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D and DD-drop Layup Optimization of Aircraft Wing Panels under Multi-Load Case Design Environment
Abstract
The aerospace industry is on a perpetual drive to optimize structures with developments in modeling and analysis capabilities. The traditionally used laminates with 0°,90°,±45° orientations are called Legacy QUAD Laminates (LQL). The recent discovery of Trace of an orthotropic stress tensor A allows reduction of design variables by the replacement of LQL with equivalent stiffness DD¹ (double-double) laminate having self-repeating orientations in a set of ±ϕ/±ψ. The optimized LQL structures are with mid-plane symmetry, excessive ply-migrations, and variability in ply-orientations, which make the manufacturing process cumbersome. On the other hand, DD-laminates are simplified, thinner and free from mid-plane symmetry, thus enable ten-fold reduction in production resources. The present study, an artificial intelligent (AI) genetic-algorithm based stochastic optimizer replaces LQL with DD-laminates, which follows DD-drop design for mass optimization. The optimization algorithm works with unit-circle failure, buckling mode, and wing-tip deflection design criteria and derives optimal-wing with lowest mass, well suited for design requirements in multiple design load-case. The application of algorithm shows 68-70% mass reduction to an initial full-length ply wing-box model of LQL. The minimization of ply-migrations by D/DD-drop optimization yields structures with better resistance for delamination and well suited for automated production.
... The ply-level innovation is ever-thriving. A new "double-double" lamination family directed by Tsai's modulus and stiffness matrix invariant theory [27][28][29][30] has established a R&D route for weight and cost reduction to find out the best laminate for a given multi-load case, and has been successfully applied to ply-drop structures of model-class avia-tion components. Learning from nature, S. T. Pinho et al. [31][32][33][34] have exploited bio-inspired layup manners for specific mechanical behaviors of CFRP laminates. ...
... To assess the warpage degree of TEP-enhanced laminates, in Fig. 3b, the sampled superficial coordinates (150 points per specimen) were fitted to quadratic polynomial surfaces in the function of where ( ) is each fitting coefficient. From the visualized results and color levels, the maximum planeness differences occurred at the diagonal ends, where no more than 0.05 % variation could be customarily acceptable as far as specimen geometry [27,29,36,49,61]. ...
... It is prospective to conduct oriented regulation on service stability for thin-walled components (e.g. wing panels [27,29], T-joints [19][20][21][22], and Ω-shaped stringers [15,30,78]) under complex working conditions, and also conduce to light-weight design for ultra-thick laminates with biaxial structural performance requirements [79,80]. Fundamentally, damage resistance is the core to preserve the residual mechanical properties. ...
Pursuing the trend of ply-level innovation in the field of high-performance CFRP composites, a pseudo-woven layup configuration has been developed by interlacing a thin-ply prepreg in the translaminar-envelope manner space-orthogonally inside a homogenized 4-ply sub-laminate to acquire mechanical superiorities for the global multidirectional laminate. This evolved layup structure possesses the stiffening feedbacks on in-plane principal properties by the locally-regulated 0°ply amount, and exerts the multi-interface synergy on shear-driven inter-laminar fractures by the long-acting binding action. Further, the high robustness of structural performances has been revealed by resistance and tolerance against severe low-velocity impact damage, achieving up to 60 % decrease in the projected delamination area and over 60 % increase in the post-impact compressive strength. The translaminar-envelope layup configuration is expected to enhance the service capability of CFRP laminates.
... For component * had a variation compared to the mean value of 1.5% while the transverse and shear components appeared to show larger coefficients of variation of up to 16.4% [1]. Many investigations explained the significance of the knowledge of trace concerning novel laminate concepts [3], aircraft certification principles [2], optimization [6], strength prediction of notched specimen [7] or fracture mechanics [8]. ...
... The next design idea is the use of double-double sublaminates ± /± and asymmetric stacking sequences. The advantages in terms of manufacturing, design and optimization have been extensively discussed in literature [2] [3] [6]. One big advantage of double-double sublaminates is that their stiffness components can be described analytically in closed form for arbitrary ply angles, see Fig. 2b). ...
... optimization incorporating further requirements for strength, buckling resistance and wing-tip deflection under multiple load cases [6]. ...
This work includes the application and evaluation of new methods to describe laminate stiffness and strength. Tsai et al. have shown that the trace of laminate stiffness is a rotationally invariant quantity and accurately describes the stiffness potential of a material [1]. In combination with a rotationally invariant strength criterion, the Unit Circle criterion, this allows a simple approach for the dimensioning of fiber composite structures [2]. The use of two biaxial, so called “double-double” [±ϕ/±ψ] sublaminates with the possibility of asymmetrical stacking sequences but homogenization of laminates further simplifies the design and manufacturing process of such structures [3]. The principles mentioned above are applied as an example for the optimization of an aerospace wing box. They are compared with classical optimization algorithms, an Evolutionary Algorithm (EA) and the Adaptive Response Surface Method (ARSM) [4]. The wing box is optimized with respect to stiffness while simultaneously minimizing weight. It is shown that the use of [±ϕ/±ψ] sublaminates instead of the traditional [0/±45/90] sublaminates can lead to a weight reduction of the composite skins of more than 10%. The simplified search algorithm based on the principles of Tsai et al. yields a different sublaminate than the classical optimization methods EA and ARSM. The computational effort though can be significantly reduced with the former.
... Notably, the strength of multi-directional laminates is often significantly higher compared with that of unidirectional laminates. Investigating legacy quad laminates composed of 0 • , 90 • , and ±45 • plies will be essential, especially concerning the influence of the number of interfaces on their mechanical properties [34]. Furthermore, for double-double laminate configurations [34,35], exploring how the properties vary with interface angles is of significant interest. ...
... Investigating legacy quad laminates composed of 0 • , 90 • , and ±45 • plies will be essential, especially concerning the influence of the number of interfaces on their mechanical properties [34]. Furthermore, for double-double laminate configurations [34,35], exploring how the properties vary with interface angles is of significant interest. However, the effort required in manufacturing various specimen configurations presents significant challenges for conducting extensive experimental studies with diverse layup configurations. ...
