Variable-stiffness Composite Panels Research Articles

Active aeroelastic flutter control of supersonic smart variable stiffness composite panels using layerwise models

This work focuses on the layerwise finite element modelling and active aeroelastic flutter control of smart variable stiffness laminated composite panels with surface bonded piezoelectric layers/patches under supersonic airflow. The proposed aero-electro-elastic models make use of the First- and Third-order Shear Deformation Theories, along with a linear through-thickness distribution of the electric potential, whereas the effect of the supersonic airflow is described by the First-order Piston Theory. Numerical applications of simply supported smart composite panels with either curvilinear or unidirectional fibres are provided for the accuracy assessment of the proposed models predictive capabilities, considering various side-to-thickness ratios and control conditions. The effect of proportional control on the aeroelastic flutter response is discussed for both airflow along the x-axis and yawed airflow, in addition to three different placement configurations of the piezoelectric patches.

Buckling Optimization of Variable Stiffness Composite Panels for Curvilinear Fibers and Grid Stiffeners

Automated Fiber Placement (AFP) machines can manufacture composite panels with curvilinear fibers. In this article, the critical buckling load of grid-stiffened curvilinear fiber composite panels is maximized using a genetic algorithm. The skin is composed of layers in which the fiber orientation varies along one spatial direction. The design variables are the fiber orientation of the panel for each layer and the stiffener layout. Manufacturing constraints in terms of maximum curvature allowable by the AFP machine are imposed for both skin and stiffener fibers. The effect of manufacturing-induced gaps in the laminates is also incorporated. The finite element method is used to perform the buckling analyses. The panels are subjected to in-plane compressive and shear loads under several boundary conditions. Optimization results show that the percentage difference in the buckling load between curvilinear and straight fiber panels depends on the load case and boundary conditions.

Buckling performance of curvilinearly grid-stiffened tow-placed composite panels considering manufacturing constraints

Tow-placement machines are able to fabricate variable-stiffness composite panels with curvilinear stiffeners. In this paper the buckling performance of curvilinearly grid-stiffened composite panels subjected to in-plane compressive loads under various boundary conditions is addressed. A Python-Abaqus script is developed to perform the buckling analysis of the panels. The skin is modelled using shell elements and the grid stiffeners are idealized by beam elements. Different design tailoring scenarios for grid-stiffened and unstiffened constant-stiffness and variable-stiffness skins are presented to demonstrate the influence of the stiffness variation created simultaneously by both the layout of the curvilinear stiffeners and by the fiber orientation variation of the skin on the buckling capacity. It is shown that the buckling resistance of the grid-stiffened quasi-isotropic skins can significantly be improved using curvilinear stiffeners compared to their straight design counterparts. A much higher degree of improvement can be achieved by concurrently tailoring both the skin and the stiffeners using curvilinear fibers. In order to guarantee the manufacturability of the designs, manufacturing constraints in terms of maximum curvature along the fiber and stiffener paths are imposed. It is demonstrated that imposing these constraints has negative effects on the buckling load improvement obtained for designs without considering manufacturing constraints.

IGA Based Bi-Layer Fiber Angle Optimization Method for Variable Stiffness Composites

This paper presents a topology optimization method for variable stiffness composite panels with varying fiber orientation and curvilinear fiber path. Non-uniform rational B-Splines (NURBS) based Isogeometric analysis (IGA) is utilized for the numerical computation of the general minimum compliance problem. The sensitivity analysis of the structure compliance function for the density and bi-layer orientation is conducted. The bi-layer fiber paths in the design domain are generated using streamline method and updated by divided pieces reselection method after the optimization process. Several common examples are tested to demonstrate the effectiveness of the method. The results show that the proposed method can generate more manufacturable fiber paths than some typical topology optimization methods.

