Optimal Fiber Angles Research Articles

Generation of Tow Paths on a Curved Shell in Three-Dimensional Space for Fiber Steering

A multimesh framework to optimize two-dimensional, flat-steered fiber laminates for a given loading condition is extended to include complex curved laminates in three-dimensional (3D) space. The optimal fiber angle distribution solution is used by a tow path planner to generate (steered) tow paths in curved laminates in 3D space. The framework utilizes two meshes in the optimization step: i) a coarse quadrilateral element-based manufacturing mesh (MM) used to discretize the fiber angle distributions with nodal values; and ii) a fine triangular element-based stress mesh used in the finite-element-based stress analysis to ensure a converged solution. Lagrangian interpolation functions are used to determine the fiber angles at the centroid of each finite element analysis (FEA) mesh element within a given MM. The number of design variables is minimized without jeopardizing the accuracy of the FEA solution. A third mesh, the tessellation mesh, is used to project the generated tow paths onto the curved laminates in 3D space accurately. This paper presents all the steps needed to go from optimized fiber angles to tow paths. In conclusion, a methodology is proposed and implemented to optimize variable-stiffness laminates on complex curved structures.

Buckling and Fundamental Frequency Optimization of Tow-Steered Composites Using Layerwise Structural Models

Variable-angle-tow (VAT) composite laminates can eventually improve the mechanical performance of lightweight structures by taking advantage of a larger design space compared to straight-fiber counterparts. Here, we provide a scalable low- to high-fidelity methodology to retrieve the tow angles that maximize the buckling load and the fundamental frequency of VAT plates. A genetic algorithm is used to solve the optimization problem in which the objective function is mimicked using a surrogate model. Both unconstrained and manufactured-constrained problems are solved. The surrogates are built with outcomes from numerical models generated by means of the Carrera unified formulation, which enables to obtain straightforwardly different degrees of accuracy by selecting the order of the structural theory employed. The results show both the validity and flexibility of the proposed design approach. It is shown that, although the optimal design fiber angle orientations are consistently similar, discrepancies in the prediction of the buckling load or fundamental frequency can be found between high-fidelity layerwise and low-to-refined equivalent-single-layer models, of which classical laminated plate or first-shear deformation theories are degenerate examples.

Optimization design of variable stiffness composite cylinders based on non-uniform rational B-spline curve/surface

Compared with a constant stiffness (CS) composite structure of traditional straight fiber path, a variable stiffness (VS) composite structure of curvilinear fiber path has a broader design space. Taking the performance of a CS cylinder as the baseline, two curved fiber formats of VS cylinders are investigated. One is that the fiber angle varies in circumferential direction (i.e., circumferential stiffness variation, VS-C), the other is that the fiber angle varies in both circumferential and axial directions (i.e., circumferential and axial stiffness variation,VS-CA). Non-uniform rational B-spline curve/surface is used to define the continuously varying fiber orientation angle, making the VS design come true. This paper focuses on the maximum buckling capacity of VS composite cylinders under two kinds of loading cases (pure bending moment at both ends, concentrated force at the middle of the axis), and the optimal fiber angles of VS-C and VS-CA cylinders are obtained. In order to improve the computational efficiency, the adaptive Kriging surrogate model is integrated with genetic algorithm to solve the above optimization problems. The results show that the anti-buckling performance of VS-CA structure is always better or close to VS-C structure under different loading conditions, and all are better than that of CS structure.

Non-linear parametric vibration of the laminated composite shallow shells including primary and 1:2 internal resonances

This research aims to study the non-linear parametric vibration of laminated composite shallow (LCS) shells with the optimal fiber angles exposed to external and parametric excitations, including primary and 1:2 internal resonances. In this regard, optimal fiber angles are found with implementations of the P-T method for the objective functions and utilization of the particle swarm optimization (PSO). Also, the non-linear model of the shallow shells is established based on the stress function and the first-order shear deformation theory (FSDT). According to FSDT, Hooke’s law, von-Kármán equation, Hamilton’s principle, and Galerkin method, two-degree-of-freedom non-linear ordinary differential governing equations are discretized.

