Optimal Fiber Orientation Research Articles

A comprehensive investigation on optimum layer thickness and fiber orientations of laminated composite plates against buckling failure under various loading conditions

A comprehensive investigation on optimum layer thickness and fiber orientations of laminated composite plates against buckling failure under various loading conditions

Buckling load optimization of laminated composite plates with elliptical hole under different non-uniform edge loads using bonobo optimizer algorithm

This present work investigates the buckling load optimization of the laminated composite plates with the elliptical hole under different non-uniform edge loads. The design objective is the maximization of the critical buckling load by determining the optimum fiber orientations in the layers. The stability equations are derived based on the first-order shear deformation theory (FSDT) of the laminated plates. The critical buckling loads are calculated using the finite element method with the nine noded rectangular element having five degrees of freedom per node. The bonobo optimizer (BO) algorithm is employed to optimize the laminated composite plates with the elliptical hole. The computer programming is developed in the MATLAB environment. Besides, the parametric studies are conducted for different types of the non-uniform edge loads, boundary conditions, cutout radius ratio and aspect ratios and the obtained numerical results are compared. Finally, the optimum results show that these factors play an imperative role in the optimum pattern and stacking sequence of the laminated composite plates with hole. The new significant findings can aid the designers in the structural design, and other industrial applications.

Fatigue-resistant design of carbon/epoxy composites based on a failure tensor polynomial model by particle swarm optimization-sequential quadratic programming algorithm

This article introduces a design procedure to find the optimum fiber orientations of carbon/epoxy composite laminates for fatigue life advancement. The approach incorporates a fatigue failure tensor polynomial model and employs a hybrid algorithm, combining particle swarm optimization and sequential quadratic programming. Firstly, material properties of quasi-static and fatigue of the carbon/epoxy composites, fabricated by the vacuum-assisted resin transfer molding method, were determined to be used in the model. Various design problems involving two optimization scenarios were then solved using the hybrid algorithm. The algorithm’s performance was also evaluated by specific test problems, confirming its speed and robustness. The optimally fiber-oriented carbon/epoxy composite laminates having maximum fatigue lives were obtained for many critical in-plane cyclic loading cases. To validate the proposed design procedure, two optimum designs were experimentally verified under uniaxial loading conditions. The results indicated a good correlation between the estimated fatigue life of the optimally designed laminates and experimental data. This methodology offers a promising approach for the design of carbon/epoxy composite laminates with superior fatigue strength, particularly significant in specific industrial applications.

Lightweighting structures using an explicit microarchitectured material framework

In this paper, a new approach to design ultralight structures is developed based on a previous work called Efficient Multiscale Topology Optimization. A parameterized (or explicit) truss-based cell is introduced to generate intrinsically well-connected microstructures and to get clear interpretable optimal multiscale structures. The method uses a pre-computed database of optimal micro-cells to be computational efficient without losing in structural performances. The parameterization allows to generate a lightweight database just storing the set of parameters, that define the optimal cells, and the cells properties, that are obtained through inverse homogenization. The method has been successfully tested on two-dimensional compliance problems. Several examples demonstrate its versatility and give quantitative results. Moreover, it allows to obtain structures compatible with additive manufacturing processes, to naturally solve concurrent multi-scale problems, as well as controlled porosity and optimal fiber orientation problems.

3D printing of topologically optimized wing spar with continuous carbon fiber reinforced composites

The necessity for more efficient manufacturing approaches of high-performance complex fiber reinforced composites parts is increasing. This study develops a framework to design and produce topologically optimized continuous carbon fiber reinforced composites (CCFRCs) with both high manufacturing efficiency and manufacturability, and experimentally validates via material extrusion (MEX) 3D printing technique in a more than 1-m wing spar for the unmanned aerial vehicle (UAV). The load-carrying structure can be topologically optimized by a solid orthotropic material with penalization method and further designed into a continuous fiber trajectory under the consideration of optimal material density, optimal fiber orientation and 3D printing process limitation. Based on this method, the complex topological CCFRCs can be realized by a single-stroke printing path with intact fiber. The feasibility and effectiveness of the proposed framework have been evaluated on the Messerschmitt-Bölkow-Blohm (MBB) beam which reveals obvious higher performance in specific stiffness and peak load compared with commonly used honeycomb structure. As a case study, a topologically optimized UAV wing spar was designed and validated experimentally. Mechanical testing shows that the designed wing spar can survive in operating loads. Furthermore, a proof-of-concept internal wing structure was presented where conventional wing spar and ribs are replaced by CCFRCs 3D printed structures. It exhibits high load-carrying characteristics, is lightweight and simple to fabricate.

