Arbitrary Lay-ups Research Articles

An analytical study on low velocity impact resistance behaviors of general bio‐inspired helicoidal composite plates

AbstractThrough evolutionary processes, helicoidal structures have been proven to exhibit exceptional load‐carrying capacity and impact resistance performance. To date, extensive experimental and numerical studies have been carried out on their impact behaviors, while few relevant analytical studies have been reported even though it is urgently needed for the preliminary assessment of structure design and optimization. In this work, based on the first shear deformation theory (FSDT) and the improved linearized Hertzian contact method, an analytical model for low velocity impact (LVI) performances of helicoidal laminates with arbitrary layups is developed. Therein, the post‐impact damage is taken into account according to continuum damage mechanics (CDM). Comparisons of load‐carrying capacity and energy‐absorbed performance between the proposed model prediction and the existing experimental data\numerical results have been made for verification. Besides, LVI behaviors of conventional laminates with unidirectional distribution andcross‐ply arrangement are discussed. Moreover, the role of rotation angle, impact velocity and the plate dimension on helicoidal laminates' LVI performances are analyzed quantitatively. There is evidence that helical layouts are better able to absorb energy and delay the in‐plane damage.Highlights The LVI responses of bio‐inspired single‐helicoidal (SH) and double‐helicoidal (DH) composite laminate are studied. An effective model to predict the LVI responses considered the post‐impact damage is developed. A comparison of the LVI performance of single‐helicoidal structures with various lay‐up schemes is carried out. DH structure has better low velocity impact resistance than SH structure when the rotation angle shares the same.

Buckling of constant/variable stiffness curved arbitrary layup composite beams by renewed constitutive relations-based sine finite element with improved in-plane and transverse responses

The elastic stability performance of constant- and variable-stiffness based composite curved beams with general layups is evaluated using an enriched finite element that accounts for three-dimensional structural response features. The variable stiffness is spatially created over the beam by layers with curvilinear fibers. The structural model in the present work is represented by sinusoidal variation based higher-order shear deformable model, augmented with improved in-plane response by zig-zag function and stretching in thickness direction by higher polynomial order. The appropriate constitutive relationships for laminated composite curved beam with arbitrary layup producing stiffness coupling effects are deduced from three-dimensional elasticity relations. The beam governing equations are formed applying the total potential energy minimum principle and the buckling parameters are predicted employing the eigenvalue analysis. The curved laminated beam element efficacy is examined for the known analytical solutions in the literature. Extensive numerical analysis by opting for different structural parameters like curved beam angle, thickness, ply-angle, curvilinear fiber angle variation from center-to-edge, layup, and beam end condition are made to visualize the buckling characteristics of general layup composite curved beams.

Variable-stiffness curved laminated-beams by curvilinear fibers with arbitrarily layup – Vibrational features by sine-based higher-order beam model with renewed-constitutive relations and improved-kinematics

The vibration characteristics of variable-stiffness based composite curved beams with general layups are examined using a higher-order beam theory that accounts for three-dimensional structural response features. The variable stiffness is spatially considered in the laminated beam by introducing the curvilinear fibres-based layers. The structural model is here represented by a sine-based shear deformable model considering zig-zag function for improving in-plane response and higher order polynomial for capturing through-thickness stretching effect. The appropriate constitutive relationships for laminated composite curved beam with arbitrary layup producing stiffness coupling effects are deduced from three-dimensional elasticity equations. The beam governing equations are then formed applying Hamilton’s principle and the free vibration features are predicted employing the eigenvalue analysis. The effectiveness of the curved laminated beam element developed here is tested against the available analytical solutions in the literature. A detailed numerical analysis by opting for different structural parameters like curved beam angle, thickness, ply-angle, layup, and beam end condition are made to investigate the vibration characteristics of general layup constant stiffness laminated curved beams and by including additional parameter, curvilinear fibre angle variation from centre-to-edge, for variable stiffness laminates.