Non-linear static and dynamic buckling analysis of laminated composite cylindrical shell embedded in non-linear elastic foundation using the swarm-based metaheuristic algorithms

In this paper, by determining the optimal fiber's angles for maximum critical buckling load, the non-linear static and dynamic buckling analyses of laminated composite cylindrical shells resting on non-linear elastic foundation subjected to external loading are investigated. The laminated composite cylindrical with three, four, and five layers is considered. In the present study, first, the optimal fiber's angles are found using the swarm-based metaheuristic algorithms, then, the non-linear static and dynamic buckling analyses are carried out at optimum fiber directions. According to classical shell theory, von-Kármán equation, and Hooke's law, the stress-strain relations are derived for the laminated composite cylindrical shell. Then, based on the Galerkin's method, the discretized motion equation is obtained. For the optimization problem, the design variables are ply angles, and the objective function is maximizing the critical buckling load. Four recently developed swarm-based metaheuristic algorithms including, grey wolf optimizer (GWO), whale optimization algorithm (WOA), grasshopper optimization algorithm (GOA), and salp swarm algorithm (SSA), are utilized to solve these optimization problems. Based on the results, the optimization algorithms have improved the value of the critical buckling load significantly. Also, the WOA algorithm had better results than the others, while the GOA was the weakest.

Modeling and Characterizing a Fiber-Reinforced Dielectric Elastomer Tension Actuator

Creating dielectric elastomer actuators (DEAs) that mimic natural muscle has proven difficult, as a DEA provides in-plane expansion when actuated, while natural muscle creates contraction upon stimulation. Using a composite fiber-mesh dielectric, a DEA can create planar contraction when compressed through the thickness due to reorientation of the fiber reinforcement. This letter investigates the performance of a fiber-reinforced dielectric elastomer tension actuator (FRDETA) under a variety of loading conditions. We present modeling that considers the extensibility and packing density of the embedded fiber reinforcement to predict the mechanical response of the actuator. We then experimentally validate the results and determine the optimal fiber angle to maximize mechanical work for a FRDETA under a dead load. The FRDETAs tested were able to obtain tensile stresses of 880 kPa, tensile strains up to 14.7%, and a mass-specific energy density of 10.7 J/kg, which all fall within the ranges reported for natural muscle. Overall, these tensile actuators present an easily implementable solution for creating tension in larger soft robotic systems.

Fundamental Frequency Optimization of Doubly Curved Aerospace Structural Panels via Variable Stiffness Concept

In the present study, the fundamental natural frequencies of curvilinear fiber composite doubly curved panel are optimized. Doubly curved panels are used in various components of the structural frames of the aerospace vehicles. The variable stiffness behavior is obtained by altering the fiber angles continuously according to curvilinear fiber path function in the composite laminates. Structural model is utilized based on the virtual work principle. The aim is to achieve the best fiber paths with maximized fundamental frequencies or in-plane strengths for a composite panels. An eight-layer composite doubly curved panel with two types of boundary conditions are considered as a case study in this research. The boundary conditions include; CCCC, FCFC where C stands for clamped, and F for free edges. Von-Karman kinematic strain relations are used and the first order shear deformation theory (FSDT) is employed to generalize the formulation for the moderately thick doubly curved panel including transverse shear effects. Generalized Differential Quadrature (GDQ) method of solution is employed to solve the governing equations of motion. Numerical results demonstrate the effectiveness fiber angle path and boundary conditions on the natural frequencies of the composite panel. The optimal fiber angle paths of each layer are presented for the above cases in free vibration analysis.

Fundamental frequency optimization of variable stiffness composite skew plates

In this study, natural frequencies and vibrational mode shapes of variable stiffness composite skewed plates are optimized applying a genetic algorithm. The variable stiffness behavior is obtained by altering the fiber angles continuously according to two selected curvilinear fiber path functions in the composite laminates. Fundamental frequency and related mode shapes of the plates are optimized for two different fiber path functions using the structural model obtained based on the virtual work principle. A three-layer composite skewed plate with four types of boundary conditions and different plate geometries is considered as case study in this research. Diverse sweptback angles as well as different aspect ratios are considered as various plate geometries. The present study aims to calculate the best fiber path with maximized fundamental frequency or in-plane strengths for a composite skewed plate. The generalized differential quadrature method of solution is employed to solve the governing equations of motion. Moreover, the linear kinematic strain assumptions are used, and the first-order shear deformation theory is employed to generalize the formulation for the case of moderately thick plates including transverse shear effects. Numerical results demonstrate the effect of the fiber angles, boundary conditions, and diverse geometries on the natural frequencies of the composite plate. The optimal fiber angles of each layer are presented for the above cases in free vibration analysis. It is verified that the application of optimized curvilinear fibers instead of the traditional straight fibers introduces a higher degree of flexibility, which can be used to adjust frequencies and mode shapes.

