Stiffness Of Composite Laminates Research Articles

Vibration of variable stiffness composite laminate and hybrid composite laminate plates coupled to sloshing fluid

In the present article, Reddy shear deformation plate theory is employed to investigate the free vibration of vertical laminated composite plates coupled to sloshing liquid. Two different types of composite plate are considered; hybrid composite laminate (HCL) plate, which consists of two types of fiber, and variable stiffness composite laminate (VSCL) plate, which is made of curvilinear fibers. The applied Reddy shear deformation theory introduces a nonlinear through-thickness distribution for the transverse shear stress, and it satisfies the zero stress conditions at the bottom and top surfaces of the plate. The sloshing fluid, which is partly in contact with the plate, is modeled as ideal, and the bulging and sloshing modes related to that are calculated using the fluid velocity potential. The interaction between fluid and solid is modeled through the continuity equation and boundary conditions at the fluid–solid interface. To extract the vibrational characteristics of the structure coupled to fluid, a polynomial approximation based on the Rayleigh-Ritz method is employed. After validating the proposed methodology, a parametric study is conducted to show the effects of various parameters associated with the fluid and structure on the natural frequencies of the system.

Fundamental Frequency Optimization of Variable Angle Tow Laminates with Embedded Gap Defects

Variable stiffness composite laminates can improve the structural performance of composite structures by expanding the design space. This work explores the application of variable stiffness laminated composite structures to maximize the fundamental frequency by optimizing the tow angle. To this end, an optimization framework is developed to design the fiber angle for each layer based on the maximization of the fundamental frequency. It is assumed that the design process includes the manufacturing constraints encountered in the automated fiber placement process and a linear fiber angle variation. The current study improves existing results by considering embedded gap defects within the optimization framework. The plates are assumed symmetric, with clamped and simply supported boundary conditions. The optimal results and a comparison between the non-steered and steered plates with and without gaps are presented. Results show that, although gaps deteriorate the structural performance, fiber steering can still lead to an increase in the fundamental frequency depending on the plate’s geometry and boundary conditions.

Free vibrations analysis of cracked variable stiffness composite plates by the eXtended Ritz method

Variable stiffness composite laminates show advantageous structural features related to their enlarged design space. They are attractive candidates for advanced engineering applications where the assessment of static and dynamic behavior and strength in the presence of cracks is often required. In the present work, a single-domain extended Ritz formulation is proposed to study the free vibrations of cracked variable stiffness composite plates. The plate model is based on the first-order shear deformation theory whose primary variable, i.e. displacements and rotations, are approximated via a set of orthogonal polynomial trial functions enriched with a set of special crack functions. These functions are able to inherently account for crack opening and crack tip singular fields. The plate governing equations are deduced by the stationarity of the energy functional and the formulation has been implemented in a computer code. The method has been validated by comparing the present results with literature solutions for cracked isotropic plates and uncracked variable stiffness plates as, to the best of author’s knowledge, no data on cracked variable stiffness plates free vibrations are available. An explicative and representative study on the free vibrations of variable angle tow composite laminates is finally presented with the aim of illustrating the approach capabilities, providing benchmarck results and identifying distinctive features and opportunities of the variable stiffness concept for the design of advanced damage tolerant structures.

Design and optimization of variable stiffness piezoelectric energy harvesters

The use of curvilinear fiber in piezoelectric structures has become a hot spot in recent years. Nevertheless, the existing researches rarely execute curvilinear fiber optimization, especially considering topology optimization simultaneously. This paper proposes an isogeometric topology optimization based on the Heaviside filter to realize the simultaneous optimization of fiber orientation and topology structure for variable stiffness composite laminate (VSCL) energy harvesters. The isogeometric formulations of the VSCL energy harvesters are derived based on the Kirchhoff plate theory and Hamilton’s principle. Then, combined with the piezoelectric material with penalization (PEMAP) model, the optimization model taking the minimum energy factor as the objective function is established. For a bimorph VSCL energy harvester, the correctness of isogeometric formulations is verified, and the effect of strain energy constraint, curvature constraint, and initial fiber paths on the optimized designs is fully analyzed. Besides, the optimization process is extended to a multilayer VSCL energy harvester. More importantly, the harmonic vibration analysis is executed to test the energy harvesting characteristics of optimized designs. The results show that the present approach can improve energy harvesting efficiency from the fiber path and topology structure point of view, and the output power increases by 37.9% compared with the initial model.