Aeroelastic analysis of pre-stressed variable stiffness composite panels

The effect of in-plane stresses on the stability behaviors of constant stiffness and variable stiffness composite panels, exposed to aerodynamic pressure, is studied using the finite element method. The dynamic pressure from the high velocity airflow is evaluated from the first-order piston theory, and the eigenvalue analysis is performed to investigate the flutter or divergence type of instabilities in such composite panels under combined mechanical and aerodynamic loads. Attempt is made to understand the effect of the lamination parameter on the stability characteristics of edge-supported and cantilever composite trapezoidal panels. Finally, the limit cycle oscillation of variable stiffness plates subjected to aerodynamic pressure is investigated.

Stability behavior of variable stiffness composite panels under periodic in-plane shear and compression

Dynamic stability characteristics of variable stiffness composite plates under periodic in-plane loads are investigated here using a shear-deformable sixteen-node plate bending element. The modal transformation technique is used to reduce the equations of motion for the flexural vibration problem of a rectangular panel into a set of Mathieu-Hill equations. The diagonal and off-diagonal dominance of the parametric coefficient matrix is studied for the representative cases of in-plane loading, i.e., periodic compression/shear in presence or absence of static compression for the isotropic and composite plates. The multi-modal response (participating and accompanying modes) of the shear panels under periodic edge traction is demonstrated through the time history analysis. Then, the method of multiple scales is used to identify the dynamic instability regions corresponding to the simple (single mode flexural vibration) or combination (two mode flexural vibrations) type of resonances in various (isotropic and laminated composite made of straight or curvilinear fibers) shear panels, for which results are not available in the literature.

Lamination Parameter Interpolation Method for Design of Manufacturable Variable-Stiffness Composite Panels

Variable-stiffness laminates have lately drawn attention because they offer potential for additional structural performance improvements. In the optimization studies, laminate stiffness properties can be described efficiently by using lamination parameters, which is a well-established formulation for constant-stiffness laminates. However, ensuring manufacturability in the design of variable-stiffness laminates with lamination parameters is difficult. In this paper, a novel method for the design of variable-stiffness composite panels using lamination parameters is proposed. The method constrains the design space by controlling the magnitude and direction of change for the lamination parameters, and subsequently leads to a smooth change in the fiber angles. The method is used to maximize the fundamental frequencies of several panels as example cases. The solutions are calculated for various panel geometries and boundary conditions using the developed finite element analysis software. After finding optimal lamination parameter distributions, corresponding discrete fiber angles and fiber paths are retrieved, and the minimum radii of curvature are calculated. The results demonstrate that the proposed design method provides manufacturable smooth fiber paths while using the compact stiffness formulation feature of lamination parameters.

Design of manufacturable fiber path for variable-stiffness panels based on lamination parameters

Compared with traditional composite panels, the modeling, analysis and design of variable-stiffness panels with curvilinear fibers are much more complicated. Although the design flexibility is greatly enhanced, the design of variable-stiffness structures must meet manufacturing constraints to ensure that the designed structures can be fabricated finally. In order to design variable-stiffness composite panels that is very challenging due to its nonlinearity and non-convexity, a novel multi-stage design method for variable-stiffness panels is developed based on lamination parameters. First, lamination parameters are taken as design variables, and the stiffness distribution is obtained efficiently by few iterations. Next, the lamination parameters are transformed into actual layups. Finally, the realistic fiber path is regenerated by considering manufacturing constraints. In addition, the isogeometric analysis, which is more suitable for variable-stiffness structure, is used instead of the traditional finite element analysis to improve the analysis accuracy. Illustrative example demonstrates the high computational efficiency and optimization capacity of proposed method, compared to gradient-based algorithm and evolutionary algorithm.

