Unsymmetric Laminates Research Articles

A Review of the Dynamic Behavior of Thermally Induced Bistable Configurations of Unsymmetrical Composite Laminates and their Applications

A Review of the Dynamic Behavior of Thermally Induced Bistable Configurations of Unsymmetrical Composite Laminates and their Applications

Investigating experimental and numerical effects of nano additives on distortion of cured unsymmetrical composite laminates

Investigating experimental and numerical effects of nano additives on distortion of cured unsymmetrical composite laminates

Free Vibration Analysis of Laminated Sandwich Plates Using Wavelet Finite Element Method

The accuracy of a wavelet depends on the choice of the mother wavelet adopted. The present work aims to predict the free vibration behavior of laminated sandwich plates using wavelet finite element (WFE). Different kinds of mother wavelets, namely, B-spline wavelet on the interval (BSWI), Gaussian, Haar, Daubechies 6 (db6), Biorthogonal 3.7 (bior3.7), Coiflet5 (coif5), Symlets (sym8), Morlet, Mexican hat (Mh), and Meyer mother wavelets, are employed in WFE for predicting the frequencies. Both symmetric and unsymmetric laminates are studied using the proposed approaches. A wide range of problems, including the influence of the geometric and material properties and end conditions on the free vibration behavior of the laminated sandwich plates, are solved. The effectiveness of the WFE over the conventional finite element method in terms of computational efficiency is discussed. In conclusion, BSWI-based WFE method (WFEM) is found to be the most accurate and computationally efficient in predicting the free vibration behavior of laminated sandwich plates. The accuracy of the WFEM depends widely on the type of mother wavelet adopted.

Investigations on the dynamic snap-through of MFC bonded self-resetting bistable laminates

Unsymmetric composite laminates having two stable equilibrium configurations have been studied extensively in the recent past due to their potential applications in morphing structures. Surface bonded Macro Fiber Composites (MFC) actuators have been considered as a viable solution to trigger the snap-through transition in bistable laminates. Although MFC bonded bistable laminates are widely used in morphing applications, they might require considerably high voltage inputs to achieve the required levels of actuation control during the shape transition. As a solution, other possible energy sources can be combined with active MFC patches to reduce the snap-through energy required from the single source of MFC actuation. In this work, we examine the dynamic behavior of bistable composite plates actuated using MFC actuators, where external vibration energy has been used to assist with the MFC-controlled actuation between stable states. A refined semi-analytical model based on the Rayleigh–Ritz formulation has been proposed, where the membrane energy and the bending energy are separately evaluated. Bending components are directly evaluated using the approximated transverse displacement functions, whereas the membrane components are evaluated separately by combining compatibility conditions and equilibrium equations. Results from the proposed semi-analytical framework are compared with a full geometrically nonlinear finite element framework and necessary experimental observations. The results show a significant reduction in the snap-through energy demand on MFC layers where external dynamic excitation assists the snap-through process. Additionally, a parametric study is performed using variable stiffness (VS) fiber orientation parameters, achieving bistable laminate-MFC configurations that lower snap-through requirements through the proposed morphing strategy. Thus, the study offers to aid a multi-efficient snap-through strategy for the morphing of multistable composite structures.

Machine learning prediction in distortion behavior of unsymmetric laminates under hygrothermal environment

This paper deals with the effects of curing process and hygrothermal environment on the distortion behaviors of continuous carbon fiber reinforced polyamide 6 (CF/PA6) unsymmetric laminates. To accurately characterize the shape of CF/PA6 unsymmetric laminates in the water absorption process, the 3D model reconstruction with different water content is carried by combining 3D scanner and secondary development in Abaqus. A full-field displacement comparison method is proposed to calculate the equivalent thermal/moisture expansion coefficient, and the effectiveness of numerical simulation is verified. The dataset with 2816 instances is further constructed through finite element method. Through grid search and five-fold cross validation, the ANN model is trained and validated according to R 2 and MSE criterion. The well-trained ANN model builds the mapping relationship between lay-up design parameters, hygrothermal environment and the distortion parameters of unsymmetric laminates.

