling loads has been found insignificant according to the assumptions made in this study. However, moisture has a noticeable effect on the postbuckling response. [ABSTRACT FROM AUTHOR]

The technology of glued laminated (glulam) timber has enabled the design of composite structures with large dimensions. The laminations are generally derived from the sawing of small trees and species of rapidly growing, which yields laminates with low mechanical properties. This study evaluates the benefits of the reinforcement of glulam beams, by employment of steel reinforcement ratios of 2% and 4%. In the beams with a ratio of reinforcement of 2%, in relation to the unreinforced glulam beams, the stiffness increased approximately 52% and the serviceability load increased 53.1%, and with the employment of steel ratio equal to 4% these increases were in the order of 73% and 79.2%, respectively. The results showed that the insertion of steel bars can reduce the inherent variability of wood and increase significantly the stiffness of glulam, which consequently increases the beam capability for serviceability limit states. [ABSTRACT FROM AUTHOR]

The mechanics of plastic–aluminum composite I-beams are studied using physical experiments and numerical predictions. These structural elements use hollow aluminum tubes in the flange locations with plastic providing the surrounding matrix and much of the shear resistance. Several tests were designed and performed on different portions of the beams to estimate the critical regions of high stress. These tests quantified the bond strength between the plastic and aluminum of the flanges and also the bond strength at the boundary between the flange and web plastics. Tensile tests were performed on the plastics per ASTM D638 -10. An internal shear connector (deboss) was used as the mechanical fastener between the aluminum and the flange plastic. A numerical finite element model was developed in ABAQUS to better understand the underlying physics of the deboss and was compared with test specimens. The results from the model closely match experimental results and the model can be used to predict the load per deboss region that can be resisted before the plastic begins to yield and extensively deform. Results of these investigations are discussed and design guidelines are presented for this relatively new class of composite. [ABSTRACT FROM AUTHOR]

In the present study, vibration of rotating composite beams is studied. Different beam theories are used in the formulation including Euler–Bernoulli, Timoshenko and Reddy beam theories. Ritz method is used in the solution of the problem. Simple polynomials are chosen for the displacement field. The continuity of transverse stresses is satisfied among the layers. Results are obtained for different orthotropy ratios, rotation speed, hub ratio, length to thickness ratio of the rotating composite beam and different boundary conditions. [ABSTRACT FROM AUTHOR]

Analytical solutions have been developed to study the free vibrations of composite beams with two overlapping delaminations under axial compressive load. The delaminated beam is analyzed as seven Euler–Bernoulli beams connected at the delamination boundaries. The continuity and equilibrium conditions are satisfied between the adjoining regions of the beams. Lower and upper bounds of the natural frequencies of the delaminated beams are identified by assuming totally ‘free’ and totally ‘constrained’ deformations of the delaminated layers, respectively. These solutions can serve as generalized solutions for vibration and buckling of delaminated composites. The relation between the square of the natural frequency of the delaminated beam and the axial compressive load is also investigated. Results show a linear relation between the square of the “constrained mode” and “free mode” frequencies of the simply supported beam and the axial compressive load. A non-linear relation is observed between the square of the “free mode” frequencies of a clamped–clamped beam and axial compressive load due to the opening of the delaminated layers in the “free mode” mode shape of the beam. [ABSTRACT FROM AUTHOR]

Statistical Moment (SM) based modelling is a quite straightforward approach in stochastic modelling of uncertain structures. However, the method still has deficiencies including determination of SMs of natural frequencies of vibratory structures, and it has not been tested yet for realistic structures. This study aims such verification by employing high-degree statistical moments in stochastic equations. In this respect, SM approach is applied for two different uncertainty cases. In the first case, uncertain parameters are experimentally reproduced from the batch of laminated composite beams. Then, those uncertainties are fed to SM equations used in finite element model to obtain descriptive statistical quantities (mean, variance, skewness, and kurtosis) of stochastic natural frequencies. Next, Pearson model is utilized to obtain probability density function of the natural frequency by using standardized SMs. Beside this, uncertain fundamental natural frequency of fifty samples of composite beams is measured by experimental modal tests. All SM based predictions and modal test results are also compared with numerical Monte Carlo Simulations. The latter case examines composite beams having nonnormal uncertain thickness. Since the results are in good harmony with each other, it is concluded that high-order SM based approach may effectively be used in uncertainty modelling of realistic structures. [ABSTRACT FROM AUTHOR]