An iso-contour method for automated fiber placement optimization of composite structures

A new method for numerical optimization of fiber-steered composites is presented, which allows to control efficiently and effectively the curvature of the fibers of single- or multi-layer composite structures. It is based on the introduction of an artificial surface defined and controlled by a relatively small number of control points, which is optimized to identify optimal fiber orientations varying smoothly over the panels. Curvature constraints like the maximum fiber curvature constraint, MFCC, or the average fiber curvature constraint, AFCC, are respected explicitly by the method to ensure manufacturability of the composite component. Three validation cases are regarded where results of the unconstrained case are compared to those of established methods to illustrate the validity of the new approach. They are complemented by results considering curvature constraints showing that optimal structures depend strongly on the chosen curvature thresholds. Finally, a rib optimization of a wingbox structure is realized as a more complex case.

Optimal design of composite cylindrical shells subject to compression buckling strength

PurposeThe objective of the present work is to present the design optimization of composite cylindrical shell subjected to an axial compressive load and lateral pressure.Design/methodology/approachA novel optimization method is developed to predict the optimal fiber orientation in composite cylindrical shell. The optimization is carried out by coupling analytical and finite element (FE) results with a genetic algorithm (GA)-based optimization scheme developed in MATLAB. Linear eigenvalue were performed to evaluate the buckling behaviour of composite cylinders. In analytical part, besides the buckling analysis, Tsai-Wu failure criteria are employed to analyse the failure of the composite structure.FindingsThe optimal result obtained through this study is compared with traditionally used laminates with 0, 90, ±45 orientation. The results suggest that the application of this novel optimization algorithm leads to an increase of 94% in buckling strength.Originality/valueThe proposed optimal fiber orientation can provide a practical and efficient way for the designers to evaluate the buckling pressure of the composite shells in the design stage.

Simultaneous Optimization of Carbon Fiber Allocation and Orientation by IFM-GA

This paper proposes an individual fitness method genetic algorithm (IFM-GA) for carbon fiber-reinforced plastic (CFRP). The strength of CFRP depends on the carbon fiber allocation and orientation. Waste carbon fiber is generated if this design is inappropriate. Consequently, CFRPs are less cost-effective. It is necessary to optimize the allocation and orientation as design variables to solve this problem. The problem involves combinatorial optimization. The genetic algorithm (GA) is suitable for combinatorial optimization. However, it is difficult to obtain an optimal solution using the GA owing to the large number of combinations. Hence, the IFM-GA is developed in this study. It is a GA-based method with a different fitness calculation. The GA calculates the fitness of each design, whereas the IFM-GA calculates the fitness of each design element. As a result, the IFM-GA yields a higher-stiffness design than the GA. To conclude, the IFM-GA can enable optimum fiber allocation and orientation, whereas the GA cannot.

Evaluating the optimum nanofiber alignment in conductive composites with a stereology-based anisotropic degree

Rationally tuning the anisotropic degree of orientation distribution for conductive fibers in composites can maximize the macro electrical conductivity in a specific direction. However, quantitative evaluation of the optimum anisotropic degree of networks with fibers of different shapes and orientation distributions remains largely unexplored. In this work, the optimum fiber orientation distribution at the maximum electrical conductivity is quantified by a newly proposed stereology-based anisotropic degree. This index applies to both straight and curved fiber networks and has one-to-one corresponding relation with the macro electrical properties. Using Monte Carlo simulations, it is found that with the increase of anisotropic degree, the electrical conductivity increases to its maximum and then decreases gradually, which shows good agreement with experimental results. Further, a universal expression to determine the optimum anisotropic degrees of networks at different fiber concentrations is obtained, which is independent of the curliness and orientation distribution laws of fibers.