Dynamic response of piezoelectrically actuated bistable cross-ply laminates under oscillating impulse voltages

Multistable composite laminates are ideal candidates for morphing applications due to their ability to switch between multiple stable states with proper actuation mechanisms. Surface-bonded macro fiber composite (MFC) actuators to trigger snap-through between one stable shape to another by applying external voltages have attracted considerable attention recently. In this work, dynamic snap-through of bistable unsymmetric cross-ply laminate using MFC actuators under oscillating impulse voltages has been investigated. Both unimorph and bimorph laminate-MFC configurations are considered for the analysis. The stable equilibrium configurations of the MFC-actuated bistable laminate, considering the effects of MFC bondage, are discussed using the proposed finite element (FE) framework. Under the action of oscillating impulse voltages, the single-well and cross-well oscillations of the active bistable plate are analyzed in detail through time responses and phase portraits. The FE results show the advantage of actuating MFC layers through the oscillating impulse voltages as it leads to a reduction in the maximum snap-through voltage requirements.

Towards reduction of bending-extension coupling in unsymmetrical laminates using multi-objective heat transfer search

The main advantage of composite materials is the ability to tailor the properties of stacking sequences. Unsymmetrical laminate involves an arbitrary even or odd number of fiber layers oriented at different angles wherein identical fiber orientation above and below mid-surface does not exist. In the case of these laminates, the coupling deformation is undesired during mechanical loads and symmetrical laminates may not be the best solution for all cases. In this work, an effort has been made to present the methodology to minimize the end effects of bending-extension coupling in the case of unsymmetrical laminates to make it widely applicable. The infinite plate containing the circular and elliptical hole is studied with various in-plane loading conditions. The end effect of bending-extension coupling is presented by the multi-objective problem of minimization of the normalized tangential force and moment. The non-dominated sorting heat transfer search algorithm is employed to solve this optimization problem wherein TOPSIS decision-making technique is used to obtain the best values from the Pareto solution. The different cluster-based methods are proposed to utilize the unsymmetrical laminates most effectively. The effects of these clusters on the bending-extensional coupling are investigated and results reveal that cluster design presenting each fiber angle value distinctly is the best design among all recommended in the present investigation. More than 70% of the bending-extensional coupling is reduced in most cases. A unique correlation is found between the cluster design and fiber angles of the optimum stacking sequences. The proposed approach and designs will support the potential use of unsymmetrical laminates by improving properties through tailoring stacking sequences.

Refined Semi-Analytical Framework to Predict the Natural Vibration Characteristics of Bistable Laminates

Bistable unsymmetrical laminates have received significant attention in morphing applications due to their ability to attain multiple shapes when subjected to thermal loads. Morphing structures in general are subjected to dynamic operating conditions. Also, the highly nonlinear snap-through transition between stable configurations possesses rich dynamic characteristics. Therefore, understanding the dynamic characteristics of bistable laminates is essential for designing morphing structures constituting bistable elements. Thus, the present study aims to explore the dynamics of bistable unsymmetrical laminates by evaluating their natural vibration characteristics associated with small-amplitude dynamic excitation around the static equilibrium configurations. A refined semi-analytical framework is proposed to analyze the natural vibration characteristics of the bistable laminate, where the potential energy is expressed only in terms of the unknown coefficients of the assumed out-of-plane displacement function. The in-plane components are separately evaluated using the in-plane equilibrium equations and compatibility conditions. In the dynamic analysis, perturbations are imposed on the static equilibrium configurations to capture the modal characteristics. A full geometrically nonlinear finite element (FE) model of the bistable laminate has been created in a commercially available FE package to compare semi-analytical solutions. To validate the proposed frameworks, an experimental strategy to capture the natural frequencies of a bistable laminate is presented in this paper. Unsymmetric laminates mounted at its center have been used for the experimental testing, where the vibrations are measured using miniature integrated electronics piezoelectric accelerometer sensors attached at the corners. The semi-analytical and FE results are validated against the experimental observations for the selected unsymmetrical cross-ply laminates. The proposed frameworks are further extended to a family of unsymmetrical variable-stiffness (VS) laminates generated using curvilinear fiber alignments. The selected VS family can generate bistable shapes without any twisting curvature similar to that of an unsymmetrical cross-ply laminate, where the designer can expand the design space with a plethora of multiple configurations. A parametric study is performed by tailoring the VS parameters to investigate the influence of curvilinear fiber alignments on the natural vibration characteristics of bistable VS laminates.