This study explores the experimental characterization of the through-thickness compression properties in unidirectional laminates using cube compression tests. Cubical specimens, each with an edge length of 10, were symmetrically outfitted with biaxial strain gauges and subjected to a compression test. While similar methodologies exist in the literature, this work primarily addresses the potential biases inherent in the testing procedure and their mitigation. The influence of friction-induced non-uniform deformation behavior is compensated through a scaling of the stiffness measurements using finite element (FE) analysis results. This scaling significantly enhances the accuracy of the resulting parameters of the experiments. The ultimate failure of the specimens, originating from stress concentrations at the edges, resulted in fracture angles ranging between 60∘ and 67∘. Such fracture patterns, consistent with findings from other researchers, are attributed to shear stress induced by friction at the load introduction faces. The key findings of this research are the comparisons between the through-thickness modulus (E33c) and strength (X33c) and their in-plane counterparts (E22c and X22c). The results indicate deteriorations of E33c and X33c from E22c and X22c by margins of 5 and 7, respectively. Furthermore, the results for E22c and X22c were compared with the results obtained through a standard test, revealing a 12 enhancement in strength X22c and 4 underestimated stiffness E22c in the cube compression test.
... This is a powerful and pivotal discovery that promises to change the way carbon composites are worked with, analysed, manufactured and tested. Many studies have already benefited from the use of trace in the mechanics of composite materials, including new laminate concepts [3,4] and structures [5], preliminary design [6][7][8] and optimization [9,10], fast notched strength prediction tools [11], generation of statistical virtual allowables [12] and fracture mechanics [13,14]. ...
... Direct material and laminate selection could be performed based on the Tsai's modulus only, without the need for additional shape iterations. Shrivastava et al. [10] also used stiffness components normalized by Tsai's modulus in layup optimization of a wing box, including thermal deformation analysis. ...
For the past six years, we have been benefiting from the discovery by [1] that the trace of the plane stress stiffness matrix (tr(Q)) of an orthotropic composite is a fundamental and powerful scaling property of laminated composite materials. Algebraically, tr(Q) turns out to be a measure of the summation of the moduli of the material. It is, therefore, a material property. Additionally, since tr(Q) is an invariant of the stiffness tensor Q, independently of the coordinate system, the number of layers, layup sequence and loading condition (in-plane or flexural) in a laminate, if the material system remains the same, tr(Q)=tr(A∗)=tr(D∗) is still the same. Therefore, tr(Q) is the total stiffness that one can work with making it one of the most powerful and fundamental concepts discovered in the theory of composites recently. By reducing the number of variables, this concept shall simplify the design, analysis and optimization of composite laminates, thus enabling lighter, stronger and better parts. The reduced number of variables shall result in reducing the number and type of tests required for characterization of composite laminates, thus reducing bureaucratic certification burden. These effects shall enable a new era in the progress of composites in the future. For the above-mentioned reasons, it is proposed here to call this fundamental property, tr(Q), as Tsai’s Modulus.
... This type of laminate design tailoring is a significant advantage specially if one considers the concept of lay-up homogenization. As explained in the recent work of Vermes et al. [34] inspired by the works of [35], [36], [37] repeating a lay-up pattern more times within a certain thickness, amplified if thin-ply plies are to be used, eventually leads to a form of macroscopic homogenization, that eventually leads to the elimination of warpage effects i.e., the bending stiffness matrix becomes equal to the extensional one and the bending-extension coupling matrix tends to zero ([A] = [D], [B] ≈ [0]). Essentially the laminate is no longer restricted to a midplane symmetric lay-up. ...
Objectives of improving efficiency and reducing costs in aerospace design are often translated to needs of developing new materials and their subsequent inclusion in design. This requires of course the understanding of the material behavior and the development of accurate tools to model them. Such a material is carbon fiber reinforced polymers (CFRPs), that for a few decades already have been of interest and vastly used. Recently a new variant, thin-ply CFRPs, have been introduced and are acting as gamechanger. This because, early studies in the direction of understanding their behavior demonstrated that, contrary to observations on standard grade (standard ply) composites, thin-ply CFRP laminates fail in a through thickness single crack net-section type pattern, not presenting delaminations and other subcritical failure events.
Along those lines and to aid in creating more efficient modeling tools for this novel type of CFRPs this study is carried out. The idea is to apply models relying on assumptions of quasi-brittle crack like failure, relying on plate level analysis that stems from an equivalent single layer representation of the laminate. This comes as a follow up to some initial studies done in that direction. The effort revolves around the specific problem of notched strength mainly open hole tension (OHT) that was selected to be studied as it is a problem very pertinent to aerospace design since structures commonly contain cutouts and holes.
Thin-ply CFRP laminates of standard and non-standard lay-ups were subjected to on-axis and off-axis loading. Their behavior is evaluated and categorized in terms of their level of anisotropy presenting interesting observations in off-axis loading hinting that strongly anisotropic thin-ply laminates tend to, in fact, behave more like standard grade CFRPs . These results are then used to validate, verify and propose the use of PF and FFM on the basis of their ability to accurately predict the experimental results. It is shown that the former was rather adequate and able to produce close enough strength predictions with strengths lying under 5%
of error. The latter did not achieve the same, nonetheless, the development aids in comparing the two methods and furthermore understanding the challenges such ESL representations of CFRP laminates entail.
Available at: https://hdl.handle.net/10216/161780
... Kappel [6] found the best DD stacking sequence and the required number of building block repetitions for panels used in aircraft fuselage and wings based on classical lamination theory (CLT) and mixed integer distributed ant colony optimization (MIDACO) technique. Shrivastava et al. [7] used an artificial intelligence genetic algorithmbased stochastic optimizer to replace QUAD wing-box panels with DD panels and reported a 24 % mass reduction attributed to the absence of mid-plane symmetry requirement in the DD panels. Vermes et al. [8] conducted an analytical study on composite shaft and bulkhead and reported a 6 % weight reduction in both cases by replacing the QUAD with DD. ...