Effects of planimetric position of delamination on compressive failure of composite laminates

Delamination is the main defect form of composite laminates. The strength and stiffness of composite laminates are greatly decreased due to delamination defects. In this paper, the FE model of composite laminates with delamination was established. And the nonlinear post-buckling response of composite laminates was investigated. The validity of the FE model was verified by comparing the analysis results with the experimental results. And a detailed parametric study was performed on the effects of planimetric position on the post-buckling behavior of laminates. Results show that the buckling mode does not depend on the planimetric position of the delamination; the closer the delamination is to the center, the greater the reduction of compressive strength.

Geometrically nonlinear bending analysis of variable stiffness composite laminated shell panels with a higher-order theory

A finite element (FE) formulation is developed by extending the third-order shear deformation theory, including the zig-zag effects using the Murakami zig-zag function, for the linear and nonlinear static analyses of variable stiffness composite laminated (VSCL) shell panels. In this work, a nine-noded isoparametric element with thirteen degrees of freedom is employed to model the VSCL shell panels. Geometrical nonlinearity according to von Kármán nonlinear strain-displacement relations is considered for the evaluation of the deflections and stresses. The assumed displacement field considers up to third-order terms for in-plane displacements and second-order terms for the transverse displacement through-the-thickness. The accuracy of the formulation is established by comparing the obtained results with the three-dimensional elasticity and two-dimensional numerical/analytical results available in the literature for static analysis of constant stiffness composite laminates (CSCL) and VSCL. New results are presented for the nonlinear deflection and stresses of VSCL shell panels considering the effect of the fibre path angles, defined by the curvilinear fibre orientation for the VSCL spherical, cylindrical and hyperboloid shells. Further, the effect of curvature ratios, number of layers, lamination configurations and boundary conditions on the nonlinear static behaviour of VSCL shells is presented.

Uncertainty quantification in buckling strength of variable stiffness laminated composite plate under thermal loading

In this paper, thermal buckling analysis of variable stiffness composite laminate (VSCL) is carried out. The first-order shear deformation theory is adopted with eight noded isoparametric element to construct a finite element model for thermal buckling analysis. The effect of the uncertain composite properties that could arise due to complex manufacturing and fabrication process to the buckling temperature is investigated using polynomial neural network (PNN). The contribution of individual properties, such as the material properties, fiber orientations, and the thermal expansion coefficients of VSCL plate are performed for various boundary conditions and lamination sequences. A sensitivity analysis is also carried out and parameters to which buckling temperature has high sensitivity are identified. The accuracy and efficiency of PNN model are compared with Monte Carlo simulation (MCS). Further, PNN is employed to evaluate the reliability parameters of VSCL plate. From the various studies, it is observed that even though the influence of different stochastic input parameters are depend on the boundary conditions, the transverse coefficient of thermal expansion (α22) is found to be most influential parameter, followed by transverse (E22) and longitudinal (E11) Young’s modulus, respectively.

Fiber misalignment analysis in PCM-UD composite materials by Full Field Nodal Method

In this work, a new full-field and non-destructive methodology for measuring process-induced fiber waviness in composites are presented, benchmarked, and successfully applied to predict long fiber-reinforced stiffness composite laminates. The proposed method, named the "Full Field Nodal Method" (FFNM), computes the misalignment angle by interpolating the displacement measured on a discrete set of sampling points. Sampling points have been traced on the prepreg surface before curing, and bilinear Lagrangian interpolating functions have been adopted and compared. Several samples, made with compression molded prepreg, have been used to test the new method capabilities in this work. A first benchmark was done measuring the fiber waviness on samples through the new method and by another one recently presented in the literature. Average fiber angles predicted by the FFNM, with bilinear interpolating functions, were in high agreement with experimental results. Fiber angle misalignment measured by FFNM was used to orientate the reference system of elements of the FEA model. Numerical results in terms of stiffness and strain field were compared to those detected by the Digital Image Correlation technique (DIC) during the tensile tests. Comparison of numerical and experimental results showed an excellent prediction of material stiffness and the strain field with an error of 15%.

