A discrete spectral model for intermediate crack debonding in FRP-strengthened RC beams

One of the common failure modes of reinforced concrete (RC) beams strengthened in flexure with a bonded fibre-reinforced polymer (FRP) is intermediate crack (IC) debonding, which is originated at a critical section in the vicinity of flexural cracks and propagates to a plate end. Despite considerable research over the last years, few reliable and simplified IC debonding strength models have been developed. This paper firstly presents a one-dimensional model based on the discrete crack approach for concrete and the spectral element method for the numerical simulation of the IC debonding process. The progressive formation of flexural cracks and subsequent concrete–FRP interfacial debonding is formulated by the introduction of a new element able to represent both phenomena simultaneously without perturbing the numerical procedure. Furthermore, with the proposed model, high frequency dynamic response for these kinds of structures can also be obtained in a very simple and non-expensive way, which makes this procedure very useful as a tool for diagnoses and detection of debonding in its initial stage by monitoring the change in local dynamic characteristics.     

Stability analysis of delaminated composite beams

This study describes the dynamic stability of composite cantilever beams subjected to periodic axial loading with delaminations at pre-set locations. A computer code based on the finite element method is developed to calculate the natural frequencies, critical buckling loads and dynamic instability regions of the woven and laminated composite beams with different stacking sequences ([0]₄, [0/90]_s and [90]₄), corresponding to this peculiar delamination case. The results of the developed code for the natural frequencies are compared with the natural frequencies obtained experimentally and numerically with commercial FEA (ANSYS). The critical buckling loads are also compared with the ones obtained from ANSYS simulations.     

Dynamic analysis of composite coil springs of arbitrary shape

The dynamic behavior of composite coil springs of arbitrary shape is investigated. The Timoshenko beam theory is adopted in the derivation of the governing equation. The material of the rod is assumed to be homogeneous, linear elastic and anisotropic. The effects of the ratio maximum diameter of the cylinder/thickness (D_max/d), the number of active turns (n), the helix pitch angle (α) and the ratio of the minimum to maximum cylinder radii (R_min/R_max) on the dynamic behavior of the composite barrel and hyperboloidal springs are investigated. The free and forced vibrations of composite coil springs of arbitrary shape such as barrel and hyperboloidal springs are analyzed through various examples.     

The Linear Matching Method applied to composite materials: A micromechanical approach

The paper considers a Direct Method for the evaluation of the maximum load corresponding to pre-assigned limits on the non-linear behaviour of the matrix and fibres in a laminate structure. This is achieved by combining a consistent micro-macro model for linear behaviour with an extension of the Linear Matching Method (LMM), previously extensively applied to Direct Methods in plasticity. The method is developed with assumptions that allow the methodology to be displayed in its simplest form. Applications to examples of laminate elements and a laminate plate containing a hole are described, assuming a matrix with a limit on ductility.     

Multiobjective design of viscoelastic laminated composite sandwich panels

The optimal design of laminated sandwich panels with viscoelastic core is addressed in this paper, with the objective of simultaneously minimizing weight and material cost and maximizing modal damping. The design variables are the number of layers in the laminated sandwich panel, the layer constituent materials and orientation angles and the viscoelastic layer thickness. The problem is solved using the Direct MultiSearch (DMS) solver for multiobjective optimization problems which does not use any derivatives of the objective functions. A finite element model for sandwich plates with transversely compressible viscoelastic core and anisotropic laminated face layers is used. Trade-off Pareto optimal fronts are obtained and the results are analyzed and discussed.     

Stiffness control in adaptive thin-walled laminate composite beams

The aim of this paper is to verify the control of the stiffness that is feasible to achieve in a thin-walled box-beam made from a laminate by including an adaptive material with variable stiffness. In this work, a material having a strongly varying Young Modulus under minor temperature changes was included in the cross-section. An analytical model was used to estimate the position of shear centre and the axial, bending, torsional, and shear stiffnesses of the cross-section. Two cross-sections were analysed, one with an adaptive wall and another with two adaptive walls. In both sections, the torsional stiffness could be strongly altered with minor temperature variations. In the section with one adaptive wall, the shear centre and thus the bending–twist coupling was also strongly modified. A study was made of the influence on the control of stiffnesses exerted by the overall cross-section thickness and the thickness of the adaptive walls.     

Indentation of a laminated composite plate with an interlayer rectangular void

We employ the Eshelby–Stroh formalism to study generalized plane strain infinitesimal deformations caused due to the indentation by a rigid circular cylinder of an elastic laminated plate with a through-the-width rectangular void between two adjoining layers. Assuming that the void does not close during the indentation process, we find the indentation modulus (i.e., the slope of the indentation load vs. the indentation depth curve) as a function of the void size, the void position, elastic moduli of the layers, and boundary conditions at the edges. The change in the indentation modulus caused by an interlayer void parallel to the major surfaces of an anisotropic plate can potentially be used to estimate the void size and location.     