Tailorability is a key advantage of fiber-reinforced composites over other material systems. While tailoring a single isolated laminate is relatively simple, challenges arise when designing larger integrated components while ensuring compatibility between laminates and avoiding sharp changes in local stiffness. The innovative Double-Double (DD) laminate design method simplifies the optimization and processing of laminates by incorporating 4-ply building blocks consisting of +ϕ, −ϕ, +ψ, and −ψ ply orientations. As a relatively new concept, DD laminate design requires careful assessment to ensure its performance is equivalent to that of conventional designs. The current study compares impact damage tolerance of quadriaxial (QUAD) laminates consisting of 0°, 90°, and ±45° ply orientations with equivalent DD laminates under Low-Velocity Impact (LVI) and Compression After Impact (CAI) loadings. To this end, a validated three-dimensional high-fidelity finite element model capable of capturing fiber breakage, splitting, kinking, as well as matrix cracking and delamination, was used. A computer tool was developed to identify equivalent DD laminates and to find the best stacking sequence for achieving layup homogenization. Three equivalent DD laminates were selected for the [0/45/90/-45]4s. The first laminate had an equal in-plane stiffness [A] matrix ([67.5/-22.5/22.5/-67.5]8T), the second laminate had an equal flexural stiffness [D] matrix ([64.5/-17/17/-64.5]8T), and the third laminate ([65.5/-18.5/18.5/-65.5]8T) had a similar [D] matrix while keeping the difference between each element of [A] matrices below 10%. The results indicate that the QUAD laminates can be replaced by equivalent DD without compromising impact damage tolerance while benefiting from the improved design and manufacturing ease of the DD laminate configuration.
... Because of the advantage of continuous ply angles variable [10], many investigations about optimization have been performed considering the cost [11], mass [12], manufacturing [13] and buckling [14,15]. Additionally, Kappel [16] evaluated DD advantages for aerospace structures and Zhang et al. [17] proposed the application of machine learning algorithms to decrease design time. ...
The most usual layup in composite design, namely QUAD, has the plies oriented at 0°, 90° and ±45°. Alternatively, double-double (DD) laminates were recently proposed, where plies are oriented at ±Φ and ±Ψ, allowing optimized application and improving structural response, since Φ and Ψ continuous variables ranging between 0° and 90°. The present research is the first effort to compare the response of QUAD and DD laminates in single lap joints. A finite element model is developed using the software Ansys. The damage onset is evaluated considering the Drucker-Prager criterion for the adhesive and Tsai-Wu criterion for the laminate. A QUAD laminate is selected and DD layups are evaluated considering the stiffness equivalence. The results indicate that all DD layups improve the joint damage onset, obtaining forces up to 25 % higher than for the equivalent QUAD and smother transition of the stress invariants.
... This avoids impacting in-plane stiffness or introducing abrupt changes in thickness. Recent efforts have shown how Quad composite stacking sequence can be converted to DD, achieving lower weight without compromising strength, possibly relieving interlaminar stresses by easing homogenization and reducing the angle difference between adjacent plies [13][14][15][16]. ...
... Moreover, symmetry and balancing requirements must be accounted for manufacturing and performance needs, limiting the optimization processes for mass and mechanical performance requirements to sub-optimal solutions. One step forward is proposed by the newly Double-Double approach introduced by Professor S.W. Tsai [1]. Double-Double laminates are made up by stacking 4-plies building blocks without symmetry and balancing requirements. ...
Mass minimization and mechanical performance maximization constitute the basic aspects of the structural optimization processes. In particular, the laminate redesign in terms of thickness and lay-up grants the main approach for the optimization of composite components. The innovative Double-Double laminate concept provides an effective approach to design composite components for weight and strength requirements, overcoming the use of the conventional 0°, 90° and ±45° ply orientations. In Double-Double designed components, 4-plies building blocks are stacked one upon the other to constitute a laminate. Each building block is made up of four [±Φ, ±Ψ] oriented plies. In the present work, the Double-Double approach has been adopted in the redesign of the composite lay-up and thickness profile of frames in a composite fuselage barrel. The DD optimized frames achieved a total mass reduction by up to 35% while ensuring mechanical performances comparable to the starting configuration.
... Analyzing a multi-bolted composite joint construction can be divided into two stages. [7][8][9] The first stage is to determine the load distribution among the bolts. And the second stage is to build on the previous step by analyzing the local stress in the key holes to ensure the structural integrity. ...
The determination of the load distribution between bolts is a crucial step in predicting the failure of bolted joints. In this paper, the purpose is to investigate the effects of stacking sequence on the load distribution and the stress distribution around hole of a double lapped and three bolted joint composite plate with shearing force. The accuracy and reliability of the finite elements model was verified by the spring method results and test results at first. Subsequently, the load distribution among bolts and the stress distribution around hole of six structural combinations of two stacking sequence composites were studied. Results indicate that the load distribution ratio of the sequential structure is more even than that of the symmetrical structure. And the symmetrical stacking structure can bear greater stress than that of the sequential stacking structure, which is about three times that of sequential stacking structure. As the external loading increases, the hole-edge stress is relatively stable at ±45° layer, while the hole-edge stress of the orthogonal layer is varied and occurs damage failure at 90° around the hole.
... DD laminates are constructed by repeating n rep times a base sub-laminate of four plies with balanced orientations +α, −α, +β, −β that can be organized in various permutations. Only the [+α/ − α/ + β/ − β] and [+α/ + β/ − α/ − β] permutations are found in the literature: (respectivly found in Vermes et al. (2021) and Shrivastava et al. (2020)). The aim is to determine which permutations of the base sub-laminate are uncoupled in the least number of repetitions. ...
This thesis addresses the challenge of designing lightweight load-bearing space-launcher structures. The objective of the thesis is to develop a method capable of simultaneously optimizing innovative stiffener layouts and composite layups. For this purpose, the bi-level framework for the optimization of composite laminates is taken as basis. In the first-level structural optimization, the local anisotropic material properties of the variable-thickness and variable-stiffness skin of the structure, parametrized by the polar parameters, are simultaneously optimized with the stiffener layout, via a gradient-based algorithm. The optimization of the stiffener layout relies on a component-based topology optimization method developed in this work, that allows to iteratively update a finite-element model of the stiffening structure made of structural elements (beams and shells), without re-meshing. By this process, the global structural stiffness is maximized considering constraints on mass, buckling and force fluxes. In the second level of the framework, laminates realizing the optimized first-level properties are retrieved either by solving an optimization-based identification problem, or analytically by assuming non-conventional stacking sequences (Quasi-Trivial and Double-Doubles). The method is developed and validated on academic test cases, and finally applied to pre-sizing a launcher skirt provided by CNES. Innovative stiffened composite structure concepts are proposed, significantly lighter than the optimized reference metallic design of CNES.