A new higher-order beam theory for buckling and free vibration responses of laminated composite and functionally graded porous beams

The present study introduces a novel higher-order shear deformation theory for assessing buckling and free vibration characteristics in laminated composite and functionally graded porous beams. The proposed theoretical framework effectively considers three variables and eliminates the need for a shear correction factor. The governing equations are derived from the Lagrange principle, while Legendre-Ritz functions are utilised to solve the resulting problem. Various types of laminated composite beams with arbitrary lay-ups and functionally graded porous beams with symmetric or unsymmetric configurations are analysed. To validate the accuracy and efficiency of the proposed theory, several numerical examples are conducted and compared against the results of existing research endeavours.

Computational model for the semi‐analytical assessment of the free‐edge effect in composite laminated shells

AbstractThe development of efficient computational models for the accurate prediction of the state variables in general composite laminated shells undergoing uniform edge loadings is a major challenge, especially when stress concentration phenomena such as the free‐edge effect have to be considered. This paper addresses this issue by introducing a higher‐order semi‐analytical approach for the assessment of the three‐dimensional stress field in circular cylindrical composite shells with arbitrary layups subjected to a uniform bending moment. The presented semi‐analytical approach combines a closed‐form analytical plane‐strain solution with a higher‐order layerwise approach, and the governing equations are derived by virtue of the principle of minimum elastic potential. The resulting system of coupled ordinary differential equations is then solved by means of the state‐space approach and the free constants are determined by evaluating the boundary conditions at the traction‐free edges. A comparison of the numerical results of the presented semi‐analytical method with finite element simulations for various composite laminates indicates that the developed method works with high accuracy, although being extremely efficient in terms of computational resources.

Continuum damage mechanics based failure prediction and damage assessment in laminated composite structures

In the present work, nonlinear mechanical response of laminated composite structures is investigated by a constitutive numerical model based on damage mechanics. A numerical method is included in progressive damage analysis to simulate the damage accumulation and failure response of composite structures under service load conditions. This model is capable of predicting the residual strength and residual stiffness of laminate with arbitrary lay-up and geometry. The state-of-the-art progressive damage model exploits a set of stress-based Hashin-type criteria and a set of appropriate degradation rule of ply discount. The constitutive model is developed wherein the damage initiation criteria are based on Hashin failure criterion for damage evolution. The proposed progressive damage model involves the steps of stress analysis, failure analysis, and material properties degradation. This work involves a comprehensive study of quasi-isotropic elliptical hole specimen to develop the failure model. Overall, the results of the exercise aid in design applications to predict the impact of progressive damage in aircraft composite structures under service loads.

A Multiaxial Fatigue Damage Model Based on Constant Life Diagrams for Polymer Fiber-Reinforced Laminates.

In the last decade, fatigue damage models for fiber-reinforced polymer composites have been developed assuming the fracture energy equivalence hypothesis. These models are able to predict a fatigue life of composite laminates, but their identification requires a significant number of off-axial tests for various stress ratios. The present study proposes the stress ratio dependent model, which phenomenologically adopts a decrease in stiffness and residual strength of a unique ply according to experimental constant life diagrams. Hashin, Tsai-Hill, and the maximum stress failure criteria are utilized for damage initiation considering the residual strength of the ply. The obtained results indicate a sufficiency of using S-N curves for UD 0°, UD 45°, and UD 90° for identification of the model. The model was verified by S-N curves for UD 10°, UD 15°, and UD 30° and its applicability was demonstrated for prediction of a fatigue life of composite laminates with an arbitrary lay-up. The model is implemented into ABAQUS finite element software as a user subroutine.

Vibration-based damage detection in anisotropic laminated composite beams by a shear-deformable finite element and harmony search optimization