Quasi-static and dynamic fracture behavior of composite sandwich beams with a viscoelastic interface crack

Fracture analysis of sandwich beams with a viscoelastic interface crack under quasi-static and dynamic loading has been studied. Firstly, a three-parameter standard solid material model was employed to describe the viscoelasticity of the adhesive layer. And a novel interfacial fracture analysis model called three material media model was established, in which an interface crack was inserted in the viscoelastic layer. Secondly, a finite element procedure based on Rice J-integral and Kishimoto J-integral theories was used to analyze quasi-static and dynamic interface fracture behavior of the sandwich beam, respectively. Finally, the influence of viscoelastic adhesive layer on the quasi-static J-integral was discussed. In addition, comparison of quasi-static Rice J-integral with Kishimoto J-integral under various loading rates was carried out. The numerical results show that the oscillating characteristic of dynamic J-integral is more evident with shorter loading rise time.     

Enhanced strength analysis method for composite open-hole plates ensuring design office requirements

The use of unidirectional carbon fibre-reinforced composites in the design of primary structures, such as the centre wing box, has spread increasingly over the past few years. However, composite structures can be weakened by the introduction of geometrical singularities, such as holes or notches. The semi-empirical aspect of the current open-hole failure approaches requires the allowables to be systematically fitted against specific test results. This point constitutes a strong limitation for optimum design. A simplified strength analysis method for perforated plates is presented, ensuring design office requirements in terms of precision and computational time. The predictions of the proposed approach are compared successfully with a large experimental database, with different configurations of perforations, different stacking sequences and in different Carbon/Epoxy materials.     

A refined dynamic stiffness element for free vibration analysis of cross-ply laminated composite cylindrical and spherical shallow shells

An exact free vibration analysis of doubly-curved laminated composite shallow shells has been carried out by combining the dynamic stiffness method (DSM) and a higher order shear deformation theory (HSDT). In essence, the HSDT has been exploited to develop first the dynamic stiffness (DS) element matrix and then the global DS matrix of composite cylindrical and spherical shallow shell structures by assembling the individual DS elements. As an essential prerequisite, Hamilton’s principle is used to derive the governing differential equations and the related natural boundary conditions. The equations are solved symbolically in an exact sense and the DS matrix is formulated by imposing the natural boundary conditions in algebraic form. The Wittrick–Williams algorithm is used as a solution technique to compute the eigenvalues of the overall DS matrix. The effect of several parameters such as boundary conditions, orthotropic ratio, length-to-thickness ratio, radius-to-length ratio and stacking sequence on the natural frequencies and mode shapes is investigated in details. Results are compared with those available in the literature. Finally some concluding remarks are drawn.     

Dynamic analysis of functionally graded plates using a novel FSDT

The purpose of this paper is to study the vibrational behavior of advanced composite plates by using a novel first shear deformation theory (FSDT). This theory contains only four unknowns, with is even less than the classical FSDT. The governing equations are derived by employing the Hamilton's principles and solved via Navier's solution. The present results were validiated by comparing it with the 3D, classical FSDT and other solutions available in the literature. Shear correction factor apper to be unfovarable in some cases (case dependent). Finally, authors recommend further study of this new manner to model the displacement field.     

Radial basis functions based on differential quadrature method for the free vibration analysis of laminated composite arbitrarily shaped plates

The conventional strong form collocation approach known as Differential Quadrature (DQ) method has been applied in the past to a vast type of engineering problems. It is well-known that its application is strictly limited to regular regions where derivatives are approximated along mesh lines. Generally, its accuracy increases when the number of collocation points is large and the method tends to be stable. However, for some numerical problems several points are needed in order to obtain an accurate solution. Changing the basis functions another numerical technique was developed called Radial Basis Functions (RBFs) method, which has the advantage of approximating derivatives using irregular point distributions and the basis functions depend on the mutual radial distance of the grid points. In order to extend the idea of DQ method to a general case a Radial Basis Function based on Differential Quadrature (RBF-DQ) method has been recently developed. This method merges the advantages of both techniques. Furthermore, this work proposes the application of RBF-DQ when a domain decomposition technique is considered. In this way it will be shown that, using some kind of basis functions the number of grid points per element can be reduced compared to other classical approaches. Furthermore, once the shape parameter is fixed for one case, it is not needed to calculate it again for other applications.     

Thermal uncertainty quantification in frequency responses of laminated composite plates

The propagation of thermal uncertainty in composite structures has significant computational challenges. This paper presents the thermal, ply-level and material uncertainty propagation in frequency responses of laminated composite plates by employing surrogate model which is capable of dealing with both correlated and uncorrelated input parameters. The present approach introduces the generalized high dimensional model representation (GHDMR) wherein diffeomorphic modulation under observable response preserving homotopy (D-MORPH) regression is utilized to ensure the hierarchical orthogonality of high dimensional model representation component functions. The stochastic range of thermal field includes elevated temperatures up to 375 K and sub-zero temperatures up to cryogenic range of 125 K. Statistical analysis of the first three natural frequencies is presented to illustrate the results and its performance.     