Topology Optimization of fiber reinforced structures considering stress constraint and optimized penalization

The use of materials reinforced with fibers has been increasing due to their advantages, for example, the ratio between its mass and strength. For this reason, new additive manufacturing technologies have been developed for this material type. Some technologies allow tailoring fiber orientation, creating space for applying optimization techniques. On this account, many works dedicated to optimizing fiber orientation have been currently published. However, the critical issue of the stress yield criteria should be addressed. Thus, this work proposes to solve the Topology Optimization problem of minimizing the volume of the structure considering local stress constraints, determining the material distribution and the fiber orientation by using a proposed method named NDFO-adapt. The penalization used in the method is a field optimized together with the material distribution and the fiber angle. The same approach is extended to the penalization of SIMP and β parameters of threshold projection. This strategy enlarges the solution space and facilitates the discovery of previously unachievable local minima while eliminating the need for a heuristic selection of continuation methods. The Augmented Lagrangian method is used to deal with the local stress constraints. A mesh refinement scheme developed in the FEniCS project is proposed. Numerical examples are presented to illustrate the performance of the proposed method.

Shape and topology optimization method for fiber placement design of CFRP plate and shell structures

In this study, we present a novel non-parametric shape-topology optimization method for fiber placement and orientation design, aiming at controlling the stiffness of CFRP (Carbon Fiber Reinforced Plastics) shell structures. The sum of squared error norm for achieving the target displacements on the arbitrarily specified position is minimized under the length constraints as a design problem. A simultaneous shape and topology optimization problem is formulated as a distributed-parameter optimization problem based on the variational method. The shape gradient function and the density gradient for this design optimization problem are theoretically derived with the Lagrange multiplier method, the material derivative method and the adjoint variable method. The solid isotropic material with penalization (SIMP) method is employed for topology optimization. The gradient functions derived are applied to the H1 gradient method for fibers to determine the optimal shape and topology. With the present method, the optimal fiber placement and orientation can be obtained without any parameterization. Numerical examples are solved to show the validity of the proposed method and the results are discussed.

Analysis of sandwich structures with corrugated and spiderweb-inspired cores for aerospace applications

The bending response of laminated composite sandwich structures developed for aircraft flaps is analyzed, in two parts. In the first part, the carbon fiber reinforced plastic (CFRP) and Aluminium 6061 based single-sided trapezoidal corrugated core sandwich panels are considered. The developed design is observed to withstand higher loads and exhibits higher flexural stiffness as compared to the similar corrugated geometries in the literature. The core design is iteratively modified to maximize the contact points between the core and panel in contact with the lift forces. The structure is treated as a cantilever, thus, representing the boundary conditions of aircraft flaps. The influence of ply-orientation, stacking sequences of face sheets, and panel thickness on the bending response are studied. As a result, an optimized sandwich composite structure with two times more stiffness and 40% lower stress levels as compared to the initial design is arrived. Furthermore, dynamic analysis is performed considering sinusoidally varying load along the space and time. In the second part, a novel bio-inspired spiderweb core design for the aircraft flap is developed. The stiffness of the bio-mimicked sandwich composite structures is observed to be better than the optimized corrugated core structures proposed in the first part. The influence of scaling and patterning the geometry is also investigated. The simulations are further extended to study the influence of hail impact on the sandwich structures with optimized corrugated and spiderweb cores to estimate the maximum induced stresses and peak forces. Finally, the corrugated design is replaced with the proposed spiderweb-based core design while preserving the optimal fiber orientation and ply-thickness developed in the first part.

Using the Finite Element Method to Simulate a Carbon Fiber Reinforced Polymer Pressure Vessel