Process-induced residual stress of variable-stiffness composite laminates during cure

One of the most important issues for designing variable-stiffness composite structures reflects on determination of the steered fiber paths. In this paper a linear variation of steered fiber curves and the change rule of the fiber angles were presented to create the mathematical model of variable-stiffness composite laminates. Compared to the straight-fiber laminate, the reference path with linearly changed angles leads to higher mechanical strength and more design freedoms. A novel methodology was developed to predict the distributions of process-induced residual stresses during cure. A three-dimensional (3D) thermochemical model of the curing process was established and the mechanical responses during cure were evaluated coupled with the results of thermochemical analyses. The distributions of the temperature and the degree of cure were obtained. The process-induced residual stresses were calculated using ABAQUS. The resin modulus was determined using the cure hardening instantaneous linear elastic (CHILE) model. The cure kinetic process was simulated using Kamal model for AS4/3501-6 prepregs. The results show that the process-induced residual stresses of variable-stiffness composite panels are reduced with increasing the end angle of the present fiber path during cure.

Adaptive gradient-enhanced kriging model for variable-stiffness composite panels using Isogeometric analysis

Variable-stiffness panel is very promising for the cutout reinforcement of composite structures. However, due to the increase of design variables, the optimization of variable-stiffness panels becomes very challenging, even if surrogate model is utilized, because the fidelity of surrogate model is difficult to guarantee for high-dimensional problems. In this study, isogeometric analysis method (IGA) is employed to predict the buckling load of variable-stiffness panels, which can produce accurate prediction with less computational cost compared to traditional FEA, moreover, it can provide analytical sensitivity for optimization. On this basis, an adaptive gradient-enhanced kriging (GEK) model assisted by a novel multiple points infilling criterion is constructed for the global optimization of variable-stiffness composite panels. The proposed method is compared with traditional surrogate model, and results show that the proposed method can find a better optimum design in a more efficient manner. It can be concluded that the proposed method is able to fully explore the advantages of IGA including exact modelling, analysis and analytical sensitivity, which is particularly suitable for the design of variable-stiffness panels and other complex structures.

An integrated framework of exact modeling, isogeometric analysis and optimization for variable-stiffness composite panels

Isogeometric analysis (IGA) is particularly suitable for the prediction of buckling load and design optimization of variable-stiffness composite panels, since curvilinear fiber path can be described exactly to improve the analysis efficiency, moreover, analytical sensitivity can be derived to improve the optimization efficiency. In this study, an integrated framework of exact modeling, isogeometric analysis and optimization for variable-stiffness panels is developed for the global optimum. Due to the inherent feature of multiple local optima for this type of problems, a novel multi-start gradient-based strategy is developed to enhance the global optimization capacity, and multiple initial designs for gradient-based optimization are determined by space tailoring method, which can guarantee the convergence rate and efficiency. Once the constraint aggregation and parallel computing methods are employed, the computational efficiency will be further improved. For typical illustrative example, it can be demonstrated that the proposed method is able to provide a more efficient optimum design with significant less computational cost compared to other traditional methods, including FEA-based optimization, direction optimization using genetic algorithm, gradient-based optimization without K–S function, gradient-based optimization based on difference method.

Buckling optimization of variable-stiffness composite panels based on flow field function

Due to the non-uniform in-plane stress distribution, variable-stiffness panel with curvilinear fiber paths is a promising structural concept for cutout reinforcement of composite structures under axial compression, due to the more diverse tailorability opportunities than simply choosing the best straight stacking sequence. However, traditional representation methods of curvilinear fiber path are usually not flexible for cutout reinforcement. In this study, the flow field function containing a uniform field and several vortex fields is utilized to represent the fiber path due to its inherent non-intersect and orthotropic features, and a bi-level optimization framework of variable-stiffness panels considering manufacturing constraints is then proposed. A typical rectangular composite panel with multiple cutouts is established to demonstrate the advantage of proposed framework by comparison with other fiber path functions. Results indicate that the flow fiber path only needs few variables to finely represent the fiber path, which can provide satisfying and manufacturable fiber paths by combination use of curvature constraint.