... The design variables can be used in the optimization design of composite materials according to the different laying forms. Meanwhile, the sensitivity-based optimization algorithm [40], the genetic algorithm [41], and the genetic/sensitivity hybrid algorithm [42] can be applied to optimization. Among them, the sensitivity algorithm belongs to a local algorithm. ...
This paper comprehensively reviews the progress of static aeroelastic effect prediction and correction methods for aircraft, including the damage and protection of aeroelastic. It is significantly important to determine the similarity conditions and static aeroelastic scaling modeling in wind tunnel experiments to obtain accurate aerodynamic characteristics. Meanwhile, similar stiffness distribution, manufacturing materials, and processing technology are strongly associated with the simulation of aircraft structural dynamics. The structural layout of the static aeroelastic model, including plate type, beam type, bearing skin type, and full structural similarity type, are described in detail. Furthermore, the wind tunnel and test technique also play an important role in static aeroelastic experiments. It is worth noting that computational fluid dynamics (CFD) and computational structure dynamics (CSD) have attracted increasing attention from researchers for application in aeroelastic analysis of the flow field. The research status and key technologies of aeroelastic numerical simulation of aircraft are introduced in detail. Additionally, this paper briefly introduces the static aeroelastic prediction and correction method, especially the widely practiced K-value method.
... Recently, a new class of laminates, referred to as Double-Double (DD) [Shrivastava et al. (2020)] has been studied for applications to aerospace structures because of the inherent advantages associated with manufacturability, especially thickness tapering and ease of automation. In these laminates, the stacking sequence is dictated by a lay-up that has the form, (θ 1 / − θ 1 /θ 2 / − θ 2 ), where the signs are interchangeable but the angle pairs occur in that order. ...
Robotic manufacturing of composites has revolutionized the aerospace industry. Traditional manufacturing of carbon fiber composite laminates involved manual hand lay-up of resin pre-impregnated sheets (prepregs) of pristine material. Such lay-up used to be cumbersome and time consuming, as well as inefficient. There is no repeatability of parts, and the method produced significant scrap material. The challenge significantly rises as the parts become larger and complex. Robotic Automated Fiber Placement (RAFP) and Automated Tape Laying (ATL) are the two robotic manufacturing techniques for CFRP laminates. While RAFP lays down “tows” of prepreg material, ATL is used for dry layup which shall require a resin infusion before curing. RAFP has started to be widely used in large scale manufacture of aerospace structures. With aircraft like the Boeing 787, Airbus A350-XWB and Airbus A220 having significant percentage of load bearing composite members, it is imperative to resort to faster and repeatable manufacturing techniques. RAFP technology also opens up a design space that was previously not explored in traditional manufacture of laminates. An aircraft structural designer now has the capability to derive optimal fiber paths that could be steered, to be spatially varying based on the applied loads and boundary conditions. While the idea of steered fiber paths have been explored since the early 1990’s, there has been a recent interest in designing parts for optimal structural performance. It is noted that while RAFP has many benefits, the drawback of the technology is manufacturing induced defects like gaps, overlaps and wrinkles of the fiber “courses”, generally called the manufacturing signature (MS). In this work, explicit care has been given to incorporate parameters that drive the manufacturing signatures within the optimization framework, so as to produce realistic, manufacturable structural parts for improved structural performance. Some of the distinctive contributions of this work include- use of parametric curves to model center-lines of individual fiber paths, use of a global manufacturing mesh to reduce the number of optimization variables, explicitly incorporating MS into the finite element framework and including the geometrical changes arising due to compaction during manufacture, and an optimization framework in conjunction with a surrogate model built using machine learning algorithms. Two design problems are studied - a flat plate under uni-axial and bi-axial, in-plane compressive loading, and a flat plate with an elliptical cut-out under in-plane tensile loading. The optimal designs for the uni-axial buckling are manufactured and studied for the manufacturing signatures using non destructive testing, and then subjected to in-plane compression to evaluate the laboratory performance to compare against analytical models. Further,a study on the optimal steered fiber paths is conducted for a rectangular plate with an elliptical cutout. Here the objective is to generate designs that incorporate the manufacturing signature and produce minimum stress concentration.
... The first one is DD ply angles. Compared to LQL, DD laminates greatly simplify the possible stacking sequence [27,39,40]. LQL has four discrete ply angles: 0 • , 90 • , 45 • and -45 • , making this a complicated permutation problem. ...
Current composite design processes go through expensive numerical simulations that can quantitatively describe the detailed complex stress state embedded in the laminate structure. Nevertheless, these processes usually involve many variables derived from traditional legacy QUAD laminates. Furthermore, numerical simulations, such as finite element method, include large computational costs that often push cost-benefit compromises. Here we propose to accelerate the simulation process of composite structures by making predictions using a data-driven strategy and adopting a novel family of composite laminates, named Double-Double, which homogenizes the stacking sequence with fewer plies and only two ply-angles. Multiple machine learning methods are applied to predict the displacement field of a 2D wing-shaped Double-Double composite model under three loading conditions (tension, shear and bending). The results show that ridge regression can make predictions with the highest accuracy of up to 99% and is faster than simulations by three orders of magnitude, also allowing us to efficiently search for the best Double-Double angles. This machine learning methodology can be a starting point for more sophisticated simulation models, such as thermo-mechanical loads, complex structures, other composite families, and above all it can simplify the optimization process of composite structures.
... It is therefore straightforward to have equal strength for the entire structure by making every point in the structure have R 1 or as close to it as possible. Weight savings in the order of 50% by tapering DD laminates were found [7,8]. This is not so with quad, because the sublaminates of quad are too thick and heterogeneous. ...
A new family of composite laminates could revolutionize composite structures to be lighter, stronger, easier to understand and design, and faster and lower cost to manufacture. For the last 60 years, traditional quad laminates (quad) based on collections of 0, ±45, 90 plies have controlled composite laminates. However, restriction to four specific angle orientations has unnecessarily limited design and production. The newly discovered laminate family, called double–double laminates (DD), based on two pairs of angle-plies, can redirect the trend instead toward simplicity and rationality. Advantages enabled by DD include homogenization, tapering to save weight, ply drop placement to improve quality, and card sliding to simplify ply stacking. A switch from quad to DD laminates can bring a renaissance to the composites industry for the production of better airplanes, cars, and other important engineering applications.