Introduction. Over the past decade, global demand for pressure vessels has increased significantly, specifically in such industries as aviation, space, chemical, and oil and gas. Being under the constant impact of high internal pressure, the walls of the tanks are under increased stress, which can cause their sudden destruction. To eliminate this probability and improve the strength characteristics, the tanks are made in the form of metal cylinders with an internal coating of composite material consisting of resin reinforced with carbon fibers. This article aimed at studying the effect of the angle of inclination of carbon fiber on cylindrical tanks and determining the maximum destructive pressure using the finite element method of ANSYS program.Materials and Methods. Using the ANSYS program, a finite element model of a tank was created. It has a central part, which is a metal cylinder with an internal coating of composite material consisting of polymer reinforced with carbon fibers. At the ends of the tank, spiral wound hemispheres were placed. In these studies, SHELL 99 was used to model the layered composite material. The Tsai-Wu theory was used to determine the pressure tank failure criterion.Results. The cylindrical tank model was calculated for two types of fiber winding paths: annular and spiral, at different angles of their inclination. The results of the pressure value analysis for different fiber inclination angles showed that, starting from the angle value of 0° and up to 45°, it increased, and then, up to the angle value of 65°, it began to decrease. The critical pressure value for a carbon fiber reinforced tank was 207 MPa, which was obtained at a fiber angle of 45º.Discussion and Conclusion. Analysis of the studies showed that at a fiber inclination angle of 45º, the value of the maximum stress turned out to be the smallest, and the maximum possible destructive pressure at the same angle was 207 MPa. It follows, that the optimal fiber orientation angle to provide safe operation of the high-pressure tank is ± 45º, and the carbon fiber tank, calculated at the same fiber winding angle, has the maximum strength value.

A design methodology for fiber layup optimization of filament wound structural components

The applications of fiber-reinforced polymer (FRP) composites extend rapidly along with the development of new manufacturing techniques. However, due to the complexities introduced by the material and fabrication processes, the application of conventional structural design methods for construction members has been significantly challenging. This paper presents an alternative methodology to find optimum fiber layups for a given tube-shape geometry via a graphical optimization strategy based on structural performance requirements. The proposed technique employs simplified shell element models based on classical lamination theory (CLT) to avoid explicit fiber modeling in the FEA simulations. Lamination parameters are utilized to generate the reduced stiffness matrices for continuous multi-layer FRP lamination. The fiber layup of the component is retrieved from the optimal lamination parameters that maximize the structural performance. The case study results demonstrate that the developed method provides compact solutions, linking the structural design requirements with optimal fiber orientations and volumetric proportions. In addition, the determined solutions can be interpreted directly by the winding fabrication settings.

Geometrical Investigation of Piezoelectric Patches for Broadband Energy Harvesting in Non-Deterministic Composite Plates.

Mechanical energy is the most ubiquitous form of energy that can be harvested and converted into useful electrical power. For this reason, the piezoelectric energy harvesters (PEHs), with their inherent electromechanical coupling and high-power density, have been widely incorporated in many applications to generate power from ambient mechanical vibrations. However, one of the main challenges to the wider adoption of PEHs is how to optimize their design for maximum energy harvesting. In this paper, an investigation was conducted on the energy harvesting from seven piezoelectric patch shapes (differing in the number of edges) when attached to a non-deterministic laminated composite (single/double lamina) plate subjected to change in fiber orientation. The performance of the PEHs was examined through a coupled-field finite element (FE) model. The plate was simply supported, and its dynamics were randomized by attaching randomly distributed point masses on the plate surface in addition to applying randomly located time-harmonic point forces. The randomization of point masses and point force location on a thin plate produce non-deterministic response. The design optimization was performed by employing the ensemble-responses of the electrical potential developed across the electrodes of the piezoelectric patches. The results present the optimal fiber orientation and patch shape for maximum energy harvesting in the case of single and double lamina composite plates. The results show that the performance is optimal at 0° or 90° fiber orientation for single-lamina, and at 0°/0° and 0°/90° fiber orientations for double-lamina composites. For frequencies below 25 Hz, patches with a low number of edges exhibited a higher harvesting performance (triangular for single-lamina/quadrilateral for double-lamina). As for the broadband frequencies (above 25 Hz), the performance was optimal for the patches with a higher number of edges (dodecagonal for single-lamina/octagonal for double-lamina).

HYIMFO: Hybrid method for optimizing fiber orientation angles in laminated piezocomposite actuators