In multilayered systems with interfacial imperfections, such as imperfect bonding of the layers or delaminations, or where the plies are separated by thin interlayers allowing relative motion, the displacement field is highly discontinuous in the thickness, with a characteristic zig-zag pattern and interfacial jumps. Stresses also have large variations, especially for highly deformable interlayers or fully debonded layers. These effects cannot be captured using classical, first- or higher-order single-layer theories. A mechanical model is formulated for the solution of multilayered beams/wide plates with an arbitrary number of imperfect interfaces/delaminations loaded dynamically. The formulation is in the framework of the discrete-layer approach and the interfaces are described through affine traction laws which relate interfacial tractions and relative displacements. Homogenization and variational techniques define novel equilibrium equations depending on only four generalized displacement functions. Comparison with 2D elasticity solutions shows that complex discontinuous fields in thick, highly-anisotropic plates with an arbitrary number of sliding-interfaces are accurately predicted. The approach extends the range of problems which can be solved analytically compared to discrete-layer models where the unknowns depend on the number of layers/interfaces. The affine traction laws describe arbitrary branches of piecewise linear functions approximating nonlinear traction laws to represent different interfacial mechanisms. [ABSTRACT FROM AUTHOR]

Abstract: The methodology used in part 1 (Zhang and Wang, submitted for publication) of the work for single-cell thin-walled closed-section composite beams is extended to multi-cell thin-walled closed-section composite beams. The effect of material anisotropies is fully considered on the mid-surface shear strain of all the cross sectional members including skin walls and internal members. Numerical comparisons with ABAQUS finite element simulations are performed for three-cell box and elliptical beams with a variety of laminate layups under various loading conditions and excellent agreements are observed. Significant deficiency of some existing models are shown. [Copyright &y& Elsevier]

Abstract: An improved structure mechanical modeling with excellent accuracy is developed for single-cell thin-walled closed-section composite beams based on previous work. Both axial warping effect and the effect of material anisotropies on the shell wall mid-surface shear strain are considered. The shear strain is calculated directly from the general constitutive law of the shell wall. Closed form expressions are obtained of one-dimensional global beam stiffness matrix. Numerical comparisons with ABAQUS simulations are performed for box and cylindrical beams with a variety of lamina layups under various loading conditions and excellent agreements are observed. The effect of material anisotropies on the shell wall mid-surface shear strain has significant influence on the accuracy of modeling. In contrast, the axial warping effect has a negligible influence in cases considered. Significant deficiency of some existing models is revealed. [Copyright &y& Elsevier]

Abstract: Thanks to their various benefits, composite beams have been increasingly used in various applications. This study will focus on two-layer composite beams with a flexible shear interface between layers. The finite element method, in particular its displacement-based formulation, has been recognized as the most popular method for numerical analysis of composite beams. However, when applied to Timoshenko beams with partial interaction, the displacement-based formulation may suffer from the so-called shear-locking and slip-locking phenomena, leading to erroneous solutions. Hybrid and mixed finite element formulations have been viewed as competitive alternatives, since they naturally avoid locking effects. Special types of these formulations are the so-called equilibrium-based formulations, producing statically admissible solutions. This work introduces for the first time an equilibrium-based finite element formulation for the analysis of Timoshenko composite beams with partial interaction. The formulation relies on a variational principle of complementary energy involving only force/moment-like variables as fundamental unknown fields. The approximate field variables are selected such that all equilibrium equations hold in strong form. The inter-element equilibrium is enforced by resorting to the Lagrangian multiplier method. Unlike traditional displacement-based finite element formulations, the proposed scheme is naturally free from both shear- and slip-locking phenomena. The accuracy and effectiveness of the new formulation is numerically assessed through the analysis of several numerical examples. In particular, the ability of the formulation to model accurately both very flexible and very stiff shear connections is numerically shown. [Copyright &y& Elsevier]

Piezoelectric actuators have been highly successful in a wide range of structural control applications. As such, there is an ongoing need for rapid and accurate structural analysis techniques, particularly for highly heterogeneous composite materials and accounting for the actuator as a patch. Here, a new model based on the Refined Zigzag Theory (RZT) formulation that includes geometric nonlinearities is proposed for buckling, postbuckling and nonlinear static response analyses of geometrically imperfect composite beams with piezoelectric actuators. Both the analytical and the finite element (FE) formulation are presented for symmetrically and non-symmetrically laminated beams. The FE approximation is further generalised to the case of beams with geometric discontinuities to model composite beams with piezoelectric actuator patches. The new RZT model is numerically verified through comparisons to Abaqus solutions for buckling and postbuckling analyses and for the geometrically nonlinear response to an applied voltage of geometrically imperfect composite beams with piezoelectric actuator patches. This work presents a new model for composite beams with piezoelectric actuators and confirms the remarkable advantages of RZT in terms of accuracy and computational efficiency also for challenging nonlinear analyses, where the RZT computational time is generally less than half the time required by the FE commercial code. [ABSTRACT FROM AUTHOR]