Integrated design of topology and material for composite morphing trailing edge based compliant mechanism

The morphing trailing edge based compliant mechanism is a developing technology which can increase lift-drag ratio for variable flight modes by bending down the trailing edge. Composite material design is integrated into topology optimization for the morphing trailing edge based compliant mechanism in the paper. A two-step optimization strategy is established to solve the integrated design problem. Initially, lamination parameters are introduced and viewed as a bridge between structure stiffness and fiber angles for composite material. Design variables include the lamination parameters and element density. The least-squares between actual and desired displacements at output points along trailing edge is adopted to evaluate the deformed capability of the trailing edge. An integrated optimization model for the composite morphing trailing edge is established with the volume constraints. The optimal topologic shape and lamination parameters are initially obtained. Subsequently, a least-squares optimization between fiber angles and the optimal lamination parameters is implemented to obtain optimal fiber angles. Finally, morphing capability of composites trailing edge based compliant mechanism is investigated by simulation and experiments. The results indicate the composites trailing edge based compliant mechanism can approximately bend down 8 degrees and satisfies the design requirement.

Optimization of vertical stabilizer structure diagram

At the present situation composite material, particularly laminate type systems are becoming increasingly important in civil aviation due to their strength and weight characteristics. However, the effectiveness of these materials depends on the rational usage of its mechanical properties. There is an optimal fiber angle in the case of ply stacking and optimal ply thickness. Both manipulations reveal the variability of composite features. This work is carried out about the optimization of aircraft structure elements. Optimization issues will cover both constituents. The process will be dividing into stages, and the most factors affecting the final result will be considered with a sight to the two main criteria (strength and weight). Using the structure diagram scheme of a vertical stabilizer, an analysis was carried out and an algorithm was developed that allows finding optimum in the structure depending on the specific loads. The optimization issues have been laid by ply stacking and thickness. Complex analysis and algorithm simplicity of the program code makes it possible to use the advantages of composite materials which showed significant weight superiority in comparison with metal analogues.

Optimal deflection and stacking sequence prediction of curved composite structure using hybrid (FEM and soft computing) technique

The bending deflections and the corresponding optimal fiber angle sequences of the subsequent layers have been predicted in this article using a hybrid technique. The structural static responses are computed numerically via the isoparametric finite element steps in association with Reddy’s higher order mid-plane theory. The final stacking sequences of individual layers are further predicted through two types of soft computing techniques (particle swarm optimization, PSO; teaching–learning-based optimization, TLBO). The responses (deflection and optimal angle) are obtained via a customized computer code (MATLAB) using the current mathematical model in association with two different optimization algorithms. The accuracy of the currently derived higher order hybrid model is established by conducting a few numerical experimentations. The study indicates the superiority of TLBO technique over PSO for any particular problem when compared to the minimum deflection constraint whereas not many deviations for stacking sequences. Finally, the influences of the different structural parameter are explored by solving a variety of numerical examples and the corresponding inferences provided in detail.

Simultaneous optimization of fiber orientations and topology shape for composites compliant leading edge

A morphing leading edge, based on the compliant mechanism, is a novel concept which can improve the aerodynamic performance of aircraft for different missions. This can obviously reduce the weight and enhance the aircraft’s fuel efficiency. A simultaneous optimization of topology and fiber orientations for a composite leading edge has been achieved in the paper. It mainly included two steps. Initially, the lamination parameters and density were taken as design variables to determinate the fiber angles and topology, respectively. The least squares between the actual and desired displacements at key points were set as the objective function. Under the volume constraints, the combined optimization model of the leading edge was built to simultaneously obtain the optimal lamination parameters and topology shape. Then the optimal fiber angles were matched with the optimal lamination parameters by transforming the nonlinear equations to the least squares optimization. The physical model of the composite leading edge and experiments for it were manufactured and designed. The morphing capability of the composite’s compliant leading edge was investigated through simulation and experiments.

