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Owing to the excellent conductivity and physical properties, graphene can significantly enhance the piezoelectric and mechanical characteristics of the piezoelectric matrix. This article studies the actuation behavior of laminated composite beams integrated with a graphene-reinforced composite piezoelectric (GRCP) actuator. Structural deformations are achieved by interlaminar stresses at interfaces between the piezoelectric actuators and the composite beams. Interlaminar stresses cannot be neglected for the structural analysis of composite beams with a GRCP actuator. Composite beams actuated by GRCP actuators exhibit more complex interlaminar mechanical behavior than traditional composite beams. Existing higher-order shear deformation theories may lose the capability for the actuation behavior of composite beams with GRCP actuators subjected to electromechanical loadings. Thereby, an advanced theory is to be proposed for the actuation performance of GRCP actuators acting on composite beams. Differing from earlier higher-order theories, the proposed theory includes an electromechanical interlaminar shear stress field that can accurately describe the distributions of interlaminar shear stresses without any additional postprocessing procedures. Additionally, a three-node beam element is constructed in terms of the proposed theory. The three-dimensional elasticity solutions, two-dimensional finite element solutions, and the results calculated by the other theories are employed to evaluate the proposed beam theory. Numerical results show that the proposed electromechanical coupling beam model can produce promising results. Additionally, the impacts of significant parameters on the actuation performance of laminated beams with a GRCP actuator are thoroughly investigated. [ABSTRACT FROM AUTHOR]

The possibility of using the universal software ANSYS to study the concentration of interlaminar stresses near the free edges of laminated composites in a two-dimensional finite element formulation is considered. In this case, the cross-section of a rectangular four-layer composite plate of finite width with free side edges subject to uniform axial deformation is simulated. To create it, an original technique is proposed which consists in using thermal stress. The presented calculation results are in good agreement with the results of other authors.

In this paper, the free-edge effects which play an important role in the failure analysis of composite laminates are studied. Pure temperature change and its combination with biaxial tension are investigated for a composite plate with a centric circular hole that is adequately small in comparison to the dimension of the plate. Moreover, the laminate is assumed to be thin, the temperature change of all points of the plate is identical and the biaxial tensile load is applied far from the center of the hole. For this purpose, a semi-analytical method based on a two-dimensional thermoelastic boundary layer theory and a minimum potential energy principle is proposed. It is shown that the present method predicts the interlaminar peeling and shear stresses surrounding the hole with good agreement compared to the results obtained by FEM analysis. [ABSTRACT FROM AUTHOR]

• Interlaminar stresses of multi-layered PV-TE hybrid device are analyzed. • Interlaminar stress without considering Thomson effect is overestimated. • Thermal contact resistance has great effect on stress of PV module. • Thermal contact resistance hardly has no effect on stress of TE module. • Interlaminar stresses decrease with decreasing thickness of TE legs. A concentrated photovoltaic-thermoelectric hybrid device made up of a six-layer composite structure is considered. The hybrid device is composed of, from top to bottom, photovoltaic cell, ethylene vinyl acetate (EVA) layer, tedlar polyester tedlar (TPT) layer, ceramic layer, electrode, and thermoelectric legs. Under the service condition, the poor interlaminar mechanical performance of the hybrid device induced by the high interlaminar stresses level can give rise to very poor power generation performance. To understand this, an analytical model is built to study the influence of the thermal contact resistance and interfacial slip stiffness on the interlaminar stresses of the hybrid device. In particular, effects of the material parameters and geometric dimensions of the hybrid device are also studied by using the state space method. It is found that the thermal contact resistance mainly affects the interlaminar stresses of the photovoltaic module. The interlaminar stresses without considering the temperature-dependent material properties are greater than the actual stresses. The highest interlaminar shearing stress appears at the lower surface of the photovoltaic cell and the maximum peeling stress occurs at the interface between the EVA layer and TPT layer. A lower interfacial slip stiffness is conducive to reducing the interlaminar stresses. The interlaminar stresses decrease with decreasing elastic modulus and coefficient of thermal expansion of the EVA layer. In addition, a thinner thermoelectric layer contributes to lower the interlaminar stresses. The results offer helpful suggestions for the optimization of the interlaminar mechanical performance of the hybrid device. [ABSTRACT FROM AUTHOR]

An improved analytical model for the axisymmetric stress state of an adhesive joint of two cylindrical shells is proposed. The adhesive layer acts in shear and cleavage. It is assumed that the tangential stresses vary linearly across the thickness of the adhesive layer. The two-parameter Vlasov–Pasternak model of an elastic foundation is used to describe the normal stresses in the adhesive. The approach proposed makes it possible to satisfy boundary conditions at the load-free butt of the adhesive layer and to describe the stress state of adhesive with a high accuracy. The closed-form solution is obtained. A model problem is also solved. [ABSTRACT FROM AUTHOR]

The free edges of layered structures require special attention in design processes. Due to the discontinuous material properties, singular stress concentrations occur where the layer interfaces meet the free edge. These bi-material points have to be closely examined as possible starting points for delamination processes. In the present study, we propose an efficient approximate closed-form method to analyze the interlaminar shear stresses in symmetric angle-ply laminates under uniform axial extension and homogeneous thermal loading. The method bases on a higher-order layerwise displacement approach. The resulting displacement and stress distributions of a first-order and a third-order analysis are compared and validated against numerical reference data gained by a self-developed finite element formulation. Especially, the results of the third-order analysis show a good agreement to the reference data along the interface, even if the singular behavior of the stresses in the very close vicinity of the free-edge cannot be reproduced exactly. A comparison of the displacement and stress distributions in thickness direction shows the benefit of the third-order over the first-order approach. In addition, the influence of the ply angle on the results is reproduced by both approaches. [ABSTRACT FROM AUTHOR]