Abstract: A set of linear differential equations of motion for coupled free vibrations of composite beams with asymmetric cross-sections is obtained in this paper based on Euler–Bernoulli beam theory. More coupling terms are included in the governing equations; and hence, both even and odd order spatial derivatives are included. All these features lead to much difficulty in solving the resultant equations. The axially unloaded condition of F 1 =0, instead of e =0, is adopted to simplify the equations of motion for the case of inextensional beams. An algorithm is developed for solving the resultant equations to obtain natural frequencies and modes of the beams. Numerical examples for validation show that the equations of motion obtained in this paper are correct and the corresponding algorithm is effective and easy to use. [Copyright &y& Elsevier]

Abstract: We present approximate analytical solutions for the nonlinear free vibrations of symmetrically or asymmetrically laminated composite beams in prebuckling and postbuckling. Simply supported and clamped–clamped boundary conditions are considered. Galerkin’s discretization is used to obtain the nonlinear ordinary differential equations governing the large-amplitude vibrations of composite beams in prebuckling and postbuckling, which are found to be of the same form. The variational method of He [20,21] is used to derive an approximate analytical solution for the nonlinear natural frequency and the nonlinear load–deflection relation. Results obtained by using the proposed analytical solution is compared with the finite element results available in the literature and a good agreement has been obtained. Numerical results to show the variation of the nonlinear natural frequency with the applied axial load for a variety of composite laminates are presented. The contribution of the amplitude of vibration on the nonlinear load–deflection response and the nonlinear natural frequency is found to be significant. [Copyright &y& Elsevier]

Abstract: Geometrically Exact Beam Theory (GEBT), a general-purpose tool for nonlinear analysis of composite slender structures, is developed to meet the design challenges associated with future engineering systems featuring highly-flexible slender structures made of composites. GEBT is based on the mixed formulation of the geometric exact beam theory which can capture all geometric nonlinearities due to large deflections and rotations, subject to the strains being small. Coupled with Variational Beam Sectional Analysis (VABS), a general-purpose cross-sectional analysis, GEBT can effectively analyze geometric nonlinear behavior of slender structures having arbitrary cross-sections made of arbitrary materials. [Copyright &y& Elsevier]

Abstract: Static behavior of composite beams with arbitrary lay-ups using various refined shear deformation theories is presented. The developed theories, which do not require shear correction factor, account for parabolical variation of shear strains and consequently shear stresses through the depth of the beam. In addition, they have strong similarity with Euler–Bernoulli beam theory in some aspects such as governing equations, boundary conditions, and stress resultant expressions. A two-noded C1 finite element with six degree-of-freedom per node which accounts for shear deformation effects and all coupling coming from the material anisotropy is developed to solve the problem. Numerical results are performed for symmetric and anti-symmetric cross-ply composite beams under the uniformly distributed load and concentrated load. The effects of fiber angle and lay-ups on the shear deformation parameter and extension-bending-shear-torsion response are investigated. [Copyright &y& Elsevier]

Abstract: In this study, effective theoretical and computational (the finite element method) procedures are introduced and used to characterize the dynamic behavior of beams and of cylindrical panels with circular cross-section; both structures have the single delamination between laminate layers. Based on the computed results it is possible to determine the effect of delamination on the overall structural dynamic behavior. Those results are used to quantify the difference between the results of the relevant parameters in the cases of perfect and defected structures. Usually, the wave propagation can be observed with the use of piezoelectric sensors. Therefore, in the next step of our analysis we modeled delaminated structures with a finite number of PZT sensors to consider also their influence on the structural dynamic response. The numerical analysis have been conducted with the use of 3D finite elements. It deals with the analysis of a cylindrical shell with an axisymmetric delamination and of a cylindrical panel having a square local delamination. A lot of numerical results allow us to understand better the influence of various parameters on the form of wave propagation in cylindrical multilayered shells. The numerical results are also validated by an experimental analysis for cylindrical panels. [Copyright &y& Elsevier]