... These laminates are composed of plies of two orientations and are defined as [±ϕ/ ± ψ] n or [+ϕ/ + ψ/ − ϕ/ − ψ] n , where n is the number of repetitions. This biangle approach to laminate design results in stronger laminates with higher resistance to micro-cracking and delamination and in other advantages such as faster layup, simpler design and easier tapering through single ply drops (Tsai et al., 2017;Shrivastava et al., 2020). ...
... This will be further commented in Section 3. n is the number of repetitions. This bi-angle approach to laminate design results in stronger laminates with higher resistance to microcracking and delamination and in other advantages such as faster layup, simpler design and easier tapering through single ply drops [35,46]. DD-sublaminate lay-ups can be fully described by two parameters, φ and ψ, which can vary continuously from 0 • to 90 • . ...
This work represents the first step towards the application of machine learning techniques in the prediction of statistical design allowables of composite laminates. Building on data generated analytically, four machine algorithms (XGBoost, Random Forests, Gaussian Processes and Artificial Neural Networks) are used to predict the notched strength of composite laminates and their statistical distribution, associated to the uncertainty related to the material properties and geometrical features. This work focuses not only on the so-called Legacy Quad Laminates (0°/90°/±45°), typically used in the design of composite aerostructures, but also on the newer concept of doubledouble (or double-angle ply) laminates. Very good representations of the design space, translating in low generalization relative errors of around ±10%, and very accurate representations of the distributions of notched strengths around single design points and corresponding B-basis allowables are obtained. All machine learning algorithms, with the exception of the Random Forests, show very good performances, with Gaussian Processes outperforming the others for very small number of data points while Artificial Neural Networks have better performance for larger training sets. This work serves as basis for the prediction of first-ply failure, ultimate strength and failure mode of composite specimens based on non-linear finite element simulations, providing further reduction of the computational time required to virtually obtain the design allowables for composite laminates.
... It is noted that recently, Tsai et al. [36] proposed a concept of double-double laminates which tend to achieve a homogenized structure so that symmetry constraint for conventional layers with quad orientations (-45°, 0°, 45°, 90°) is no longer required. In this way, the laminated structures are able to be tapered easily without warpage issues [37] . Therefore, this proposed topology optimization method is also extended to design of a doubledouble laminated structure to showcase its applicability of a different ply configuration in this study. ...
This study develops a topology optimization approach for design of carbon fiber reinforced plastic (CFRP) laminated components with different failure criteria to reduce the risk of structural failure. The discrete material and thickness optimization (DMTO) method is presented to parameterize the design variables of thickness and orientation of CFRP composites, which is driven by the Method of Moving Asymptote (MMA) algorithm. A large number of local constraints associated with the failure criteria are aggregated with a p-norm function. Analytical sensitivities are derived with respect to the design variables. In this study, a battery hanging structure in electrical vehicle (EV) is exemplified; and a DMTO based design is prototyped and validated through the in-house experimental tests first. To prevent different failure modes, the Hashin, Hoffman and Tsai-Wu failure criteria are then imposed as the design constraints together with manufacturing requirements in the optimization. A comparative study is performed for the design with and without such failure criteria. The results demonstrate that the maximum failure index of the optimized structure with Tsai-Wu failure criterion decreases the most by 40%; and follows by the Hashin and Hoffman criteria by 24% and 33%, respectively. Finally, the CFRP structure is also optimized to design double-double laminates for demonstrating the generality of the proposed method. The study is anticipated to gain in-depth understanding of how the failure criteria would affect the design of fiber reinforced composite structures to ensure structural integrity and reliability.
... OHT failure and the effects of ply blocking in less conventional laminates employing non-standard angle (NSA) with nonorthogonal ply orientations are still largely unexplored. NSA laminates have the potential to decrease manufacturing time, reduce stacking errors and facilitate laminate design selection, in particular in the form of dispersed stacking sequences using double set of double helix [ ± ∕ ± ] (double-double) angles [10][11][12]. In addition, NSA laminates can offer benefits in formability due to increased compatibility in [10/-10/-57/57/-10/10/57/-57/10/-10 2 /10/57/-57/-10/10/-57/57/10/-10] 3 NSA2 ...
The failure strength of carbon-fibre reinforced plastic laminates under open-hole tension varies considerably with ply angle, ply blocking and loading direction. Here, laminates with various standard-angle and non-standard angle stacking sequences are subjected to both on- and off-axis loading in a comprehensive experimental and progressive damage finite element analysis testing campaign. It is found that interlaminar and intralaminar matrix damage can be beneficial when accumulated sub-critically in ply blocks aligned with loading direction, but can also lead to significant strength decreases owing to edge failure. In such cases, a numerical edge treatment is proposed for more accurate representation of open-hole tensile strength in large structures where holes are positioned away from free edges. The solution suppresses edge failure and results in up to 80% strength increases, challenging the validity of standard open-hole tension testing and current design rules for some applications.
... Many studies have already benefited from the use of trace in the mechanics of composite materials, including new laminate concepts [3,4] and structures [5], preliminary design [6][7][8] and optimization [9,10], fast notched strength prediction tools [11], generation of statistical virtual allowables [12] and fracture mechanics [13,14]. ...
Composites design has always been perceived to be complicated, time-consuming and therefore not affordable. With a paradigm shift, it is possible to make composites are as straightforward as metals. Each metal is characterized by two key material properties: its Young’s modulus and strength. The adoption of the Tsai’s modulus as the only stiffness constant characterising any CFRP, and failure strain as the only measure of strength, we can make composite design as straightforward as metals design. Actually, with these two material characteristics, for any CFRP, material, laminate, and strain allowable can all be scaled, just like metals. Another break-through is the replacement of the traditional quad laminates of 0, ±45, 90 by double-double (DD) in [±Φ/±ψ]. This replacement allows to substuture a discrete collection by a continuous field of orientations. A few dozen choices, replaced by hundreds. Indeed, double-double can make structures lighter that quad cannot do, thanks to the Lam-search optimizer, which is able, in combination with Fem tools, to sort, instantaneously, the best DD angles allowing laminates stiffness and strength tailored on specific loading conditions. The bottom line: Tsai’s modulus and double-double are new but are simple conceptually, and Lam-search makes their use practical. In the end, lower weight and lower cost are derived by DD to deliver aggressive taper and 1-axis layup that will be stiff, strong, easy to layup, not prone to error, wrinkle, warpage and delaminatnion.