The present work introduces two novel semi-analytical methods for the three-dimensional stress analysis of thick, circular cylindrical cross-ply laminated shells subjected to hygrothermomechanical loadings under consideration of the free-edge effect. Comparisons with full-scale three-dimensional finite element computations and existing semi-analytical approaches from literature confirm the good accordance of the numerical results. Furthermore, parametric studies, wherein the influence of various hygrothermomechanical loading conditions on the free-edge stress fields are investigated, revealed that the interlaminar stresses in laminated shells are impacted significantly by the orientation of the load introduction and can even be reduced when the composite laminate is exposed to humidity. [ABSTRACT FROM AUTHOR]

Adhesive lap joints are widely used in modern structures. Known analytical mathematical models of the stress state of lap joints describe the joints of straight beams or cylindrical coaxial pipes. It is assumed that the stress state of these structures depends on only one coordinate. The study of the stress state of plates with defects, which are reinforced by patches, in most cases requires the use of at least two-dimensional mathematical models. In this work, it is shown that the axial symmetry of the plate, the cut-out, the patch, and the applied load makes it possible to reduce the problem to a one-dimensional problem in the polar coordinate system. An adhesive lap joint with circular symmetry is considered for the first time. The stress-strain state of the structure is described in an analytical form. Comparison of the results of calculating the stress state of the joint with the results of finite element modelling showed good adequacy of the proposed mathematical model. [ABSTRACT FROM AUTHOR]

In this research a novel probabilistic numerical approach is developed to investigate the effectiveness of piezoelectric (PZT) materials to enhance the reliability of composite laminates under edge delamination onset (EDO). To achieve this, finite element (FE) modeling is employed as an implicit limit state function (LSF) based on a quadratic failure criterion and the concept of critical length. An interactive interface that integrates FE analysis and reliability analysis is then established to execute both processes simultaneously until the convergence condition of the reliability index is satisfied. To validate current FE analysis, the interlaminar stress peaks, and resulting edge delamination probability obtained in this study are compared with available data. Subsequently, the probability of EDO in angle-ply composite laminates under applied longitudinal strain and an applied electric field on the PZT layer is assessed using both the first-order reliability method (FORM) and the second-order reliability method (SORM). The Monte Carlo simulation (MCS) is employed to verify the numerical results. Findings reveal that employment of PZT reduces EDO probability. Moreover, as the applied voltage increases, the critical strain required for definitive EDO also increases, and the positive influence of PZT on enhancing reliability becomes more pronounced, particularly with increased thickness under higher applied strain. [ABSTRACT FROM AUTHOR]

• Explored factors influencing interlaminar stresses and energy release rates within carbon fibre-based laminated structures. • Derived non-dimensional functions to characterise stresses and energy release rates. • Introduced a semi-elliptical crack at the free edge to estimate energy release rates. • Employed finite element and Virtual Crack Closure Technique. • Demonstrated the framework's applicability across various laminate configurations. Traditional approaches that rely on stress or energy-based criteria to predict delamination require the determination of stresses before crack onset or energy release rates after crack initiation, respectively. While a relatively new coupled criterion, Finite Fracture Mechanics, necessitates the computation of both stresses and energy release rates. This study discusses the numerical determination of the interlaminar stresses and energy release rates of interlaminar semi-elliptical cracks emanating at the free edge in carbon fibre-reinforced polymer materials. The method establishes a new semi-analytical framework, based on dimensional analysis, which permits obtaining a functional expression for the stresses and the energy release rates in function of material and geometrical parameters. This framework eliminates the need to re-solve the underlying boundary value problem for a different material, geometry, and load. The non-dimensional functions are obtained by performing careful interpolation from a set of finite element solutions, ensuring predictions are accurate and within acceptable numerical limits. The influence of material contrast and relative ply thickness on interlaminar stresses and energy release rates are investigated using the semi-analytical framework. Additionally, the fracture mechanics analysis is also conducted to investigate the influence of semi-axes of semi-elliptical crack on energy release rate distributions. Understanding the interlaminar stresses and energy release rates is essential for applying either stress, energy, or coupled criterion to predict the structural strength of a layered body. [ABSTRACT FROM AUTHOR]