Flutter of variable stiffness composite laminates in supersonic flow with temperature effects

The nonlinear thermal flutter behavior of variable stiffness composite laminates (VSCL) with curvilinear fibers in high supersonic flow is investigated. The first order shear deformation theory (FSDT) combining von Karman large-deflection strain-displacement relations, quasi-steady first-order piston theory aerodynamics and quasi-steady thermal stress theory are used to formulate the nonlinear panel flutter finite element equations of motion. The fiber orientation within a layer is assumed to vary linearly from [Formula: see text] at the center to [Formula: see text] at the vertical edges of the rectangular lamina. The flutter characteristics of variable stiffness composite laminates with different temperature distributions are then studied. The results show that the critical dynamic pressure decreases as [Formula: see text] or [Formula: see text] increases, whereas the limit cycle amplitude increases as [Formula: see text] or [Formula: see text] increases for the same dynamic pressure. The critical dynamic pressure and limit cycle amplitude both increase when the temperature gradient along panel thickness increases. Simple harmonic motions, unharmonic but periodic motions, and chaotic motions can be observed on VSCL under different temperatures. It also turns out that temperature distribution has similar influence on both the critical dynamic pressure and limit cycle amplitude of VSCL.

Approximate Bayesian assisted inverse method for identification of parameters of variable stiffness composite laminates

The uncertainties of parameters are important for the performance of Variable Stiffness (VS) composite laminate plates. When parameters of VS composite laminate are given, it is easy to investigate physical characteristics of VS composite laminate. However, it is difficult to identify values of parameters due to a typical ill-posed inverse problem. In order to address this problem, an innovative approximate Bayesian computation (ABC) is suggested to identify composite parameters by considering uncertainties in this study. Compared with traditional Bayesian framework, ABC can avoid the calculation of likelihood which makes inverse procedure more complex or even intractable in practice. Generally, four advanced techniques are integrated to satisfy demands of ABC method in this study. In the suggested framework, a powerful Auto-Encoder (AE) is used to reduce calculation of the response with little information loss. Sequentially, Tikhonov regularization is integrated into ABC. Furthermore, to reduce computational cost, a high sample accepted rate-adaptive nested sampling method and Neural Network (NN) used to construct the mapping between parameters and responses are utilized. Finally, the efficiency and flexibility of the proposed method are validated by three cases.

Energy harvesting in variable stiffness composite piezolaminated plates

Harnessing ambient vibrational energy to power small and medium power electronic devices has been greatly explored in the past decade. Most of the available energy harvester models use straight fibers. Use of curvilinear fiber in bimorph energy harvester is explored in this computational study and its effect on tailoring the resonance frequency and extracted power is also investigated. The variable stiffness composite laminate (VSCL) bimorph energy harvester is modelled using first order shear deformation theory (FSDT) and equations are derived using a nine noded isoparametric finite element. Curvilinear fiber based composite and PZT-5A materials are utilized for the analysis of harvester. Curvilinear fiber model is validated by comparing the natural frequency of VSCL plate with the already published results. Power frequency response function (PFRF), voltage frequency response function (VFRF) and relative tip motion frequency response function are plotted for a fixed curvilinear fiber orientation. Effects of plate aspect ratio on the peak power is also investigated.

Buckling Analysis of Variable Stiffness Composite Laminates by Semi-Analytical Finite Strip Method

Buckling Analysis of Variable Stiffness Composite Laminates by Semi-Analytical Finite Strip Method

Buckling performance of high-precision variable stiffness composites laminate based on automatic placement technology

The buckling resistance of the variable stiffness composite laminates laid by the automatic placement can be effectively improved by tailoring the in-plane stiffness. During the placement process, laying the trajectory path planning is one of the key technologies to achieve variable stiffness design. So, the fiber trajectories composed of angle linear variation, constant-curvature curve and quadratic Bezier curve were taken as the research object, and the parametric analysis of its compression buckling performance was carried out. Finally, the influence of tape width on the surface profile accuracy and buckling resistance mechanical properties was studied using a finite element model. The results show that under the compression condition, the secondary Bezier curve has the best buckling resistance, and the equal curvature curve is least affected by the curvature constraint. The width of the tape is negatively correlated with the area of the overlap area and the buckling resistance, when the tow width of the fiber placement head is constant. Using the largest tape size can minimize the overlapping area and improve the profile accuracy of the composite structure. At the same time, it is guaranteed that the buckling performance of the structure is improved by 37.3%.