Numerous engineering applications employ composite materials due to the advantages that the combination of their components can provide. Fiber-reinforced composites are a particular group of composites which allows designing optimized structures by tailoring the orientation of the fiber. For this reason, new additive manufacturing technologies have been developed nowadays. These tools allow the manufacturing of fiber-reinforced structures designed by using optimization algorithms. Consequently, there are several works in recent literature determining the optimized fiber orientation in composite structures, where the methods based on gradient stand out due to their better efficiency. There are two main approaches to determine the fiber orientation by using gradient-based methods, Continuous Fiber Angle Optimization (CFAO), where the angle is the design variable and commonly present local minima problems, and Discrete Fiber Angle Interpolation Models, which consider candidate angles a priori and by using weighting functions choose one of them as the optimized angle. This work proposes a method named HYMFO, which uses a combination of both approaches. To verify the efficiency of the method, two design problems of Laminated Piezocomposite Actuators (LAPA) are solved by using several mesh discretizations with the discrete methods DMO, HPDMO, BCP, and NDFO, the continuous method SPIMFO and the newly proposed hybrid method. Therefore, the method is not evaluated with the traditional problem of maximizing the stiffness in structural design. A new fiber orthogonality regularization is presented, facilitating the appearance of continuous paths in fiber distribution by imposing a specified maximum angle between adjacent fibers. A comparative analysis based on the performance of the structure and the computational cost is carried out to determine the most appropriate method for each situation.

Multi-step buckling optimization analysis of stiffened and unstiffened polymer matrix composite shells: A new experimentally validated method

A new multi-step optimization method is developed to predict the optimal fiber orientation in glass fiber reinforced polymer (GFRP) composite shells. The method contains 1) a regenerated genetic algorithm (GA) optimization strategy coupled with, 2) an analytical approach regarding assessing the failure of the tubular structure. Two critical factors, namely “ultimate buckling load” and “weight of structure” are particularly taken into account, while other crucial limitations, including angle and number of layers, shell thickness, and size of stiffeners, are considered in this study. Some experiments are conducted to evaluate the critical buckling pressure in GFRP specimens, and the obtained analytical results are verified through comparison with experimental ones. The results suggest that the application of this novel optimization algorithm leads to a decrease of 21% and 28% in optimum local mass of stiffened unsymmetrical angle-ply and unstiffened symmetrical angle-ply laminated composite shells, respectively.

An engineering interpretation of Nesterov’s convex minimization algorithm and time integration: application to optimal fiber orientation

An engineering interpretation of Nesterov’s convex minimization algorithm and time integration: application to optimal fiber orientation

Parametric Optimization of Isotropic and Composite Axially Symmetric Shells Subjected to External Pressure and Twisting

The present paper is devoted to the problem of the optimal design of thin-walled composite axially symmetric shells with respect to buckling resistance. The optimization problem is formulated with the following constraints: namely, all analyzed shells have identical capacity and volume of material. The optimization procedure consists of four steps. In the first step, the initial calculations are made for cylindrical shells with non-optimal orientation of layers and these results are used as the reference for optimization. Next, the optimal orientations of layers for cylindrical shapes are determined. In the third step, the optimal geometrical shape of a middle surface with a constant thickness is determined for isotropic material. Finally, for the assumed shape of the middle surface, the optimal fiber orientation angle θ of the composite shell is appointed. Such studies were carried for three cases: pure external pressure, pure twisting, and combined external pressure with twisting. In the case of shells made of isotropic material the obtained results are compared with the optimal structure of uniform stability, where the analytical Shirshov’s local stability condition is utilized. In the case of structures made of composite materials, the computations are carried out for two different materials, where the ratio of E1/E2 is equal to 17.573 and 3.415. The obtained benefit from optimization, measured as the ratio of critical load multiplier computed for reference shell and optimal structure, is significant. Finally, the optimal geometrical shapes and orientations of the layers for the assumed loadings is proposed.

A hybrid multilevel method for simultaneous optimization design of topology and discrete fiber orientation

This paper proposes a hybrid multilevel approach of simultaneous optimization design of topology and discrete fiber orientation for maximum stiffness design of constant-stiffness laminated plates. The lamination parameters are selected as the intermediate variables to overcome the local optima behaviors derived from directly optimizing fiber orientation. The hybrid multilevel method incorporates two different types of optimization techniques to benefits from the advantages of them. At the first level, lamination parameters and density are taken as the design variables, the method of moving asymptotes (MMA) is applied to obtain the optimal lamination parameter and topology shape simultaneously. At the second level, taking the discrete fiber orientation angles of individual layers as the design variables, a detailed lay-up design optimization considering some limitations on manufacturing is implemented by an improved direct simulated annealing (IDSA) algorithm. Thus, the hybrid multilevel optimization procedure can achieve a global optimum and obtain a faster convergence. Finally, Numerical examples are tested to illustrate and validate the proposed hybrid method.