Abstract: The aim of this study is to characterize the free non-linear vibration behavior of composite beams by using polynomial finite element method with shape functions based on Legendre polynomials or sinusoidal functions. The beams are subjected to different boundary conditions. Non-linear frequencies and modes shapes are obtained using asymptotic linearization method applied on the fundamental vibrating mode. The different composite beams are subjected to different layer dispositions. The nature of the interface between layers is of no object in this study. Navier–Bernoulli hypothesis on the transverse sections is adopted. The study concerns the influence of geometrical non-linearities of the free dynamical behavior. The analysis is performed thus by considering the influence of the vibration amplitude on the modal frequencies of the structure. The solutions are obtained by numerical simulation and by semi-analytical method using asymptotic linearization applied in the real temporal modal space. The numerical values are compared to the different ones obtained in literature. [Copyright &y& Elsevier]

Abstract: Fiber reinforced plastic composite (FRPC) beams have been widely used as effective stand-alone structural elements and/or reinforcing agents in various engineering applications. Such lightweight, stiff and strong structural elements may suffer, however, from inter-ply defects (referred to as delaminations), arising from various causes and factors. A delamination in such structural components could propagate into severely large damage zone, thus compromising the structural integrity. Therefore, detection of delamination at an early stage is of paramount importance. The application of a relatively new empirical-mode-decomposition-based, non-destructive damage detection methodology for detecting delamination damage in composite beams is introduced. The method uses the vibration signature of the structure, captured through piezoelectric sensors. The integrity of the methodology is established through both experimental and computational investigations. The method was successful in distinguishing lengthwise and through-the-thickness locations of delamination, as well as the growth in delamination size. [Copyright &y& Elsevier]

Abstract: The nonlinear response of composite beams modeled according to higher-order shear deformation theories in postbuckling is investigated. The beam ends are restrained from axial movement, and as a result the contribution of the midplane stretching is considered. The equations of motion and the boundary conditions are derived using Hamilton’s principle. The shear deformation effect on the critical buckling load and static postbuckling response is introduced using classical, first-order, and higher-order shear deformation theories. This paper presents an exact solution for the static postbuckling response of a symmetrically laminated simply supported shear-deformable composite beam. The shear effect is shown to have a significant contribution to both the buckling and postbuckling behaviors. Results of this analysis show that classical and first-order theories underestimate the amplitude of buckling while all higher-order theories, considered in this study, yield very close results for the static postbuckling response. [Copyright &y& Elsevier]

Abstract: This paper presents results of experimental and numerical investigations on the structural behaviour of composite beams made of annealed glass panes and glass fibre reinforced polymer (GFRP) pultruded profiles. The main goal of the transparent structural solutions presented here is to increase the post-cracking residual strength and ductility of glass by using GFRP strengthening laminates. The experimental programme included (i)tensile tests on double lap joints between glass and GFRP pultruded laminates, bonded with different types of structural adhesives, and (ii) full-scale flexural tests on glass beams and glass–GFRP composite beams, with different strengthening geometries and structural adhesives. Results obtained in this study show that, unlike glass beams, in glass–GFRP composite beams it is possible to obtain relatively ductile failure modes, with a significant increase of both strength and deformation capacity after the initial cracking of glass. The stiffness of the structural adhesive used, together with the geometry of the GFRP strengthening element, have a major influence on the structural response of the composite beams. Finite element models were developed for all tested beams, allowing to simulate their serviceability behaviour (prior to glass cracking) with fairly good accuracy, namely in what concerns the degree of shear interaction at the bonded interfaces. [Copyright &y& Elsevier]

Abstract: The present study proposes simple, elegant, and accurate closed-form expressions for predicting the post-buckling behavior of composite beams with axially immovable ends using the Rayleigh–Ritz (R–R) method, where geometric nonlinearity arises from mid-plane stretching of the beam. The displacement fields used for the analysis are coupled using the axial equilibrium equation of the composite beam. An exhaustive set of beam boundary conditions are studied, namely, hinged–hinged, clamped–clamped, clamped–hinged, hinged–guided, and clamped–guided beams in order to prove the efficacy of the present formulation. Post-buckling analysis results are presented for laminated composite beam with symmetric and asymmetric layup schemes. Post-buckling analysis results obtained using the R–R method are compared with the results obtained from the finite element (FE) method for all layup schemes considered and comparison shows an excellent match for all the beam boundary conditions considered and thereby proves simplicity, accuracy, and robustness of present closed-form analytical expressions for predicting the buckling and post-buckling behavior of composite beams with symmetric and asymmetric layup orientations. [Copyright &y& Elsevier]