Bistable characteristics of unsymmetric cross-ply composite laminates considering different boundary shapes

The aim of this paper is to study the bistable characteristics of unsymmetric cross-ply composite laminates induced by thermal stress during the curing process when considering different boundary shapes. The changes in geometry for five types of planform shapes, have been focused, which are named rectangular planform (RP), elliptical planform (EP), trapezoidal planform (TP), diamond planform (DP) and cruciform planform (CP) respectively. The parameters that characterize the bistable performance of the laminates, including the principal curvature and snap load, were measured. The principal curvatures in different stable configurations were determined with analytical, numerical, and experimental methods, and the load-displacement curves in the snapping process were successfully obtained. Moreover, the boundary effect caused by the difference in planform shapes, which cause the local curvature of the bistable composite laminate to change, were also discussed. Predictions from an analytical shell model are verified through comparisons with nonlinear finite element simulations and experimental test results.

Uncertainty quantification of bistable variable stiffness laminate using machine learning assisted perturbation approach

Morphing structures have received growing interest in aerospace structures and wind turbines due to their rapid shape-changing ability in response to the change in operating conditions. Bistable laminates using variable stiffness composites are considered potential candidates in morphing structures for their ability to tailor the design space with a plethora of multiple stable configurations and satisfy the conflicting requirements of load-carrying capacity and deformability. Even though extensive works have been reported on the analysis and design of the cured shape of unsymmetrical variable stiffness laminates for morphing application, the effect of uncertainty in design variables on the behavior of bistable laminates is not profoundly assessed in the literature. In particular, uncertainty propagation through a highly non-linear map can lead to a significant discrepancy between the numerically predicted and experimental observations. Therefore, for adaptability in practical application, it is imperative to quantify the uncertainty as well as to characterize the non-linearity present near the design point of interest. In this work, a general purpose machine learning assisted uncertainty quantification (MLAUQ) framework is developed and demonstrated on unsymmetrical bistable laminate. The study considers three different variants of the approach based on the order of approximation (O(hk)) used for the training purpose. It is found that the MLAUQ−3 approach performs better than other approaches, and a theoretical justification for the same is provided. The method relies on the fact that expensive computation of the Hessian required for standard perturbation approaches can be bypassed by training a neural network while retaining accurate gradient information near the design point of interest. In the case of bistable laminate, a network trained with a few training samples can capture the local model non-linearity. Further, numerical investigations reveal that the proposed approach is computationally efficient and accurate compared to traditional uncertainty quantification (UQ) approaches.

Closed‐form buckling analysis of unsymmetrically laminated plates

AbstractThe local stability of thin‐walled fibre‐reinforced plastic composite beams can be reduced to individual laminates using discrete plate theory. These individual plates receive a supporting effect from their surrounding structure, which is modelled with rotational restraints. In the present investigation, this buckling problem is described by a closed‐form solution. The energy‐based method works with the Rayleigh quotient and the principle of the stationary value of the elastic potential energy. For the analysis of unsymmetrically laminated plates, the classical laminated plate theory (CLPT) considers both the plate deflection and the in‐plane displacements. The first‐order shear deformation theory (FSDT) and third‐order shear deformation theory (TSDT) additionally describe the cross‐sectional rotations and thus take transverse shear deformations into account. In addition to the direct consideration of the bending‐extension couplings, these have also been investigated using the reduced bending stiffness (RBS) method. The investigation shows the influence of bending‐extension coupling on the stability of compressively loaded unsymmetrically laminated plates. Moreover, it is found that the transverse shear stiffness reduces the critical load at relatively high plate thicknesses. The closed‐form analytical solution and the RBS method show good agreement with finite element analyses. The presented closed‐form analytical methods provide explicit solutions for the critical compressive load of unsymmetric laminates under different boundary conditions. Due to the explicit solution, this method is significantly more computationally efficient than numerical, semi‐analytical or exact methods. The present methods are characterised by a simple applicability as well as a very high computational efficiency and are very suitable for preliminary design as well as optimisation of laminated structures.

Resonant Actuation Based on Dynamic Characteristics of Bistable Laminates

Bistable or multi-stable structures have found broad applications in the fields of adaptive structures, flow control, and energy harvesting devices due to their unique nonlinear characteristics and strong local stability behavior. In this paper, a theoretical model based on the principle of minimum potential energy and the Rayleigh–Ritz method is established to study the dynamic characteristics of a bistable unsymmetric laminate with a fixed center. Numerical results of this theoretical model were obtained and verified by an FEA model using ABAQUS. The nonlinear dynamic characteristics and the structural response under different levels of external excitation were investigated and verified by experiments. The realization conditions of single-well vibration and cross-well vibration of bistable laminates were determined, with which the actuation strategies can be optimized for targeting modal frequencies of bistable laminates.