• The delamination onset at free edges in angle ply laminates is investigated using 3D Finite Fracture Mechanics (FFM). • A semi-elliptically shaped crack is assumed to emanate from the dissimilar interface post-crack onset. • Dimensional analysis allows for generalizing the expression of the incremental energy release rate and interlaminar stresses. • A homothetic crack extension is presumed, keeping the aspect ratio of the semi-ellipse constant. • The FFM criterion's predictions closely align with experimental test results from existing literature. The layered structures exhibit a weakly singular stress state in the vicinity of free edges, attributable to the elastic mismatch of adjacent plies, thereby promoting delamination. In the present study, this so-called free edge effect is investigated for symmetric angle-ply laminates in the framework of the Finite Fracture Mechanics (FFM). For a given intrinsic properties, such as fracture toughness and strength, the computation of the interlaminar stresses and energy release rate is imperative for the evaluation of coupled FFM criterion. These quantities are determined in terms of non-dimensionalised functions employing a comprehensive three-dimensional Finite Element Method (FEM) model. Dimensional analysis facilitates finding these functions for all laminate configurations only once while preserving the generality of functions. A semi-elliptically shaped crack is presumed to nucleate at the dissimilar interface post-crack initiation. Given that, the considered crack has two dimensions, the solution of 3D FFM model leads to an optimisation problem. It is hypothesised that homothetic crack extensions occur, i.e., cracks extend only in a self-similar manner, maintaining a constant aspect ratio of semi-ellipse. For validation purposes, the prediction of the laminate fracture using proposed 3D FFM fracture criterion is compared with the experimental test results found in the literature for various laminate types (AS1/3501-6, T800/914, G947/M18) and layups ( [ ± 10 n ] s , [ ± 15 n ] s , [ ± 20 n ] s , [ ± 30 n ] s). It is observed that close agreement can be achieved between prediction and experiments when intrinsic properties are known. [ABSTRACT FROM AUTHOR]

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Abstract This paper proposes a new finite-element modelling of a recent layerwise model for multilayered plates. This layerwise model is built from a specific 3D stress-field expansion along the thickness direction and involves, in particular, interlaminar transverse shear and out-of-plane stresses as generalized stresses. Its main feature is that 3D equilibrium equations and free-edge boundary conditions are directly taken into account into the stress-based construction of the model. A dual displacement-based finite-element discretization is implemented using the FEniCS software package and a remeshing strategy is proposed based on a novel error indicator. The error indicator is built based on the 3D stress field directly deduced from the layerwise generalized stresses and compared to a reconstructed stress field based on the model generalized displacements. The proposed error indicator is shown to identify the most critical parts of a laminate structure associated with complex 3D stress fields such as boundaries or stress concentration/singularity regions (near free-edges or delamination fronts). Through the combination of thickness discretization and in-plane mesh refinement in regions of interest, the proposed framework therefore offers an attractive alternative to 3D solid finite elements for an accurate prediction of stress states in composite laminates.

This paper introduces a new loading condition considering the combined thermo-electro-mechanical coupling effect in a series solution-based approach to analyze the free-edge interlaminar stresses in smart composite laminates. The governing equations are developed using the principle of complementary virtual work. The assumed stress fields satisfy the traction-free and free-edge boundary conditions. The accurate stress states of the composite structures are acquired through the procedure of generalized eigenvalue problems. The uniform temperature is employed throughout the laminate, and the electric field loading is applied to the symmetric piezo-bonded actuators to examine the combined effect of thermal and electrical stresses on the overall deformation of smart composite laminates. It was observed that the magnitude of the peeling stresses generated by mechanical loading was reduced by the combined thermal and electric excitation loading (up to 25.3%), which in turn resulted in expanding the service life of the smart composite structures. The proposed approach is implemented on three different layup configurations. The efficiency of the current methodology is confirmed by comparing the results with the 3D finite element (FEM) solution computed by ABAQUS.

A semi-analytical solution theory is presented by combining the separable Hamilton canonical equation and finite element method. The problem of free-edge effect of orthotropic laminates is studied in symplectic system. First, the separable Hamilton canonical equations are established with modified Hellinger-Reissner variational principle. And the state equations are established with finite element method. Then, an example analysis of the distribution of interlaminar stresses in composite laminates is calculated. The numerical results show the efficiency of the proposed method.

This paper proposes a new finite-element modelling of a recent layerwise model for multilayered plates. This layerwise model is built from a specific 3D stress-field expansion along the thickness direction and involves, in particular, interlaminar transverse shear and out-of-plane stresses as generalized stresses. Its main feature is that 3D equilibrium equations and free-edge boundary conditions are directly taken into account into the stress-based construction of the model. A dual displacement-based finite-element discretization is implemented using the FEniCS software package and a remeshing strategy is proposed based on a novel error indicator. The error indicator is built based on the 3D stress field directly deduced from the layerwise generalized stresses and compared to a reconstructed stress field based on the model generalized displacements. The proposed error indicator is shown to identify the most critical parts of a laminate structure associated with complex 3D stress fields such as boundaries or stress concentration/singularity regions (near free-edges or delamination fronts). Through the combination of thickness discretization and in-plane mesh refinement in regions of interest, the proposed framework therefore offers an attractive alternative to 3D solid finite elements for an accurate prediction of stress states in composite laminates. [ABSTRACT FROM AUTHOR]

• Interlaminar stresses of laminated piezoelectric plates are obtained using analytical solution. • Electromechanical coupling effect of the piezoelectric plate is taken into account. • The solution is obtained using 3-D multi-term extended Kantorovich method. • Coupling influence on the edge effects of piezolaminated plates with various layups is investigated. In this paper, the interlaminar stresses of generally laminated piezoelectric (PZT) plates are presented. The electromechanical coupling effect of the piezoelectric plate is considered and the governing equations and boundary conditions are derived using the principle of minimum total potential energy. The solution procedure is a three-dimensional multi-term extended Kantorovich method (3DMTEKM). The objective of this paper is to study coupling influence on the edge effects of piezolaminated plates with finite dimensions and arbitrary lay-ups under uniform axial strain. These results can provide a benchmark for checking the accuracy of the other numerical methods or two-dimensional laminate theories. To verify the accuracy of the 3DMTEKM, special cases such as cross-ply or symmetric laminates are investigated and the results are compared with other analytical solutions available in the literature. Excellent agreement is achieved and then other numerical results are presented for general cases. Numerical examples imply on the singular behavior of interlaminar normal/shear stresses and electric field strength components near the edges of the piezolaminated plates. The coupling influence on the free edge effect with respect to the lay-ups of piezoelectric plate is studied in several examples. [ABSTRACT FROM AUTHOR]