Buckling behavior of variable-stiffness composite laminates manufactured by the tow-drop method

The current investigation deals with the buckling behavior of variable-stiffness composite panels manufactured by the automated fiber placement (AFP) process. In order to minimize the occurrence of AFP-inherent defects as gaps and overlaps, the so-called tow-drop method was adopted. Compression-buckling tests were performed on large panels containing gaps or overlaps under simply-supported boundary conditions. The specific responses of the out-of-plane deflections, which were tracked by four laser sensors focused on the axial centerline of the panels during compression loading, were explained by the measured initial geometric curvatures, which were characteristic of variable-stiffness panels. The tracking of the in-plane strains using sixteen strain gauges located strategically on the panels confirmed that the presence of gaps and overlaps does not affect the symmetry of variable-stiffness panels. Finally, it was established that the tow-drop method significantly improved the structural performance in terms of the pre-buckling stiffness, buckling load, and the failure load while keeping minimal geometric disturbances.

Compression Buckling Response of Tow-placed, Variable Stiffness Composite Panels with Sine Curved and Tangent Curved Fibers

Tailoring of composite laminated panels by Variable Angle Tow (VAT) steering fibers in their optimal spatial orientations provides a unique opportunity to maximize performance. Increased buckling response of the laminates by VAT steering technique may directly provide significant weight savings by redistributing loads in a benign manner. The aim of this work is to design tow-placed, variable stiffness composite panels with resistance to buckling by steering sine curved and tangent curved fibers. Buckling behaviors of two types of VAT panels and three typical types of straight fiber panels ([45/-45/0/90]s,[±45]2s, [0/90]2s) are investigated by finite element numerical simulations. It is found that the VAT panels with sine curved and tangent curved fibers show much better buckling performance to traditional straight fiber panels, with 9.25%-30.75% and 8.18%-29.47% improvement in buckling load respectively and a more uniform stress distribution. These results demonstrate that the design of composite laminated panels with sine curved and tangent curved fiber formats has the potential for buckling performance improvements in structural efficiency, and sine curved fibers may enhance buckling property of composite laminates better than tangent curved fibers do.

Variable-stiffness composite panels: As-manufactured modeling and its influence on the failure behavior

The introduction of tow-steered laminates in structural applications demands reliable design methodologies to predict and simulate their mechanical response. The full details about the mechanisms that lead to damage and failure of these novel panels are not yet known. In this work, a numerical analysis tool has been developed for structural simulations in a three-dimensional domain. This paper presents a comparison between different configurations and modeling approaches of these panels. Finite element analyses are carried out to simulate the first-ply failure of tow-steered panels under tensile load. The simulations show how matrix cracking is affected by discontinuities in the fiber angle between adjacent courses and fiber-free areas resultant from manufacturing effects; whereas fiber tensile failure is directly influenced by the orientation angles of the fiber, whose distribution depends on the chosen course cutting method: on one side, or on both sides.

A study of interlaminar stresses in variable stiffness plates

Variable stiffness composite panels have been in continuous development for the last two decades. Several studies have been carried out to evaluate their structural response under different hypotheses. It is known that correct prediction of the onset of delamination in multilayer composite laminates requires an accurate evaluation of interlaminar stresses. Although finite element codes provide results for interlaminar stresses, they are not continuous both across and along layer interfaces due to the use of C 0 interpolated elements. In this work, a methodology for obtaining interlaminar stresses is extended and applied to the case of variable stiffness composite panels. Pagano’s three layer reference case is investigated for both constant stiffness and variable stiffness cases. A set of analyses are carried out to demonstrate the performance of the method and the variation in the stress response of the panel due to changes in composite layup. Results show that the distribution of shear stresses in the panel presents an significant variation depending on the stacking sequence. A debonding failure criteria is used to evaluate the performance of different variable stiffness configurations, obtaining improvements compared with constant stiffness panels.