... It is therefore straightforward to have equal strength for the entire structure by making every point in the structure have R 1 or as close to it as possible. Weight savings in the order of 50% by tapering DD laminates were found [7,8]. This is not so with quad, because the sublaminates of quad are too thick and heterogeneous. ...
Double–Double (DD) laminates, incorporating a repetition of sub-plies featuring two groups of balanced angles, offer broad design flexibility together with the ease of design and manufacturing. In this work, a novel optimization design method is proposed for DD composite laminates based on multi-material topology optimization. First, the uniform multiple laminates interpolation (UMLI) model is proposed to describe the certainty of the stacking direction in multi-layer composite structures, inspired by the interpolation model in multi-material topology
optimization. Specifically, the stiffness matrices of all alternative angle combinations of laminates are interpolated to form virtual laminates. The UMLI model eliminates the need for adding interlayer constraints during the optimization process. Then, the optimization problem is defined
to minimize the compliance of the composite structures and is solved using the gradient-based
optimization algorithm. Finally, the proposed method is applied to the design of the composite stiffened panel, the composite Unmanned Aerial Vehicle (UAV) wing, and the rear fuselage. The results demonstrate that the UMLI model and proposed optimization method have considerable potential in the angle optimization design of multi-layer structures.
This article analyzes the damage tolerance after impact of an unconventional carbon/epoxy laminate (AS4/8552) of the Double-Double (DD) type tested with different impact energies and compares it to a traditional laminate with equivalent properties. Quadriaxial (QUAD) laminate has stacking sequence [0 3 /90/±45] S and the DD equivalent laminate has stacking sequence [0/-55/0/+55] 3T . These materials were subjected to the low velocity impact test (LVI) with three energy levels (30 J, 45 J and 74 J), the uniaxial compression test and the compression after impact (CAI). The objective of this article is to validate whether the proposed DD laminate can be a replacement for the QUAD presented, considering the behavior under impact. In addition to the comparative study, this article also has the objective of evaluating whether it is possible to relate the damage tolerance with the delaminated area, and for this purpose, X-ray computed tomography (CT) was performed, making it possible to measure and locate the damage found in the samples.
Wing ribs, which play a critical role in aviation, are an important design element, especially for unmanned aerial vehicles. Aircraft wing ribs are structural elements that generally extend from the wing root to the tip, used to maintain the shape of the wing, provide aerodynamic stability and add durability to the wing surface. In this study, the wing root rib of the MQ-1B Predator unmanned aerial vehicle were modeled with cavities with different geometric structures and its mechanical behavior were examined. Wing rib structures were created from circular, elliptical, slot and beam geometry gaps. The hybrid structure was created by considering the combined use of Carbon–Kevlar–Aramid. In the hybrid structure, the thickness of each fiber layer was taken into account as 0.25 mm and the wing rib consisted of six layers. The effects of different fiber angles in hybrid composite structures were also examined. As a result of the analyses, equivalent stress (von-Mises stress) and total deformation results were examined.
Double-double (DD) configuration has been proposed as a new concept in which a double set of double helix [±ϕ/± ψ] n angles are stacked up to form a composite laminate. This concept promises significant advantages over conventional layups for composite design optimization and manufacturing. This experimental study evaluated the performance of two elastically in-plane equivalent glass/epoxy laminates suited for wind turbine blade applications: a quadriaxial (Quad) [±45/(0/90) 3 ] s and a double-double (DD) [±15/±75] 4T . Mechanical tests were performed under cyclic uniaxial tensile-tensile load using unnotched and open hole specimens. Delamination initiating from the free edges resulted in premature failure of the unnotched DD specimens. For open hole specimens, fatigue tests results obtained from both stacking sequences showed similar performance. Ultimately, the study presented constitutes a valuable contribution to the understanding of fatigue behavior of double-double glass/epoxy laminates subjected to tensile cyclic loading.
The use of optimization procedures can provide a valuable contribution in optimizing the laminate design of composite components for mass minimization and mechanical performance maximization. Design for weight and strength requirements of composite structures can be efficiently provided with the newly developed double‐double laminates concept, which allows to overcome the conventional 0, 90, and ±45° ply orientations and symmetry requirements in laminates. In the double‐double designed components, composite laminates are made up stacking thin sub‐laminates with four [±Φ, ±Ψ] oriented plies without symmetry requirements. In the present paper, the lay‐up and thickness profile of the composite frames in a fuselage section have been redesigned according to the double‐double design concept taking into account the operating loads. The starting quad configuration has been replaced by an optimized double‐double configuration with suitable lay‐up and thickness profile for each of the frames, while achieving a reduction in the total components mass.
Highlights
Double‐double laminates offer a novel approach to composite laminate design.
Double‐doubles aim to simplify design with composites as with metals.
Laminate optimization performed varying plies orientations and number.
Double‐double design of components optimized with respect to the acting loads.
In aviation double‐doubles allow lightening of composite laminate components.