Panel stiffener debonding analysis using a shell/3D modeling technique

A shear loaded, stringer reinforced composite panel is analyzed to evaluate the fidelity of computational fracture mechanics analyses of complex structures. Shear loading causes the panel to buckle. The resulting out-of-plane deformations initiate skin/stringer separation at the location of an embedded defect. The panel and surrounding load fixture were modeled with shell elements. A small section of the stringer foot, web and noodle as well as the panel skin near the delamination front were modeled with a local 3D solid model. Across the width of the stringer foot, the mixed-mode strain energy release rates were calculated using the virtual crack closure technique. A failure index was calculated by correlating the results with a mixed-mode failure criterion of the graphite/epoxy material. The objective was to study the effect of the fidelity of the local 3D finite element model on the computed mixed-mode strain energy release rates and the failure index.     

A novel approach based on ALE and delamination fracture mechanics for multilayered composite beams

A novel approach able to predict debonding or fracture phenomena in multilayered composite beams is proposed. The structural model is based on the first-order shear deformable laminated beam theory and moving mesh strategy developed in the framework of Arbitrary Lagrangian–Eulerian (ALE) formulation. The former is utilized to evaluate fracture parameters by using a multilayer approach, in which a low number of interface elements are introduced along the thickness, whereas the latter is utilized to reproduce crack tip motion due to the crack extension produced by moving boundaries. The model is able to avoid computational complexities introduced by an explicit crack representation in bi-dimensional structures, in which typically high computational efforts are expected for handling moving boundaries. To this aim, a moving mesh strategy is proposed for the first time in the context of beam modeling based on a multilayered configuration. Such an approach, essentially based on ALE formulation, is able to reproduce interfacial crack paths by using a low number of computational elements. The numerical method is proposed in the framework of the finite element formulation for a quasi-static or dynamic evolution of the crack tip front. In order to investigate the accuracy and to validate the proposed methodology, comparisons with experimental data and existing formulations available from the literature are developed. Moreover, a parametric study in the framework of dynamic fracture is developed to investigate the capability of the proposed model to reproduce more complex loading cases.     

Efficient structural computations with parameters uncertainty for composite applications

The aim of this paper is to propose a methodology in order to take into account the influence of uncertain data in structural calculations. To attain this goal, an approximation of the responses as a function of the uncertain data response called surface method (RSM) is proposed. In order to decrease the number of identification points necessary for the RSM, a progressive strategy is proposed. Error indicators are also used in order to increase the confidence. This strategy is applied to a laminate plate subjected to bending tests. The results are compared to Monte-Carlo simulations (considered as a reference). The method proposed in the present work permits to estimate correctly the whole response and is very simple to use (pre- and post-processing). This method is applied to asses the robustness of the point-stress method used to predict the rupture of perforated plates.     

Simulating damage and delamination in fibre metal laminate joints using a three-dimensional damage model with cohesive elements and damage regularisation

This paper investigates the capability of a three-dimensional finite element model with damaging material behaviour, cohesive elements and damage regularisation to simulate complex damage patterns in fibre metal laminate (FML) joints. The model incorporates a three-dimensional continuum damage mechanics approach for the composite plies, a plasticity model for the aluminium layers, and a delamination model between layers. A nonlocal averaging scheme is implemented to mitigate the mesh sensitivity that occurs with strain-softening material models. Bearing stress-strain responses and variations in stiffness are calculated, and damage progression is described in detail for all plies and interfaces. Microscopy and stress-strain data from a parallel series of experimental tests are presented, and damage and failure phenomena observed in the tests are compared with the model. Generally, good agreement between model and tests was achieved but certain limitations of the numerical model were observed and are discussed. The combined numerical and experimental information provide a detailed understanding of the failure sequence of FML joints.     

A new analytical method for particulate composites

A new semi-analytical approach to predict the mechanical behavior of heterogeneous (composite) media is presented. The eigenfunctions for the governing partial differential equation that the composite is subject to are derived in series form. The permissible functions that satisfy the continuity condition across the interface as well as the homogeneous boundary condition are obtained with the help of a computer algebra system. The Green’s function for the composite is then constructed from the eigenfunctions. Using the Green’s function, the physical/mechanical field in the composite is expressed. Numerical examples are shown.     

Vibrational analysis of advanced composite plates resting on elastic foundation

This paper presents a free vibration analysis of functionally graded plates (FGPs) resting on elastic foundation. The displacement field is based on a novel non-polynomial higher order shear deformation theory (HSDT). The elastic foundation follows the Pasternak (two-parameter) mathematical model. The governing equations are obtained through the Hamilton’s principle. These equations are then solved via Navier-type, closed form solutions. The fundamental frequencies are found by solving the eigenvalue problem. The degree of precision of the current solution can be noticed by comparing it with the 3D and other closed form solutions available in the literature.