A numerical procedure to detect and quantify damages in laminated composite beams with arbitrary lay-up using limited vibration data and harmony search optimization is presented. Since any damage in a structure changes its vibration characteristics, they can be considered as the diagnostic parameters with the help of an optimization technique. For the present study, frequencies and mode shapes are used as the damage diagnostic parameters, and the harmony search algorithm is used as the optimization tool. For finite element analyses, a five-node, thirteen-degree-of-freedom shear-deformable beam element is employed. This element can take into account the elastic couplings among extension, bending, and torsion arising due to material anisotropy existing in generally laminated composites as well as the Poisson’s effect. The damage to the beam is introduced by a stiffness loss coefficient at the elemental level while mass is assumed to be unchanged. Two different objective functions to be minimized are considered for damage detection. The efficacy of the proposed method with and without the presence of noise is demonstrated by two numerically simulated composite beams including single and multiple damages. Although its accuracy somewhat decreases in case of multiple minor damages, the proposed method is successful to detect moderate and severe single and multiple damages in practice. To overcome this weakness, (i) the algorithm can be hybridized with other metaheuristics, (ii) objective function can be enhanced by combining it with other vibration characteristics such as curvature, flexibility, and so on, or (iii) two- or multi-stage damage identification methods can be considered.

A general higher-order shear deformation theory for buckling and free vibration analysis of laminated thin-walled composite I-beams

A general higher-order shear deformation theory for buckling and free vibration analysis of laminated thin-walled composite I-beams is proposed in this paper. It is based on a unified nonlinear variation of shear strains in the wall thickness and then theoretical formulation is derived in the general form which can recover the previous conventional theories such as classical and first-order thin-walled beam theory. Series-type solutions with hybrid shape functions are developed for different boundary conditions. Numerical examples are performed on laminated thin-walled composite I-beams with arbitrary lay-ups. Effects of transverse shear strains, fiber angles and slenderness ratio on the critical buckling loads and natural frequencies of the beams are reported.

A special finite element method applied to off-axis tunnel cracking in laminates

Off-axis oriented tunnel cracking in a laminated structure is modeled using a special 2D off-axis finite element formulation, thus replacing full 3D finite element simulations with much less demanding 2D simulations. The 2D off-axis element is formulated as a user element in the commercial finite element code ABAQUS, and the user element code is made available for the reader. The finite element formulation is used to predict the steady-state energy release rate and the mode-mixity for either one isolated crack or multiple interacting tunnel cracks in the central ply of a [0/θ/0/−θ]s layup. The laminate is loaded uni-axially or bi-axially, and analyses are presented for glass and carbon fiber composites for arbitrary layup angles θ. The 2D finite element model is found to give precise predictions when comparing the detailed simulations made by a full 3D finite element model. It is demonstrated that despite being a 2D method, the model rigorously provides detailed solutions for the out-of-plane deflection and strain. With a speed-up of more than four orders of magnitudes, it is thus possible to perform new, detailed, and very accurate studies of the dependency of laminate thickness as well as neighboring cracks on off-axis tunnel cracking.

Prediction of transverse crack progression based on continuum damage mechanics and its application to composite laminates and filament-wound cylindrical pressure vessels

To predict the damage variable of a 90° ply in an arbitrary lay-up laminate subjected to a certain loading, we formulated a damage progression law that represents the damage variable as a function of the damage-associated variable based on continuum damage mechanics (CDM). Utilizing the three-dimensional laminate theory and this CDM model, we predicted the damage progression of a 90° ply in cross-ply and quasi-isotropic laminates. In this analysis, the effective compliance of Lopes’ model was adopted. Additionally, the failure pressure of a filament-wound (FW) cylindrical vessel was predicted by coupling the analytical solution with the present CDM model, and the predicted failure pressure was compared with the results obtained using Christensen’s failure stress criteria. As a result, it was indicated that the prediction of the final fracture of FW vessel requires the CDM approach.

Prediction of net-tension failure of multi-bolt composite joints: A fast approach for laminates with arbitrary layup

In this study, a new fast approach to predict the net-tension failure strength of multi-bolt composite joints was developed based on finite fracture mechanics and p-version parametric finite element methods. In the proposed approach, stress distribution and stress intensity factor are obtained using the principle of superposition, based on which the problem can be divided into open hole tension and hole bearing problems. The stress distribution and stress intensity factor are determined by using p-version parametric finite element models, which is very computational efficient and can address laminates with arbitrary layup. For the validation purpose, the failure strengths of three multi-bolted joints were predicted and compared to the test data from public literatures, and good agreements were obtained. In addition, the effects of typical parameter variations on the net-tension failure strength were presented by performing a series of parametric studies, which would be a reference for engineering design of multi-bolt composite joints.