Continuous Fiber Angle Topology Optimization for Polymer Composite Deposition Additive Manufacturing Applications

Mechanical properties of parts produced with polymer deposition additive manufacturing (AM) depend on the print bead direction, particularly when short carbon-fiber reinforcement is added to the polymer feedstock. This offers a unique opportunity in the design of these structures since the AM print path can potentially be defined in a direction that takes advantage of the enhanced stiffness gained in the bead and, therefore, fiber direction. This paper presents a topology optimization approach for continuous fiber angle optimization (CFAO), which computes the best layout and orientation of fiber reinforcement for AM structures. Statically loaded structures are designed for minimum compliance where the adjoint variable method is used to compute design derivatives, and a sensitivity filter is employed to reduce the checkerboard effect. The nature of the layer-by-layer approach in AM is given special consideration in the algorithm presented. Examples are provided to demonstrate the applicability of the method in both two and three dimensions. The solution to our two dimensional problem is then printed with a fused filament fabrication (FFF) desktop printer using the material distribution results and a simple infill method which approximates the optimal fiber angle results using a contour-parallel deposition strategy. Mechanical stiffness testing of the printed parts shows improved results as compared to structures designed without accounting for the direction of the composite structure. Results show that the mechanical properties of the final FFF carbon fiber/polymer composite printed parts are greatly influenced by the print direction, and optimized material orientation tends to align with the imposed force direction to minimize the compliance.

Relative planar strain control and minimizing deformation work in elastomeric sheets via reinforcing fiber arrays

This study investigates soft composite sheets that undergo significant deformations. The fiber reinforcement in these systems not only increases the stiffness of sheets like a traditional composite, but also controls the relationships between strains in orthogonal planar directions. Such an ability is useful in controlling the deformation of soft robots, and also enhancing the output of soft actuation techniques like electro-active polymer actuators (also called dielectric actuators). The inspiration for this work comes from squid mantle structures that couple orthogonal components of strain using helical fiber reinforcement. The resulting null space of deformations corresponding to the fiber restrictions creates a family of body deformations that optimize propulsion.The strain dynamics in the composite sheet are modeled geometrically from fiber orientations, assuming that the fibers are inextensible. After the strain dynamics have been determined, the stress/strain relationship is modeled by considering the matrix and reinforcing fibers to be two separate homogeneous systems interacting through local stresses. Both steps of this modeling technique are validated experimentally showing planar strains in a preferred direction to be as high as 16 times the resulting planar strain of an equivalent unreinforced sheet by forcing negative strains in the orthogonal planar directions. The work required for deformation is derived from the stress/strain relationship by calculating the strain energy stored in the material, and an optimal balance between increased planar strain output and increased material stiffness is analyzed. It is shown that for the specific materials used to create the soft composite sheets (thermoplastic elastomer with cotton fibers) optimal fiber angles lie between 15° and 25° to minimize work required for deformation, but this optimal range will increase with increasing ratio of fiber to matrix modulus.

Patterns of Intersecting Fiber Arrays Revealed in Whole Muscle with Generalized Q-Space Imaging

The multiscale attributes of mammalian muscle confer significant challenges for structural imaging in vivo. To achieve this, we employed a magnetic resonance method, termed “generalized Q-space imaging”, that considers the effect of spatially distributed diffusion-weighted magnetic field gradients and diffusion sensitivities on the morphology of Q-space. This approach results in a subvoxel scaled probability distribution function whose shape correlates with local fiber orientation. The principal fiber populations identified within these probability distribution functions can then be associated by streamline methods to create multivoxel tractlike constructs that depict the macroscale orientation of myofiber arrays. We performed a simulation of Q-space input parameters, including magnetic field gradient strength and direction, diffusion sensitivity, and diffusional sampling to determine the optimal achievable fiber angle separation in the minimum scan time. We applied this approach to resolve intravoxel crossing myofiber arrays in the setting of the human tongue, an organ with anatomic complexity based on the presence of hierarchical arrays of intersecting myocytes. Using parameters defined by simulation, we imaged at 3T the fanlike configuration of the human genioglossus and the laterally positioned merging fibers of the styloglossus, inferior longitudinalis, chondroglossus, and verticalis. Comparative scans of the excised mouse tongue at 7T demonstrated similar midline and lateral crossing fiber patterns, whereas histological analysis confirmed the presence and distribution of these myofiber arrays at the microscopic scale. Our results demonstrate a magnetic resonance method for acquiring and displaying diffusional data that defines highly ordered myofiber patterns in architecturally complex tissue. Such patterns suggest inherent multiscale fiber organization and provide a basis for structure-function analyses in vivo and in model tissues.