Thermomechanical Design Optimization of Variable Stiffness Composite Panels for Buckling

Both numerical and experimental research have shown that variable stiffness laminates allow for significant design improvements. Variable stiffness laminates can be manufactured by exploiting the built-in steering capabilities of modern fiber placement machines (FPM). Such variable stiffness panels optimized for buckling were built and tested previously. Test results yielded higher buckling loads than those predicted numerically, which was later found to be related to the residual stresses present after curing. Hence, to benefit fully from the design freedom offered by variable stiffness panels built by FPMs it is essential to include the influence of thermal stresses in the optimization formulation. In this paper, an optimization framework, developed by the authors, is extended to include the influence of thermal loads. Numerical results confirm the importance of including thermal effects in the optimization process. Designs including thermal stresses are found to have improved buckling performance over a larger range of operating temperatures. Proper tailoring of both stiffness and thermal properties allows for ultimate buckling load improvements in the order of four to six times that of the corresponding quasi-isotropic panel.

Thermomechanical Response of Variable Stiffness Composite Panels

Analysis of non-traditional Variable Stiffness (VS) laminates, obtained by steering the fiber orientation as a spatial function of location, have shown to improve buckling load carrying capacity of flat rectangular panels under axial compressive loads. In some cases the buckling load of simply supported panels doubled compared to the best conventional laminate with straight fibers. Two distinct cases of stiffness variation, one due to fiber orientation variation in the direction of the loading, and the other one perpendicular to the loading direction, were identified as possible contributors to the buckling load improvements. In the first case, the increase was attributed to the favorable distribution of the transverse in-plane stresses over the panel platform. In the second case, a higher degree of improvement was obtained due to the re-distribution of the applied in-plane loads. Experimental results, however, showed substantially higher levels of buckling load improvements compared with theoretical predictions. The additional improvement was determined to be due to residual stresses introduced during curing of the laminates. The present paper provides a simplified thermomechanical analysis of residual stress state of variable stiffness laminates. Systematic parametric analyses of both cases of fiber orientation variations show that, indeed much higher buckling loads could result from the residual stresses present in such laminates.

Design of variable-stiffness composite panels for maximum buckling load

A generalized reciprocal approximation is presented for design of variable-stiffness laminated composite panels for maximum buckling load. The buckling load is expanded in terms of the inverse of the stiffness tensor. For discretized panels such an approximation has the important property of being separable, which allows the maximization to be carried out at each discrete node separate from the others. This makes the algorithm particularly suited to parallel computations. The sensitivity analysis is performed exactly using an adjoint method, requiring only one back substitution using the already factored inplane stiffness matrix with different right hand sides to compute the sensitivities for all design variables. A conforming CLPT finite element is used for the buckling analysis of rectangular plates and the proposed reciprocal approximation is used to update fiber orientation angles at each finite element node. Numerical results obtained for rectangular plates show that significant improvements can be gained in the buckling load by allowing the stiffness properties to vary spatially. The case of repeated eigenvalues is handled using a dual formulation.

Variable stiffness composite panels: Effects of stiffness variation on the in-plane and buckling response

Descriptions of fiber orientation variation for flat rectangular composite laminates that possess variable stiffness properties are introduced. The simplest definition employs a unidirectional variation based on a linear function for the fiber orientation angle of the individual layers. Analyses of variable stiffness panels for in-plane and buckling responses are developed and demonstrated for two distinct cases of stiffness variations. The first case assumes a stiffness variation in the direction of the loading, and numerical results indicate small improvements in buckling load for some panel configurations due to favorable distribution of the transverse stresses over the panel planform. The second case varies the stiffness perpendicular to the loading, and provides a much higher degree of improvement due to the re-distribution of the applied loads. It is also demonstrated that the variable stiffness concept provides a flexibility to the designer for trade-offs between overall panel stiffness and buckling load, in that there exist many configurations with equal buckling loads yet different global stiffness values, or vice versa.