Theoretical definition of a new custom finite element for structural modeling of composite bolted joints

The general definition of a novel finite element for structural analysis of composite bolted joints is presented. The work aims to define an accurate and computationally efficient simulation tool for multi-jointed composite structures characterized by a low entry of degrees of freedom. The modeling approach exploits the full stiffness evaluation of the bolted region from the analytical standpoint. Two main stiffness contributions are defined: the first one is the elasticity of the plates around the bolt that is evaluated by means of an original theoretical approach based on the FSDT of composite plates and the Ritz method. The second one is associated with the stiffness of the bolt and is related to its shank, bolt head and bolt-hole bearing deformation. This methodology can further precisely assess friction, preload and radial clearance effects. The user-defined Composite Bolted Joint Element (CBJE) is obtained by transferring the stiffness of composite laminates to a set of radially arranged custom beam elements, whose tailored stiffness matrix is expressly derived, whereas bolt stiffness values are taken into account through beam and spring elements. The proposed methodology is verified with experimental data from literature; results are in remarkable agreement. Sensibility analysis of FE models featuring the CBJE are reported in comparison with refined 3D FE models.

An element-free study of variable stiffness composite plates with cutouts for enhanced buckling and post-buckling performance

In this paper, an efficient element-free modeling framework for variable stiffness composite laminates with cutouts is developed. In comparison with other numerical methods or semi-analytical methods, element-free meshless methods offer many advantages in modeling variable stiffness materials and structures, e.g. complex geometries with cut-outs, providing accurate stress computations and stable nonlinear behavior modeling. In this study, an element-free Galerkin (EFG) method based modeling framework is developed to model variable stiffness composite plates containing circular holes, specifically for buckling and post-buckling analysis. Weighted orthogonal basis functions are used to further reduce the computational costs of the meshless method. Modeling accuracy for variable stiffness composite structures using node-based fiber angle definitions in this element-free framework are validated against FEM results obtained from ABAQUS. The critical buckling loads of linearly varying fiber composite laminates with different sizes of central circular holes are then computed. Based on the proposed element-free modeling scheme, nonlinear post-buckling equilibrium paths of variable stiffness composite plates are traced using an incremental loading step control method, which enables efficient post-buckling analysis. Changes in both critical buckling loads and nonlinear post-buckling performance with respect to hole size and the linear variation of fiber angles are investigated with the results presented in the form of parametric studies. The numerical results show that stress redistribution remains the major factor driving improvements in the buckling and post-buckling performance of variable stiffness composite plates with cut-outs. The research work presented in this paper for composite plates with linearly varying stiffness provides a basis for the analysis of general variable stiffness soft materials in the future.

Free vibration analysis of composite laminated beams with curvilinear fibers via refined theories

In this article, free vibration finite element analysis of variable stiffness composite laminate (VSCL) beams is carried out. The variable stiffness of laminated beams is acquired by using laminates with curvilinear fibers instead of straight fibers. The analysis is based on the higher-order theories that have been presented by Carrera Unified Formulation (CUF). Equivalent Single Layer (ESL) model, which is independent of the number of constitutive layers, has been utilized to consider a number of unknown variables. Several numerical results for the analysis of VSCL beams are presented and the effect of the fiber orientation angle and various boundary conditions on the natural frequencies are demonstrated.