Shear-deformable finite element for free vibrations of laminated composite beams with arbitrary lay-up

Copyright © 2019 Techno-Press, Ltd. A shear-deformable finite element model (FEM) with five nodes and thirteen degrees of freedom (DOFs) for free vibrations of laminated composite beams with arbitrary lay-up is presented. This model can be capable of considering the elastic couplings among the extensional, bending and torsional deformations, and the Poisson’s effect. Lagrange’s principle is employed in derivation of the equations of motion, and thus the element matrices are obtained. Comparisons of the present element’s results with those in experiment, available literature and the 3D finite element analysis software (ANSYS®) are made to show its accuracy. Some further results are given as referencing for the future studies in vibrations of laminated composite beamst.

Progressive fatigue damage modelling of fibre-reinforced composite based on fatigue master curves

In this paper, fatigue progressive damage of fibre-reinforced composite is modelled by the present fatigue model, in which the fatigue damage incorporates two parts of the delamination and in-plane damage. The in-plane fatigue life is determined by the method of fatigue master curves. Further, Hashin and cohesive fatigue failure criteria are adopted for the determination of in-plane and delamination failure initiation, respectively. The fatigue master curve successfully predicts the fatigue life of fiber-reinforced composite with arbitrary layup sequence under fatigue loading of arbitrary stress ratio. Moreover, the delamination of interlayer subjected to arbitrary stress ratio is simulated based on the modified cohesive element. Finally, the proposed fatigue finite element model shows good agreements with the experimental data of notched glass fibre-reinforced plastic (GFRP) composite laminate and carbon fibre-reinforced plastic (CFRP) composite bolted joints.

Derivation of circumferential guided waves equations for a multilayered laminate composite hollow cylinder by state-vector and Legendre polynomial hybrid formalism

A new spectral method based on the hybrid formula system of the state-vector and Legendre polynomials are used to derive the explicit expressions of circumferential guided waves in the anisotropic multilayer composite cylinders with an arbitrary lay-up. In this hybrid method, the state vector was utilized to transform the wave equation, boundary conditions, and interface continuous conditions in the cylinder coordinate system to form the dispersion equation in terms of the state matrix. Then, following the principle of the Galerkin method, projecting the dispersion state matrix equations onto the weight functions consisting of Legendre polynomials, the system of algebraic equation is obtained. The dispersion curves and mode shape can be obtained by solving the eigenvalues and eigenvectors of the system of algebraic equations. This hybrid method uses the orthogonal and recursive properties of the Legendre polynomial to simplify the integral expressions involved in all the matrices and yields the closed-form solutions. Numerical verification, including the cases of isotropic and anisotropic viscoelastic/elastic multilayer cylinders, was conducted to evaluate the performance of the proposed method. The results show that the proposed method overcomes the cumbersome of the traditional Legendre polynomial method to treat the interface displacement and stress continuity. The results also confirm that the hybrid method has the exponential convergence.

A nonlinear dynamical model for rotating composite thin-walled beams subjected to hygrothermal effects

A rotating composite thin-walled beam structure usually works in environment with strong hygrothermal characteristics. Temperature variation and moisture absorption can influence physical properties of composite, and furthermore change mechanical behavior of the structure. Hygrothermal influences depend on composite, layup scheme, geometry and nonlinearity of the beam. However, a comprehensive analytical model including these factors is lacking. This work aims to establish such a model for rotating composite thin-walled beams subjected to hygrothermal effects so that relevant problems can be solved analytically, which can aid numerical simulation and experimental test. Many important factors including hygrothermal effects, nonlinearity, mode coupling, arbitrary layup schemes, rotation, external forces, transverse shear, non-uniformity of cross section, constrained torsion, warping, setting angle and pretwist angle are considered. Governing equations of the coupled vibration are established by using the generalized Hamiltonian principle. Reduction verification, simplification principles and reduced models are discussed. The solution of the model is illustrated and some examples are given. Finally, the influences of temperature, moisture absorption and ply angle on hygrothermal internal forces of constrained thin-walled beams with CUS and CAS configurations are analyzed.