The successful combination of low weight and high strength is envisaged for an optimised aeronautical structure. The use of composite materials is particularly attractive to meet the required challenging weight saving. Nowadays, the use of these materials is established for many structural components of modern aircrafts, such as the Airbus A380 or the Boeing 787, while their adoption for Unmanned Aerial Vehicles (UAVs), such as drones, which is progressively increasing, especially for civil applications, such as fire prevention, emergency operations, surveillance, and research missions.In this paper, the redesign of an aluminium drone components have been re-performed by using carbon fibre composite materials, with the aim to lighten the overall structure of the drone and to increase its strength. Conventional quasi-isotropic stacking sequence has been considered to study the performance of the structure under operational tensile and torsional loads. Later, a sensitivity analysis has been performed to find a new design configuration with Double-Double laminates [1–4]. The different materials and stacking sequences have been compared to find the best combination between performances and weight.Keywordsdouble-doubledroneUAVscomposite materialsoptimization
A novel family of composite laminates with a simplified stacking sequence and double-double layup [±ϕ/±ψ] n has significant potential to reduce weight and increase strength, while facilitating design optimization and simplifying the manufacturing process. In this study, the low-velocity impact response of a double-double (DD) laminate and a quadriaxial (Quad) laminate of equivalent stiffness and thickness were compared. Carbon/epoxy laminates were produced with stacking sequences of [±0/±50] 10 and [0 3 /90/±45/0 2 /±45] 2S corresponding to double-double and quadriaxial varieties, respectively. Low velocity impact tests were conducted at 74 J of energy and damage areas were examined using X-ray computed tomography. Compressive strength and compression after impact (CAI) strength were equivalent for the two laminates. However, differences in impact damage morphology were observed and are discussed.
The double–double (DD) laminate families that contain two continuous angles, which were proposed by Tsai (“Double–Double: New Family of Composite Laminates,” AIAA Journal, Vol. 59, No. 11, 2021, pp. 4293–4305), opened up a whole new era for composite layups, which are easy to manufacture and design. In the present study, the design space referred to as feasible regions is derived explicitly based on novel formulations for the lamination parameters of DD laminates. This enables the boundaries of the design space to be obtained analytically, providing mathematical support for DD families. The obtained result shows that their design space is larger than that of conventional quadaxial laminates in terms of industrial practices. A homogenization criterion is implemented into the design space, based on which a tailored DD laminate is proposed, expanding design possibilities and enabling homogenization to be achieved using only 16 plies/4 repeats. The work proposed offers significant benefits through practical solutions to making design, manufacturing, and testing simpler and more competitive.
A novel Bayesian optimisation framework is proposed for the design of stronger stacking sequences in composite laminates. The framework is the first to incorporate high-fidelity progressive damage finite element modelling in a data-driven optimisation methodology. Gaussian process regression is used as a surrogate for the finite element model, minimising the number of computationally expensive objective function evaluations. The case of open-hole tensile strength is investigated and used as an example problem, considering typical aerospace design constraints, such as in-plane stiffness, balance of plies and laminate symmetry about the mid-plane. The framework includes a methodology that applies the design constraints without jeopardizing surrogate model performance, ensuring that good feasible solutions are found. Three case studies are conducted, considering standard and non-standard angle laminates, and on-axis and misaligned loading, illustrating the benefits of the optimisation framework and its application as a general tool to efficiently establish aerospace design guidelines.
Traditional lay-ups in laminated composite structural parts have largely focused on using quasi-isotropic laminates made of permutations of 0°,90° and ±45° laminae. These laminates are referred to as legacy quad laminates (LQL). In this study, three different lay-ups of symmetric laminates to compute critical buckling loads under uniaxial in-plane compressive loads is first investigated. An optimization problem is solved to determine the lay-ups that maximize the buckling performance. The resulting laminates are compared against a new class of laminates, referred to as double-double (DD), which have distinctive advantages for thickness tapering and therefore manufacturability. Both, symmetric and unsymmetric DD laminates are studied, while in the latter case, a thermal cure cycle followed by the application of in-plane loads is used to determine the structural performance in compression. To further verify the versatility of DD laminates, biaxial buckling loads are computed for quad, DD and optimized lay-ups. It is concluded that DD laminates, because of their manufacturability advantages, are promising candidates for several aerostructural applications.
An invariant-based design procedure using trace-normalized plane stress stiffness matrix and unit circle failure criterion for carbon fiber reinforced polymer (CFRP) is presented and compared to the traditional design approach. Using the invariant-based design approach, the optimal stiffness-based layup solution is material independent and thus valid for any CFRP. Then, trace of the plane stress stiffness matrix is the only material property needed for strain scaling. Moreover, the unit circle failure criterion is invariant with respect to ply orientation and requires only the unidirectional longitudinal tensile and compressive strains-to-failure, which greatly simplifies testing. In this study, smooth and open-hole plates are evaluated using the traditional design approach and invariant-based design procedures. The results show that the invariant-based design approach greatly simplifies the design procedure of CFRP structural components.
The minimization of weight and maximization of payload is an ever challenging design procedure for air vehicles. The present study has been carried out with an objective to redesign control surface of an advanced all-metallic fighter aircraft. In this study, the structure made up of high strength aluminum, titanium and ferrous alloys has been attempted to replace by carbon fiber composite (CFC) skin, ribs and stiffeners. This study presents an approach towards development of a methodology for optimization of first-ply failure index (FI) in unidirectional fibrous laminates using Genetic-Algorithms (GA) under quasi-static loading. The GAs, by the application of its operators like reproduction, cross-over, mutation and elitist strategy, optimize the ply-orientations in laminates so as to have minimum FI of Tsai-Wu first-ply failure criterion. The GA optimization procedure has been implemented in MATLAB and interfaced with commercial software ABAQUS using python scripting. FI calculations have been carried out in ABAQUS with user material subroutine (UMAT). The GA's application gave reasonably well-optimized ply-orientations combination at a faster convergence rate. However, the final optimized sequence of ply-orientations is obtained by tweaking the sequences given by GA's based on industrial practices and experience, whenever needed. The present study of conversion of an all metallic structure to partial CFC structure has led to 12% of weight reduction. Therefore, the approach proposed here motivates designer to use CFC with a confidence.
This article introduces the concept of stacking sequence table (SST) for the optimal design of laminated composite structures with ply drops. The SST describes the sequence of ply-drops ensuring the transition between a thick guide laminate and a thinner one. A blended design is represented by a SST combined with a thickness distribution over the regions of the structure. An evolutionary algorithm is specialized for SST-based blending optimization. Optimization of the sequence of ply-drops with the proposed algorithm enables satisfying design guidelines that could not have been considered in previous studies. An extensive set of design guidelines representative of the actual industrial requirements is introduced. The method is applied to an 18-panel benchmark problem from the literature with convincing results. In particular, the present results show that strength-related guidelines can be enforced without significantly penalizing the stiffness behavior and consequently the mass of the structure.