In this article, a displacement model for micro and nano laminated composite Timoshenko beam is presented. The layer-wise displacement model is refined in order to calculate interlaminar stresses correctly. In the presented model, the behavior of displacements at the interface of adjacent layers is modeled by transverse and tangential springs of high stiffnesses. The reaction of various springs in different directions indicates an approximation of transverse and tangential interactions between adjacent layers of the laminated beam. Using the presented model and also modified couple stress theory, the in-plane stresses of the laminated composite Timoshenko beam subjected to different boundary conditions including simply–simply supported, clamped–clamped, and clamped–free are studied. In addition, the effects of material length scale parameter and elastic foundation on the stresses are investigated. The advantage of this method is accurate calculation of interlaminar stresses without using the equilibrium equations. [ABSTRACT FROM AUTHOR]

Abstract In this paper, the interlaminar stresses in open-hole laminates subjected to compressive loads are analysed using a numerical model. This model implements the Serial/Parallel Mixing Theory (S/PMT) and a Continuum Damage Mechanics (CDM) approach. The S/PMT estimates the global stiffness in the laminate from fibre and matrix properties. The CDM approach models the damage initiation due to fibre microbuckling. The global response estimated by the model was verified with experimental data from the literature. The model predicts that the damage initiates in the laminate middle-plane where the thickest block of plies oriented in the load direction is located, and progressively propagates to the nearest block of layers with the same orientation. Two laminate stacking sequences were analysed. The interlaminar stresses around the hole presented symmetry with respect to the load direction and the perpendicular axis, being located the maximum and minimum values in different angular positions for each stress component and laminate. [ABSTRACT FROM AUTHOR]

Abstract This paper develops a formulation for displacement-only beam elements based on isogeometric analysis, with intended application to laminated composite members. The main purpose of the current study was to overcome some deficiencies of commonly used beam theories, such as shear-locking, the lacking relevance of isotropic materials for multi-layer composites, the incompatibility with other continuum elements, and the limited continuity in interpolation. A bi-variable non-uniform rational B-spline (NURBS) beam element with complete plane-stress elasticity terms and geometrical expressions was developed. Shear-locking, interlaminar stresses, the deep-beam situation, and vibration features were evaluated for several aspect ratios, ply orientations, and NURBS degrees, in order to verify the efficiency and accuracy. h -, p - and k -refinements were used to improve the displacement field. The validity of the solutions was measured based on results from plane-stress finite element analysis, and compared to the alternative Carrera unified formulation. Results show that the isogeometric displacement-only beam theory can provide the interlaminar stress distribution, gives high accuracy for mid and high-range eigen-frequencies, and avoids the shear-locking phenomenon. Highlights • A displacement-only beam element was formulated based on an IGA-approach. • In-plane elasticity was used for a bi-variate NURBS form. • h-, p- and k-refinements were studied for improving results. • Interlaminar stresses in a laminated composite beam could be evaluated. • Formulation gave good accuracy for static and vibration problems. [ABSTRACT FROM AUTHOR]

Innovative manufacturing methodologies offer opportunity to fabricate tapered composite laminates without layer terminations. However, the complex mechanical behaviour of tapered composite beams has yet to be studied. We introduce an accurate cost-efficient analytical method in line with Timoshenko theory to predict transverse stresses of composite laminated beams comprising orthotropic tapered layers under transverse loading, including pressure loads and transverse body forces. The transverse stress components are derived by introducing taper into the lamina constitutive relation followed by Cauchy stress equilibrium. The main conclusions of this study include: (i) transverse stresses are fully coupled with the internal forces and their derivatives; (ii) transverse stresses can be discontinuous through the thickness; (iii) Classical Laminate Theory underestimates transverse stress magnitudes of composite laminated beams. Results are validated with 2D and 3D solid-like finite element analyses inferring high levels of accuracy for the transverse stresses valid up to 8 ° of taper. • Analytical interlaminar stress field of composite tapered beams in bending. • External loads are prescribed by layer, including body forces and pressure loads. • Transverse stress field is discontinuous through the thickness. [ABSTRACT FROM AUTHOR]

The boundary layer hygrothermal stresses in the thick sandwich cylinder with laminated face are investigated. Uniform and through the thickness steady-state distribution for temperature and moisture content can be considered in the analysis. A displacement based layer-wise formulation is presented for analysis of thick sandwich composite cylinders subjected to hygrothermal loading conditions. Considering a general displacement field and employing a displacement based layer-wise theory, the governing equations of thick laminated sandwich cylinder are obtained. The displacement based formulation is derived for thick sandwich cylinder, which is subjected to non-uniform hygrothermal loading conditions. The faces of the sandwich cylinder are made of laminated composite with general layer stacking. The governing equations of the system include a set of coupled differential equations on the displacement components of the numerical surfaces. A semi-analytical solution is developed and the governing equations are solved for free edge boundary conditions. The accuracy of the numerical results is validated by the results of the finite element simulation and good agreements are seen between the predicted results. The free edge interlaminar stresses distributions are presented for thin and thick sandwich composite cylinders for uniform and non-uniform loading conditions. It is concluded that the presented layer-wise formulation is efficient and accurate method for analysis of thermal and hygroscopic stresses in thick and thin sandwich cylinders with general layer stacking. [ABSTRACT FROM AUTHOR]