The dynamic regimes of the unsymmetric bistable laminate

A dynamic model built theoretically and simulated numerically for an unsymmetric bistable laminate is elucidated, elaborating the dynamic regimes. Peak-to-peak amplitude diagrams being amplitude-frequency and amplitude-force response curves are derived. The single-well vibrations, the limit-cycle oscillations, the multiple-period dynamic snap-through, the chaotic dynamic snap-through and the intermittency dynamic snap-through can be detected. The amplitude-frequency response curves exhibit the softening stiffness effect. The dynamic regimes are correlated with the excitation amplitude and the modal frequencies. Deploying the high-level excitation amplitude and the low-level modal frequency leads to the limit-cycle oscillations. Besides, the single-well vibrations are characterized by the period-doubling bifurcation.

Effect of snap-through force location on morphing of bistable variable stiffness laminates

Unsymmetric composite laminates exhibit two or more stable states due to the presence of residual thermal stresses induced during the curing process. The paper aims to exploit the possibility of assessing the morphing behaviour of bistable composite laminates using semi-analytical and numerical models. A Rayleigh-Ritz based semi-analytical model is used to investigate the variable stiffness (VS) bistable laminates generated using curvilinear fibre alignments. The obtained results are verified using a fully non-linear numerical model developed in a commercially available finite element package. In order to identify the influence of loading location on the snap-through behaviour, a parametric study is proposed in the present research. Snap-through is achieved through transverse point loads. The novelty of this work resides on the investigation of load application location on the snap-through action where the transverse load is applied at various locations on the lamina surface. Earlier research on the morphing of bistable square composites is mainly on the application of concentrated load at the centre of the laminate geometry, which is considered as an ideal location for snap-through action. The designer may also have to choose other locations for the application of snap-through loads since the lamina centre may not be appropriate always in structural applications. Four different loading locations are selected for the present analysis, and snap-through loads are calculated to check the effect of loading location. Parametric studies are performed using the proposed semi-analytical and numerical models to investigate the effect of selected loading point positions on the snap-through process. The analysis is extended to a selected VS laminate family to understand the influence of loading point positions on the curvilinear fibre alignments.

Vibration Analysis of Bistable Unsymmetric Laminates with Curvilinear Fiber Paths

Multistable laminates have been actively studied in recent years due to its potential applications in morphing and energy harvesting devices. Variable stiffness (VS) bistable laminates provide opportunities for further improvements in design space in comparison with constant stiffness bistable laminates. The snap-through process involving shape transition between the stable configurations is highly nonlinear in nature and exhibits rich dynamics. Exploiting the dynamic characteristics during the snap-through transition is of considerable interest in designing the morphing structural components. In this paper, we present a semi-analytical model based on Rayleigh–Ritz approach in conjunction with Hamilton’s principle to predict the natural frequencies of bistable VS laminates. The obtained results are compared with the results from the full geometrically nonlinear finite element (FE) model. The proposed FE model is further extended to study the dynamics of VS laminates subjected to external forces with different amplitudes. Subsequently, a parametric study is performed to explore the effect of different curvilinear fiber alignments on natural frequencies, mode shapes, free vibration characteristics and forced vibration characteristics (single-well and cross-well vibrations).

Nonlinear dynamic modeling of bistable variable stiffness composite laminates

The room-temperature equilibrium stable states of cured unsymmetric composite laminates have been the focus of recent research, with a particular emphasis on shape morphing applications. It has been shown that changing the fiber orientation of unsymmetrical laminates using curvilinear fiber path description can results in a plethora of bistable configurations with an enriched design space. In bistable structures, snap-through involves transition from one stable shape to another, which is a non-linear phenomenon exhibiting rich dynamics during the shape transition. Past works involving such dynamic characteristics show encouraging potential in designing efficient morphing strategies. In this work, a novel semi-analytical model using Föppl von Kármán kinematics has been formulated to predict the non-linear dynamic characteristic of bistable variable stiffness (VS) laminates. An efficient energy formulation is adopted where the membrane and bending energies are decoupled using the semi-inverse constitutive equation. The in-plane stress resultants and the energy components are expressed in terms of curvatures using the in-plane equilibrium equations and compatibility conditions. Using Hamilton’s principle in conjunction with the Rayleigh–Ritz approach, a set of non-linear equations are generated, which is solved to obtain the dynamics of the snap-through process. The accuracy of the predicted non-linear vibration results of bistable plates from the semi-analytical model is verified using a fully non-linear finite element framework and validated exemplarily by tests on a straight fiber laminate configuration. Finally, a parametric study is performed by tailoring the VS parameters to identify the effect of different curvilinear fiber alignments on the dynamic characteristics of bistable VS laminates.