Variational analysis of cracking in general composite laminates subject to triaxial and bending loads

A robust variational approach is first developed for predicting stress/displacement fields and effective thermo-elastic constants in a laminate with arbitrary lay-up, containing uniformly spaced ply cracks, subject to general triaxial and bending loads when the effects of thermal residual stresses are also considered. The methodology extends some previously developed variational approaches so that general non-symmetric lay-ups (not only cross-ply) under through-thickness loading conditions can be analyzed. Secondly, an approximate methodology is introduced which enables the approach to predict all effective thermo-elastic constants of laminates having non-uniformly spaced ply cracks, including new types of constant required to account for out-of-plane loading. Thirdly, some novel inter-relationships among effective thermo-elastic constants of cracked and uncracked general laminates are obtained showing that just three macroscopic parameters define the dependence of all relevant laminate constants (thirty five) on the state of cracking. The results are compared with those obtained from finite element methods, experiments and other high accuracy models.

A general energy based fatigue failure criterion for the carbon epoxy composites

A normalized energy-based fatigue failure criterion, which employs off-axis stress and strain components to compute strain energy during cyclic loading, is presented in the current research. The new model is capable of predicting the fatigue life of unidirectional laminates subjected to tension-tension, compression-compression and tension-compression loading in any arbitrary fiber orientation. Furthermore, the proposed model is used to predict the fatigue life of multidirectional composite laminates under different cyclic loading conditions, including various stress ratios. The model is validated by the experimental data of unidirectional, cross-ply, angle-ply and multidirectional carbon/epoxy composite laminates taken from the literature. In the unidirectional and multidirectional laminates effect of fiber orientation and stress ratio are diminished, respectively. The suggested fatigue model is capable of predicting the fatigue life of angle-ply and cross-ply laminates using limited experimental data. Nonetheless, it does not result in good accuracy for multidirectional laminates with arbitrary lay-up sequence under compression-dominant loadings.

A failure criterion to predict the onset of matrix cracking induced delamination in general composite laminates

In this study, a new energy-based failure criterion is developed to predict the onset and growth of matrix cracking induced delamination, known as MCID in composite laminates. This criterion is formulated upon the concept of fracture mechanics by comparison of energy release rate obtained due to MCID and interface fracture toughness. This failure criterion is developed as a general model so that it can be appropriated for any arbitrary lay-up, under any in-plane or out of plane loading. The developed failure criterion is validated against several experimental studies in the unconstraint condition. It is revealed that the criterion is of excellent agreement with the experimental results. Furthermore, for the generalized plane strain condition, validation is performed using two different models. Lastly, some of the potential applications of the proposed failure criterion are presented in different laminates. Considering the unique characteristics of this criterion, it can be employed along with other failure criteria in the design of composite structures.

Modeling guided wave propagation in multi-layered anisotropic composite laminates by state-vector formalism and the Legendre polynomials

This research presents a numerical method to analyze the propagation characteristics of guided waves in multi-layered anisotropic composite laminates. The dispersion equations were derived theoretically, while the displacement and stress components of each layer are expressed in the form of state vectors, by combining the state-vector formalism and the Legendre polynomials (SVF-LP). The displacement fields are fitted approximately by Legendre polynomials, and the system of linear equations are constructed by the orthogonal projection. The eigenvalue/eigenvector solution is established to compute the phase dispersion curves instead of solving the transcendental dispersion equations. This overcomes the problem of missing roots in traditional matrix method effectively. In order to verify the robustness of the SVF-LP, three cases of multi-layered laminates, formed by isotropic material, unidirectional carbon-fiber epoxy prepreg and fiber-metal laminate (GLARE 3-3/2) are investigated, respectively. The influences of fiber angle change and the stacking sequence are primarily analyzed, on the dispersion characteristics and the displacement and stress profiles. The matrix method is also carried out to compare the accuracy of this proposed method, which is done by the commercial software Disperse. Finally, the displacement and stress profiles of fundamental modes of the guided waves in an arbitrary lay-up quasi-isotropic plate at a given frequency is discussed in details.