The free-edge effects and relative layer shifting in the interlaminar and intralaminar stresses of plain woven composite laminates under uniaxial extension is investigated numerically using a finite element approach. A computational framework of the free-edge problem for periodic structures with finite width is applied to woven laminates. First, two-layered laminates with three different shifting configurations are studied considering repeating unit cells simulating finite and infinite width. For each configuration, two different widths are considered by trimming the model at different locations in order to investigate different free-edge effects. Then, two four-layered laminates with no shifting and a maximum shifting configuration are analyzed to illustrate the effect of neighboring layers in the stresses. For each shifting configuration, different delamination mechanisms are expected. When considering more layers, it is found that the stacking configuration affects the state of stress and the free-edge effects depending on the shifting. In general, a different behavior than that of unidirectional tape laminates is found, since the interlaminar and intralaminar stresses can be higher than those generated at the free-edges. Particularly, for the maximum shifting configuration results are in agreement with experimental results in the literature where no debonding between yarns was observed at the free-edges. [ABSTRACT FROM AUTHOR]

In this paper, an analysis method for the determination of displacement, strain and stress fields in cylindrically curved cross-ply laminates under bending load is presented. The considered cross-ply laminates may be either symmetrically or unsymmetrically laminated and are clamped at one end while the other end is loaded by an evenly distributed bending moment. The analysis method employs a layerwise plane strain approach in the inner regions of the laminate in which the stresses in each layer are represented by adequate formulations for Airy’s stress function. In the regions of the free laminate edges where significant three-dimensional and possibly singular interlaminar stress fields are to be expected, the plane-strain approach is upgraded by a layerwise displacement-based formulation wherein the physical laminate layers are discretized into a number of mathematical layers with respect to the thickness direction. The governing differential equations for the unknown additional displacement functions with respect to the width coordinate in the form of the Euler-Lagrange equations stemming from the underlying variational statement can be solved exactly and eventually lead to an eigenvalue problem that needs to be solved numerically. Usage of continuity conditions between the individual laminate layers and formulation of adequate boundary conditions at the free edges in an integral sense then lead to complete representations for displacements, strains and stresses at every location in the considered laminate. While the analysis approach relies on a discretization of the laminate into a number of mathematical layers with respect to the thickness direction and further requires a numerical solution of a quadratic eigenvalue problem, it provides closed-form analytical solutions concerning the width direction and can thus be classified as being a semi-analytical solution. The presented analysis method is compared to the results of comparative finite element simulations and is shown to be in good agreement, however with only a fraction of the computational effort that is required for according finite element simulations. [ABSTRACT FROM AUTHOR]

Present paper deals with layered shells subjected to static loading. The basic equations include besides the global equilibrium formulated in terms of stress resultants, the local equilibrium in terms of stresses, the geometric field equations, the constitutive equations, a constraint which enforces the correct shape of the superposed displacement field through the thickness and the boundary conditions. Thereby an interface to three-dimensional material laws is created. The weak form of the boundary value problem is derived and a finite element formulation for quadrilaterals is specified. The mixed hybrid shell element possesses the usual 5 or 6 nodal degrees of freedom. This allows standard geometrical boundary conditions and the elements are applicable also to shell intersection problems. For linear elasticity the computed transverse shear stresses are automatically continuous at layer boundaries and zero at the outer surfaces. In comparison to fully 3D computations present element formulation needs only a fractional amount of computing time. [ABSTRACT FROM AUTHOR]

The laminate load bearing capability is often compromised when delamination occurs even though the laminae remain intact. The out-of-plane components of the stress tensor, defined at the interfaces between plies, are typically responsible for the delamination of multi-layered materials. Commonly used failure criteria for delamination make use of both shear and normal interlaminar stresses. In this work the out-of-plane stresses inside a woven laminate were numerically evaluated using a micromechanical model. Under three point bending the existence of local normal interlaminar stress related to the fabric architecture was demonstrated. The influence of the due to texture normal interlaminar stress on the fracture occurrence was discussed. The reduction of the apparent interlaminar shear strength as effect of the span-to-depth ratio increase was successfully reproduced introducing a dependence of the delamination shear limit from the stress triaxiality gradient. [ABSTRACT FROM AUTHOR]

Nitsche’s method had recently demonstrated its potential for a seamless and continuity-preserving coupling of NURBS patches in isogeometric shell analysis. Trimmed and non-conforming patches and even blended models including classical thin-shell and solid-shell formulations can be coupled successfully while preserving a continuous flux along the coupling interfaces. In this paper, we take advantage of the method’s modeling flexibility for an extension to NURBS-based laminate composite shell structures. We introduce a global-local model coupling approach to enrich laminate composite thin-shell Kirchhoff-Love models locally with a full three-dimensional continuum solution. The approach provides a reliable coupling of the classical lamina theory with a layerwise formulation revealing the full interlaminar stress state at reduced computational cost. The layerwise shell model is based purely on a mid-surface NURBS description of the shell body thus supporting the direct application of a surface-defined CAD data representation of shells. We apply a refined finite cell approach to handle efficiently trimmed geometries, as common in CAD models. We demonstrate reliability, accuracy of the coupling approach and efficiency in terms of numerical costs and modeling effort of our approach with several examples. [ABSTRACT FROM AUTHOR]