Investigations on the multistability of series-connected unsymmetric laminates

Multistable composite shells have received great attention in shape-changing morphing applications due to their ability to attain more than one stable shape when cooled down from curing to room temperature. However, an individual bistable shell may not completely fulfil all the requirements of a morphing structure as they may require more than two stable states during the morphing action. Also, on several occasions, cylindrical bistable shapes can be found to be limiting for morphing applications. Therefore, studies on highly multistable non-cylindrical shapes are a subject of interest. In this study, we explore how unsymmetric laminates connected in series can result in an increased number of stable shapes. To analyze series-connected laminates, a semi-analytical model is developed using the Rayleigh-Ritz approach. The shapes predicted by the semi-analytical model have been validated using the results from a full geometrically non-linear finite element model and corresponding experimental results. A further enhancement in the design space of series-connected laminates is proposed by replacing the conventional cross-ply laminate with curvilinear fiber variable stiffness (VS) laminates as they allow the designer to tailor stiffness properties. Although VS laminates can be used to generate the similar stable configurations as that of conventional cross-ply laminates, they may result in different curvature values leading to tailored snap-through requirements. The developed finite element model is extended to account for unsymmetric variable stiffness laminates, where effect of curvilinear fiber alignment on the multistable design space is investigated.

Higher order theories for the free vibration analysis of laminated anisotropic doubly-curved shells of arbitrary geometry with general boundary conditions

The present work investigates the modal response of doubly-curved shells characterized by unsymmetric lamination schemes embedding anisotropic materials and externally constrained with general boundary conditions along the edges. The Equivalent Single Layer (ESL) methodology has been adopted for the assessment of the fundamental governing equations, employing a generalized formulation for the setup of each component of the kinematic field variable, leading to a higher order through-the-thickness expression of the displacement field. A two-dimensional non uniform discrete grid has been sat up within the mapped physical domain. The fundamental equations have been derived from the Hamiltonian Principle, and the problem has been solved employing a weak formulation of the field variable based on a higher order Lagrange polynomials-based interpolation algorithm. General boundary conditions have been obtained starting from a series of translational springs for each principal direction of the shell, each of them distributed following a generalized analytical expression. After some validations with respect to refined three-dimensional models, a systematic analysis has been performed, where the mode frequencies and shapes of structures with different syngonies and curvatures have been investigated. It has been shown that the modal response of anisotropic doubly-curved shells can be significantly oriented if governing distribution parameters are correctly selected.

Procedure to determine deformed shape of laminates made by unsymmetric layup sequences- basis for 4D printing of composites

Un-symmetric laminates, such as those of layup sequence [0m/90n], do not remain flat after curing and cooling to room temperature. The laminate exhibits a curved configuration. While the curvature may be determined using laminate theory, or extended laminate theory, the use of the curvature to determine the deformed shape needs to follow a special procedure in order to obtain the correct result. For the first time, this paper presents this special procedure. In this procedure, the coordinate axes of adjacent material increment need to be updated. The procedure to determine the final shape of un-symmetric laminates serves to enhance the development of composite structures made by using the method of 4D printing of composites.

Procedure to determine deformed shape of laminates made by unsymmetric layup sequences – Basis for 4D printing of composites

Un-symmetric laminates, such as those of layup sequence [0m/90n], do not remain flat after curing and cooling to room temperature. The laminate exhibits a curved configuration. While the curvature may be determined using laminate theory, or extended laminate theory, the use of the curvature to determine the deformed shape needs to follow a special procedure in order to obtain the correct result. For the first time, this paper presents this special procedure. In this procedure, the coordinate axes of adjacent material increment need to be updated. The procedure to determine the final shape of un-symmetric laminates serves to enhance the development of composite structures made by using the method of 4D printing of composites.