Abstract: The characterization and commissioning of composite structures for impact resistance requires extensive analytical, computational and experimental studies. It is usually necessary that scaled model tests are carried out that represent real structure behavior as much as possible. Reliable methods are thus required that provide accurate scaling rules for dynamic similarity between models and prototypes. This paper presents a general similitude method for scaling the low-velocity impact response of different composite structures. It is demonstrated that impact cases or situations in different structures having the same set of three non-dimensional parameters will be dynamically similar, and have the same normalized impact response despite being different with respect to their type, boundary conditions, materials and size. In cases of simple structures, such as rods, beams and plates with standard boundary conditions, the parameters can be obtained analytically. In cases of complex structures and boundary conditions, either finite element simulations or simple physical experiments can be carried out to measure the necessary parameters. It is expected that the proposed similitude rules will help researchers to optimize their resources for parametric and experimental studies. [Copyright &y& Elsevier]

Abstract: The static and dynamic response of geometrically imperfect composite beams is presented. The proposed model accounts for the midplane stretching of the beam that follows the classical beam theory and its curvature is assumed to be shallow. The assumption of a small strain, moderate deformation is used. The governing equations are nonlinear integral partial-differential equations. A unified approach is used to handle the postbuckling response of composite beams with and without imperfection. As a result, an analytical solution for the beam’s static response in terms of the applied axial load, imperfection, and lay up is obtained. Moreover, the free vibrations in the postbuckling domain are investigated. Having the beam’s imperfection as a control parameter, the beam’s static and dynamic response is investigated and presented. Results show that the imperfection has a significant effect on the static and dynamic response of composite beams. [Copyright &y& Elsevier]

Abstract: The exact dynamic stiffness matrix of a uniform laminated composite beam based on trigonometric shear deformation theory is developed in this paper. A refined laminated beam constitutive equation is derived that takes into account the breadth direction strains. The dynamic stiffness matrix is formulated directly in an exact sense by solving the governing differential equations of motion that describe the deformations of laminated beams according to the trigonometric shear deformation theory, which includes the sinusoidal variation of the axial displacement over the cross-section. The derived dynamic stiffness matrix is then used in conjunction with the Wittrick–Williams algorithm to compute the natural frequencies and mode shapes of the composite beams. The results obtained from the present theory are compared with those available in the literature wherever possible. [Copyright &y& Elsevier]

Abstract: An exact solution for the postbuckling configurations of composite beams is presented. The equations governing the axial and transverse deformations of a composite laminated beam accounting for the midplane stretching are derived. The inplane inertia and damping are neglected, and hence the two equations are reduced to a single nonlinear fourth-order partial–integral–differential equation governing the transverse deformations. We find out that the governing equation for the postbuckling of symmetric or asymmetric composite beams has the same form as that of beams made of an isotropic material. Composite beams with fixed–fixed, fixed–hinged, and hinged–hinged boundary conditions are considered. A closed-form solution for the postbuckling deformation is obtained as a function of the applied axial load, which is beyond the critical buckling load. To study the vibrations that take place in the vicinity of a buckled equilibrium position, we exactly solved the linear vibration problem around the first buckled configuration. Solving the resulting eigen-value problem results in the natural frequencies and their associated mode shapes. Both the static response represented by the postbuckling analysis and the dynamic response represented by the free vibration analysis in the postbuckling domain strongly depend on the lay-up of the laminate. Variations of the beam’s midspan rise and the fundamental natural frequency of the postbuckling domain vibrations with the applied axial load are presented for a variety of lay-up laminates. The ratio of the axial stiffness to the bending stiffness was found to be a crucial parameter in the analysis. This control parameter, through the selection of the appropriate lay-up, can be manipulated to help design and optimize the static and dynamic behavior of composite beams. [Copyright &y& Elsevier]

Abstract: Analytical prediction methods for axial stresses and deflections at the serviceability limit state and for ultimate failure loads are proposed for hybrid bridge girders consisting of FRP bridge decks adhesively bonded to steel girders. The methods allow for the consideration of partial shear connection layers in hybrid cross-sections. It was found that the adhesive bond always provides full composite action between FRP decks and steel girders, even in the case of flexible polyurethane adhesives with a layer thickness up to 50mm. For pultruded bridge deck systems, however, the webs or diagonals between the upper and lower face panels provide only partial shear connection of the upper face panels in the longitudinal bridge direction. The results of these prediction methods were compared to experimental results from full-scale girders with two different pultruded FRP bridge deck systems and were found to match well. [Copyright &y& Elsevier]