Interlaminar stresses in thick a composite cylinder with general layer stacking subjected to uniform and nonuniform distributed radial pressure are studied. The layerwise theory of Reddy is employed for formulation of the problem. An analytical method is presented for solving the governing equations. To increase accuracy, interlaminar stresses are obtained by integrating the equilibrium equation of elasticity. After a convergence study, the accuracy of the layerwise laminate theory is investigated using the predictions of finite element method. Predictions of Hooke's law and integration method for interlaminar stresses are compared. Uniform and nonuniform internal and external loads are considered and a parametric study is done for various cylinders. [ABSTRACT FROM PUBLISHER]

An analytical approach is presented to investigate nonlinear dynamic responses of sandwich plates. To obtain governing differential equations of motion, the higher order shear deformation theory is employed together with Hamilton’s principle. The Navier’s solution and Runge-Kutta method using available mathematical package software MAPLE 14 are used to solve the governing equations. This method can consider any required number of layers through the sandwich plate thickness. To evaluate the method validity a sandwich plate with FGM face sheets and the FRC core resting on an elastic foundation is subjected to the blast load due to the burst of 5 kg charge. The maximum plane-normal displacement is obtained by the analytical method and numerical approach. Comparison between results shows good agreement. Thereafter, time histories obtained from both analytical and numerical approaches are compared. The interlaminar stresses are obtained through the sandwich plate thickness. The results show that neither material failure nor delamination occurs. [ABSTRACT FROM AUTHOR]

A novel semi-analytic model is developed to determine interlaminar stresses in laminates including highly curved parts, for obtaining a rapid, accurate and reliable design tool for evaluating the reserve factor of a certain aeronautic composite component prone to unfolding failure. The model assumes plane conditions and is based, firstly, in an approximation of the 2D displacement components by using a series of functional products of separate variables and, secondly, in the use of higher-order moments of the stress components, which allow an enriched beam model to be constructed. The solution is obtained as the sum of products of a set of known functions, written in terms of the eigenvalues and eigenvectors of the matrix governing the model, and a set of integration constants. These constants can be determined with the boundary conditions, in isolated parts, and the continuity conditions, in laminates containing parts with different curvatures. In comparison with an existing analytical method, the present model has the advantage of offering an extremely accurate solution at the zones in which the analytical method may yield errors of even a 100%. In comparison with a detailed finite elements model, the present model obtains a similar accuracy in much lower computational times. [ABSTRACT FROM AUTHOR]

Curved laminates are prone to delamination failure from applied bending moments that straighten out the laminate and induce tensile stresses in the unreinforced radial direction. These non-classical through-thickness stresses are important even for thinner configurations and need to be accounted for in the design of lightweight composite structures, preferably in a computationally efficient manner. Here, we investigate failure-inducing critical stresses for a number of curved laminates using a higher-order beam model derived from the Hellinger–Reissner mixed variational principle, which guarantees that the hoop, interlaminar shear and radial stresses are equilibrated. By solving the governing equations of the theory in the strong form using the pseudo-spectral differential quadrature method, the model is capable of predicting accurate 3D stress fields in curved laminates, even in the vicinity of localised features such as supported edges. The model is used alongside commonly used failure criteria to reproduce experimental failure initiation results found in the literature, and the comparison suggests that failure mode, location and load are all predicted accurately. Finally, failure maps that highlight the critical stress component for failure initiation are constructed. As the thickness of the curved laminate increases, the critical stress component transitions from intralaminar hoop stress to interlaminar shear or radial stress depending on the specific laminate configuration. These findings and failure maps collectively provide insights into the mechanics of failure initiation that should also prove useful for design purposes. [ABSTRACT FROM AUTHOR]

Determination of the local interlaminar stress distribution in a laminate with a bolt-filled hole is helpful for optimal bolted joint design, due to the three-dimensional (3D) nature of the stress field near the bolt hole. A new interlaminar stress distribution phenomenon induced by the bolt-head and clamp-up load, which occurs in a filled-hole composite laminate, is investigated. In order to efficiently evaluate interlaminar stresses under the complex boundary condition, a calculation strategy that using zero-thickness cohesive interface element is presented and validated. The interface element is based on a linear elastic traction-separation description. It is found that the interlaminar stress concentrations occur at the hole edge, as well as the interior of the laminate near the periphery of the bolt head. In addition, the interlaminar stresses near the periphery of the bolt head increased with an increase in the clamp-up load, and the interlaminar normal and shear stresses are not at the same circular position. Therefore, the clamp-up load cannot improve the interlaminar stress distribution in the laminate near the periphery of the bolt head, although it can reduce the magnitude of the interlaminar shear stress at the hole edge. Thus, the interlaminar stress distribution phenomena may lead to delamination initiation in the laminate near the periphery of the bolt head, and should be considered in composite bolted joint design. [ABSTRACT FROM AUTHOR]