Optimization of Composite Laminates for Fundamental Frequency

To maximize the fundamental frequency of composite laminates, a hybrid optimization algorithm which combines the respective merits of the genetic algorithm and the simulated annealing algorithm is adopted. This hybrid algorithm also incorporates adaptive mechanisms designed to adjust the probabilities of the cross-over and mutation operators. Then, this algorithm is applied to optimize the fiber angle of each layer of a composite laminate such that its fundamental natural frequency is maximized. The results indicate that this hybrid optimization algorithm could quickly find the optimal fiber angles and maximize the fundamental frequency, even under complicated choices of fiber angle and boundary conditions.

풍하중을 받는 복합재료 풍력타워의 최적 섬유 보강각도

This study analyzes performance-cost ratio of composite(GFRP) wind-towers by fiber reinforcement angle and determines their optimal fiber angle. The finite element models for composite structures using the ANSYS program described in this paper is attractive not only because it shows excellent accuracy in analysis but also it shows the effect of the geometrical combination. New results reported in this paper are focused on the significant effects of the cost for various parameters, such as thicknesses of outer shells and stiffeners. From the numerical examples, optimal fiber angles were determined as <TEX>$80^{\circ}{\sim}90^{\circ}$</TEX>.

New perspectives on collagen fibers in the squid mantle

The squid mantle is a complex structure which, in conjunction with a highly sensitive sensory system, provides squid with a wide variety of highly controlled movements. This article presents a model describing systems of collagen fibers that give the mantle its shape and mechanical properties. The validity of the model is verified by comparing predicted optimal fiber angles to actual fiber angles seen in squid mantle. The model predicts optimal configurations for multiple fiber systems. It is found that the tunic fibers (outer collagen layers) provide optimal jetting characteristics when oriented at 31°, which matches empirical data from previous studies. The model also predicted that a set of intramuscular fibers (IM-1) are oriented relative to the longitudinal axis to provide optimal energy storage capacity within the limiting physical bounds of the collagen fibers themselves. In addition, reasons for deviations from the predicted values are analyzed. This study illustrates how the squid's reinforcing collagen fibers are aligned to provide several locomotory advantages and demonstrates how this complex biological process can be accurately modeled with several simplifying assumptions.

Stacking-sequence Optimization for Wing Flutter using FBBM (An Investigation for Improvement of Optimal Results by Means of Base Fiber Angle Optimization)

The fractal branch and bound method (FBBM) has been developed by authors for optimizing the stacking-sequence of composite structures. The method can directly optimize feasible stacking-sequences comprising of limited fiber angles, 0°, ±45°and 90°layers. The applicability of the method has been confirmed for buckling load maximization and flutter limit maximization problem in the previous studies. In this paper, we focus on the composite wing flutter problem. The relationship between the base fiber angle variance and the optimized flutter limit by means of fractal branch and bound method is discussed. To improve the optimal flutter limit of the composite wing structure obtained from fractal branch and bound method, the base fiber angle optimization method using Kriging method is developed. As a result, the method is successfully applied, and the optimal base fiber angle is obtained using newly proposed base fiber angle optimization method.

Creep of Polymer Matrix Composites. II: Monkman-Grant Failure Relationship for Transverse Isotropy

This research concerns polymer matrix composite (PMC) materials having long or continuous reinforcement fibers embedded in a polymer matrix. The objective is to develop comparatively simple, designer friendly constitutive equations intended to serve as the basis of a structural design methodology for this class of PMC. Here (Part II), the focus is on extending the damage/failure model of an anisotropic deformation/damage theory presented earlier. A companion paper (Part I) by the writers deals with creep deformation of the same class of PMC. The extension of the damage model leads to a generalization of the well known Monkman/Grant relationship to transverse isotropy. The usefulness of this relationship is that it permits estimates of (long term) creep rupture life on (short term) estimates of creep deformation rate. The current extension also allows estimates of failure time for various fiber orientations. Supporting exploratory experiments are defined and conducted on thin-walled specimens fabricated from a model PMC. A primary assumption in the damage model is that the stress dependence of damage evolution is on the transverse tensile and longitudinal shear traction acting at the fiber/matrix interface. We conjecture that a supplemental mechanism of failure is the extensional strain in the fiber itself. The two postulated mechanisms used in conjunction suggest that an optimal fiber angle may exist in this class of PMC, maximizing the time to creep failure.