Analytical model for determining effective stiffness and mechanical behavior of polymer matrix composite laminates using continuum damage mechanics

The present paper proposes a new analytical model for predicting the effective stiffness of composite laminates with fiber breaks and transverse cracks. The model is based on continuum damage mechanics and the classical laminate theory. We derived damage variables describing stiffness reduction due to fiber breaks and its maximum value during ultimate tensile failure from the global load-sharing model. Furthermore, a simplified analytical model is presented for obtaining two damage variables for a cracked ply subjected to transverse tensile loading or in-plane shear loading. This model was developed assuming that the displacement field of the longitudinal direction can be expressed in the form of a quadric function by loosening the boundary condition for the governing differential equation. For verifying the developed model, the elastic constants of damaged composite laminates were predicted for cross-ply and angle-ply laminates and compared with the finite element analysis results. As for the appropriate expression of the effective elastic stiffness matrix of the damaged ply, we verified four types of effective compliance/stiffness matrices including the Murakami, Yoshimura, Li, and Maimí models. We found the Maimí model to be the most appropriate among these four models. Moreover, we successfully simplified the expressions for damage variables in the complicated infinite series obtained in our previous study. We also proved that this could contribute toward improving the accuracy of our analysis. After verifying the present model, the stress–strain response and failure strength of carbon- or glass-fiber-reinforced plastic cross-ply laminates were predicted using Maimí’s compliance model and the simplified damage variables.

An enhanced curvature-constrained design method for manufacturable variable stiffness composite laminates

In this paper, design strategies are developed to explore better approaches of enforcing local layer-wise curvature constraints in the optimization of variable stiffness laminates in order to ensure the manufacturability of optimized designs based on the limitations of automated fiber placement. The methods developed here aim to improve an existing approach of imposing the curvature constraint directly on the fiber angles (i.e., direct control method) and are suitable for a design framework that uses lamination parameters as primary design variables. One approach developed here, termed the indirect control method, enforces the curvature constraint indirectly with better computational efficiency through the spatial gradient of the lamination parameters. It is shown that the curvature constraint on the actual fiber angles can also be satisfied with a sufficiently stringent upper bound albeit it produces overly conservative designs. Alternatively, an enhanced approach, termed the hybrid control method, is developed by combining the direct method and a relaxed version of the indirect control method. The case studies of minimum compliance design indicate that it provides the best manufacturable design among the three methods in the context of variable stiffness laminates using lamination parameters.

Adaptive importance sampling based neural network framework for reliability and sensitivity prediction for variable stiffness composite laminates with hybrid uncertainties

In this work, we propose to leverage the advantages of both the Artificial Neural Network (ANN) based Second Order Reliability Method (SORM) and Importance sampling to yield an Adaptive Importance Sampling based ANN, with specific application towards failure probability and sensitivity estimates of Variable Stiffness Composite Laminate (VSCL) plates, in the presence of multiple independent geometric and material uncertainties. The performance function for the case studies is defined based on the fundamental frequency of the VSCL plate. The accuracy in both the reliability estimates and sensitivity studies using the proposed method were found to be in close agreement with that obtained using the ANN based brute-force Monte Carlo Simulations (MCS) method, with a significant computational savings of 95%. Moreover, the importance of taking into account the randomness in ply thickness for failure probability estimates is also highlighted quantitatively under the sensitivity studies section.

Modal analysis of a Variable Stiffness Composite Laminated plate with diverse boundary conditions: Experiments and modelling

The modes of vibration of a Variable Stiffness Composite Laminate were obtained by experimental modal analysis and compared with the ones resulting from theoretical/mathematical models. Three types of boundary condition were considered: CFFF, CFCF and FFFF, where C stands for clamped and F for free edges. Frequency response functions were experimentally obtained and employed to identify natural frequencies, modal damping ratios and mode shapes of vibration, using methods known as CMIF - Peak picking and circle-fit. The identified natural frequencies and mode shapes of vibration were compared with the ones resulting from models based on Classical Plate Theory and on First-order Shear Deformation Theory. Although two massive, stiff, steel blocks were bolted with the plate in-between in order to approach a clamped boundary, the modal properties are still significantly influenced by the flexibility of the resulting fixture. After introducing springs along the boundaries in the mathematical model, to better represent a “real clamped” boundary, quite good agreement between theoretical and experimental results was obtained. The experimental results here presented can be used to validate theoretical models of Variable Stiffness Composite Laminated plates.