A refined 6-node two-dimensional mixed finite element has been developed to analyze laminated composite using the minimum potential energy principle. This model uses four primary variables, two displacements u , w and two transverse stresses σ z and τ x z at each node. In the formulation process, fundamental elasticity relations, that is, displacement-strain relations, stress–strain relations, and the equilibrium equations, have been explicitly satisfied. The transverse stress terms have been invoked using the displacement-strain relation and then the stress–strain relation. The refinement in the model has been performed using the equilibrium equation in the x and z direction. This formulation is an improvement over the Desai and Ramtekkar (2002) model and contributes to the computational mechanics domain of laminates analysis. Refinement in the formulation has been performed by satisfying the equilibrium equation explicitly at the nodes. This refinement helps in getting better results with a fewer number of elements. Results obtained through the model has been compared with the elastic solution given by Pagano (1969) and the mixed finite element method by Desai and Ramtekkar (2002) model. Results show excellent agreement with the elastic solution and more economical as only 2/3rd number of the element as compared to Desai and Ramtekkar (2002) model is required for the converged results. • A two-dimensional six node mixed finite element model has been developed. • All three elasticity equations have been explicitly satisfied at the nodes. • Minimum potential energy principle was used as extremum functional in the formulation to obtain the solution. • This formulation is more accurate and economical. [ABSTRACT FROM AUTHOR]

On the basis of the finite-layer method, a technique for calculating the two-dimensional stress-strain state and interlaminar stresses in edge-cracked specimens in tests on determination of the Mode I, II, and III fracture toughnesses of composites is proposed. Taking into account the symmetry and antisymmetry of specimens, the calculation is reduced to a boundary-value problem for a system of partial differential equations describing the deformation of one of the layers. Using the method of straight lines, the two-dimensional problem is reduced to a one-dimensional boundary-value problem, which is solved by the stable Godunov-Grigorenko numerical method. Calculations for specimens subjected to three types of the tests are performed, and the distributions of normal and tangential stresses on the specimen midplane and the distributions of modal components of the fracture toughnesses G, G, and G along the delamination front line are presented. Comparisons with results of the one-dimensional solution and with known results obtained by the virtual crack closure technique are presented. [ABSTRACT FROM AUTHOR]

A higher-order beam model for analyzing the flexural response of curved multilayered beams with constant curvature and arbitrary constant thickness is developed. The new model is derived from the Hellinger–Reissner mixed variational statement and predicts inherently equilibrated 3D stresses from an equivalent single-layer model. As a starting assumption, the hoop stress is formulated as a series of higher-order stress resultants multiplied by Legendre polynomials. The governing equations are derived in a generalized manner such that the modeling order can be adjusted and is not defined a priori. Hence, the highest order Legendre polynomial determines the modeling order. The through-thickness shear and normal stresses are derived by integrating the generalized hoop stress in Cauchy’s polar equilibrium equations. As a result, all stress fields are based on the same set of variables, thereby considerably reducing the computational effort. The three stress fields, and two displacements in the radial and hoop directions are used in the Hellinger–Reissner functional to derive a new set of stress-displacement relations. The enforcement of the classical membrane and bending equilibrium equations of curved beams in the Hellinger–Reissner functional guarantees that all interlaminar and surface traction equilibrium conditions are satisfied exactly. A validation study of a composite laminate using a high-fidelity 3D finite element model shows that the stresses are captured very accurately by the present model, but with much less computational effort than the finite element model. As a result, the developed model can provide rapid and accurate insights into the expected damage onset behavior of curved laminates. [ABSTRACT FROM AUTHOR]

This paper proposes a new layerwise model for multilayered plates. The model, called SCLS1 for Statically Compatible Layerwise Stresses with first-order membrane stress approximations per layer in thickness direction, complies exactly with the 3D equilibrium equations and with the free-edge boundary conditions. As in the LS1 model initially proposed by Naciri et al. (1998), the laminated plate is considered as a superposition of Reissner plates coupled by interfacial stresses which are considered as generalized stresses. However, the divergences of the interlaminar transverse shears are introduced as additional generalized stresses in the SCLS1 model. Also, a refined version of the new model is obtained by introducing several mathematical layers per physical layer. Contrary to the LS1 model which is derived by means of the Hellinger–Reissner principle, the new model is derived by means of the minimum of the complementary energy principle. This ensures the convergence of the refined SCLS1 solution to the exact 3D solution as the number of mathematical layers per physical layer increases. The new model has been implemented in a new version of the in-house finite element code MPFEAP . Several comparisons are made between LS1, SCLS1 and full 3D FE models in order to assess the performances of the new model which shows itself very effective. [ABSTRACT FROM AUTHOR]

Based on the finite-layer method, a method for evaluating the stress-strain state and energy release rate for specimens with delaminations in double-cantilever beam and end-notched flexure tests is proposed. Exact numerical solutions of boundary-value problems for the 'stiff' systems of differential equations describing deformations of test specimens are obtained. The distributions of forces, moments, displacements, and rotations in the specimens and the distributions of normal and tangential stresses on their midline are presented. New closed-form expressions for these functions and for compliance of the specimens are developed. Calculation results for the energy release rate obtained by a numerical differentiation and from analytical relations are presented. Two new techniques for estimating the energy release rate are proposed: (1) using the calculated values of peak stress and jumps of displacements at the tip of delamination; (2) by evaluation of indeterminacy at the tip of delamination with the use of stresses and derivatives of stresses and displacements. The effect of the transverse shear and Poisson ratio on the results is estimated. A comparison of the numerical and analytical solutions obtained with known results and the ASTM standard is presented. [ABSTRACT FROM AUTHOR]

In this study, based on three-dimensional multi-term extended Kantorovich method (3DMTEKM), an analytical method is established to obtain the interlaminar stresses resulting from bending of thick cylindrical laminated shells with arbitrary laminations and boundary conditions. Numerical results show that this approach can accurately predict the 3D behavior of interlaminar stresses. Also, they clearly indicate the singular behavior of interlaminar normal and shear stresses in the boundary-layer regions near the edges of the shells. The results obtained from this theory are compared with numerical or analytical results of the existing solutions in simplified cases or with those of ABAQUS finite element software for the cases which there exist no results in the literature. Finally, the power of the present approach in obtaining the interlaminar stresses in thick cylindrical laminated shells with general lay-ups, boundary conditions and finite dimensions is examined. [ABSTRACT FROM AUTHOR]

Curved laminates of composite materials are analytically investigated in this paper. Curved zones are a critical part of many kinds of composite beams, for example, L-shaped, C-shaped, Ω -shaped or T-shaped beams, which are susceptible to unfolding failure. A new stress calculation procedure is presented to determine the radial, circumferential and shear stresses in a curved laminate under normal and tangential surface loads and tension, out of plane shear and bending end loads, assuming a 2D stress state. The method assumes that the laminate is made up of a set of fictitious laminas. Making the number of fictitious laminas tend to infinity, analytical solutions are obtained. The nature of the method makes it extremely easy to apply to composite laminates. Firstly, the accuracy of the method is proved by comparing its results with those obtained from the literature for the problems concerning the pure bending of a homogeneous and a layered curved beams. Secondly, the results obtained using this analytic method with the problem of a layered curved beam subjected to surface loads (for which no previous closed-form analytical solution has been found in the literature) are compared with the results obtained using a finite element model, showing excellent agreement. [ABSTRACT FROM AUTHOR]

A coupled three-dimensional piezoelasticity solution for rectangular piezoelectric laminated plates with Levy-type boundary conditions is presented using the mixed-field multi-term extended Kantorovich method (EKM) and Fourier series expansion. The solution considers two-way electromechanical coupling, and satisfies all the essential and natural boundary conditions as well as the continuity conditions at the interface exactly at all points. The objective is to accurately characterize the edge effects in finite dimensional piezolaminated plates under mechanical and actuation potential loading, and also to provide a benchmark for assessing the accuracy of the two-dimensional laminate theories. The interlaminar shear stress is also accompanied by a singular stress field of the transverse normal (peel) stress near the edge. The numerical study is conducted for both single layer PZT plates for sensory applications and hybrid sandwich plates for smart structural applications. It is shown that the EKM solution predicts the displacement, stress, electric potential and electric displacement fields very accurately including the sharp variations of stresses near the edge, under the potential loading with just two/three terms in the trial function. [ABSTRACT FROM AUTHOR]

In axially loaded corrugated laminates consisting of more than one layer interlaminar stresses occur due to the curvature which potentially cause delamination of the laminate. Therefore, it is crucial to know how geometry and lay-up influence the interlaminar stress and hence the risk of delamination. In this paper, a parameter study is presented that studies the influence of corrugation amplitude and different lay-ups on interlaminar stresses. We considered two geometries, one consists of circular sections and the other is a sinusoidal shape. From the parameter study we can derive favorable configurations to minimize normalized interlaminar stresses. A numerical model is used to calculate the stress distribution in the cross-section of the corrugation. It considers a generalized plane strain state and uses a unit-cell approach. The model is validated with experiments in a tensile test using digital image correlation (DIC). [ABSTRACT FROM AUTHOR]

Three-dimensional Finite Element Method (FEM) based thermo-mechanical stress analysis of a laminated Fibre Reinforced Polymer (FRP) composite made spherical shell structure subjected to an elevated thermal filed has been carried out. FE simulation has been carried out through ANSYS 14.0, using Brick 8-node solid 185 layered elements. Shell structures due to curvature effect show thermo-mechanical stress concentration effects not only at the edges but also at various other critical locations in its domain. Appropriate FE mesh size has been adopted to capture these stress concentration effects and has been established through validation with analytical results. Out-of-plane thermo-mechanical interlaminar stresses (σ rr , τ θr , τ ɸr ) has been assumed to be responsible for damage initiation and hence have been analysed in details in order to reveal the critical ply-interface. In order to study dynamic stability of the shell structure under thermal environment, different lamination schemes have been adopted ([0/θ] 4 , θ 0 0 , 15 0 , 30 0 , 45 0 , 60 0 ,75 0 , and 90 0 ). It has been observed that, plies oriented parallel to the cantilevered edge of the shell structure are providing minimum deformation under an elevated thermal environment. However, the laminated shell shows a geometrically non-linear behaviour as the ply-orientation angle has been varied. [ABSTRACT FROM AUTHOR]

Three-dimensional thermo-mechanical stress analyses of cylindrical shell structures made with laminated Fibre Reinforced Polymer (FRP) composites have been carried out. Brick 8-node 185 layered solid elements have been used in the present finite element simulation. Due to curved geometry and interaction of different coupling modes at the ply-interfaces, stress concentration effects have been realized throughout the domain of the laminated shell structure. Appropriate finite element mesh size obtained through convergence study has been adopted to capture these stress concentration effects. Thermal field induced out-of-plane interlaminar stresses (σ rr , τ θr , τ zr ) responsible for delamination damage initiations have been analyzed in details. Effect of different stacking sequences on thermo-mechanical dynamic stability of shell structures has also been studied. It has been observed that, structural dynamics of composite shell structures get significantly affected under elevated thermal field. [ABSTRACT FROM AUTHOR]