A novel invariant-based approach to describe elastic properties and failure of composite plies and laminates is proposed. The approach is based on the trace of the plane stress stiffness matrix as a material property, which can be used to reduce the number of tests and simplify the design of laminates. Omni strain failure envelopes are proposed as the minimum inner failure envelope in strain space, which defines the failure of a given composite material for all ply orientations. The proposed approach is demonstrated using various carbon/epoxy composites and offers radically new scaling to improve design and manufacturing.
The present paper deals with the method of optimum design of laminated composite structures using the finite element method (FEM) and the genetic algorithm (GA) for single-material as well as hybrid laminates. Eight-noded layered elements have been used for 3-D finite element analysis. Weight and cost optimization of Graphite-epoxy/Kevlar-epoxy hybrid composite plate subjected to Tsai-Hill criteria-based design constraint have been carried out. Fiber orientation and material in each lamina, as well as the number of lamina in the laminate have been used as design variables. A multi-objective approach has been used to achieve the optimum design of a laminate for combined weighted cost and weight minimization. The results obtained from the integrated module show that GA with FEM can lead to a global optimal solution for both single as well as multiple objective functions.
The design of laminate layups using a genetic algorithm (GA) search-based function optimizer has been investigated using both a generate-and-test evaluation function and the layup-synthesis rule-base from a knowledge based design system. (The small rule-base from the laminate design was translated into a procedural evaluation function which could be called by the GA.) A simple coding of plies to genes is shown to be applicable in each case, but only when coupled with a penalty function which constrains genetic search to permissible layup candidates. Two experiments have been performed: a comparison of the GA search algorithm with a random/greedy search algorithm and a comparison of the GA with a rule based design system. Comparative tests with the rule based laminate design system are presented for four different load types. These demonstrate the robustness and accuracy of the system for the design of small scale asymmetric laminates.
A multi-objective robust optimization (MORO) of carbon and glass fibre-reinforced hybrid composites under flexural loading based on an a posteriori approach has been presented in this paper. The hybrid composite comprised of T700S carbon/epoxy laminate at the tensile side and E glass/epoxy laminate at the compressive side. The conflicting objectives for optimization were to minimize the cost and weight of the composite subject to the constraint of a minimum specified flexural strength. Fibre angles and thicknesses of each lamina were considered as uncertain but bounded variables with the worst-case analyses being performed as a non-probabilistic method and the effect of uncertainties being determined. A hybrid multi-objective optimization evolutionary algorithm (MOEA) was introduced through modification of an elitist non-dominated sorting genetic algorithm (NSGA-II) and combining it with the fractional factorial design method. The performance of the hybrid algorithm was found to be superior to that of the original version of NSGA-II. The multi-objective robust optimization of the hybrid composite was solved by utilizing the proposed algorithm for several levels of strength with the robust Pareto optimal sets being generated and compared. Three scenarios have been considered to illustrate the applicability of the obtained solutions in an a posteriori decision making process.
As the length of main span of cable-stayed bridge
increases, several technical challenges become more prevalent
with traditional materials. Such technical challenges include:
large axial stresses in main girders, cable sagging effect, and
aerodynamic instability, consequently limiting the prospects
of extending the span length of future cable-stayed bridges
with traditional materials. In order to remedy these issues,
we propose fiber reinforced polymeric (FRP) composites for
the deck and cable system of cable-stayed bridges in combination
with traditional materials. To use FRP composites most
effectively, we developed a genetic algorithm (GA)-based optimization
procedure to solve for the distribution of Glass FRP
and concrete in the hybrid deck system, and the distribution of
carbon FRP and steel in the hybrid cable system. This proposed
optimization-based procedure aimed at developing two
systems: (1) optimized hybrid Glass FRP-concrete deck system
(OHDS), and (2) optimized Carbon FRP-steel cable system
(OHCS), which can maximize static and aerodynamic
performances concurrently. As an example, we utilized an
existing long-span composite cable-stayed bridge and implemented
these two systems. For a typical long span cablestayed
bridge, the results of this benchmark example provide
insights about the typical composition of OHDS and OHCS
and suggest that these two systems can concurrently improve
the static and aerodynamic performances by 33 and 12 %,
respectively
Although composite materials have numerous advantages, some disadvantages, including high manufacturing costs, are relevant. In particular, if the material is applied to large structural components, such as the wings, flaps or fuselage of an airplane, efficient manufacturing processes are required to generate products that are both high quality and cost effective. Therefore, monolithic designs often become integral due to the lower overall part count and simplified designs (e.g. reducing the number of joints and fasteners significantly). For highly integrated monolithic structures, developing a robust manufacturing process to produce high quality structures is a major challenge. An integral structure must conform to the tolerance requirements because those requirements may change. Process-induced deformations may be an important risk factor for these types of structures in the context of the required tolerances, manufacturing costs and process time. Manufacturing process simulations are essential when predicting distortion and residual stresses. This study presents a simulation method for analysing process-induced deformations on the structure of a composite multispar flap. The warpage depends on the thermal expansion and shrinkage of the resin. In this study, a sequentially coupled thermo-mechanical analysis of the process will be used to analyse temperature distribution, curing evolution, distortion and residual stresses of 7.5m long composite part.
An aerodynamic/structural multidisciplinary design with, multiple objectives was carried out for the supersonic fighter wing using response surface methodology. Through a series of static aeroelastic analyses of a variety of candidate wings, the aerodynamic performance and structural strength were calculated. Nine wing and airfoil parameters were chosen for the aerodynamic design variables, and four structural variables were added to determine the wing skin thickness. To consider various flight conditions, multipoint design optimization was performed on the three representative design points. As expected, the single-point design shows the most improved performance on its own design point, but it produces inferior results by not satisfying some constraints on other design points. To improve the performances evenly and moderately at all design points, a multipoint optimal design was conducted. A genetic algorithm was also introduced to control the weight of the multiple objectives. The multipoint designed wing features improved performance and satisfies whole constraints at all design points. It is similar to the real supersonic fighter wing that was developed through numerous wind-tunnel tests and tradeoff studies. The proposed multidisciplinary design optimization framework, could be adopted as an efficient practical design tool for the supersonic fighter wing to fix the basic geometry at a conceptual design stage.
An operationally simple strength criterion for anisotropic materials is developed from a scalar function of two strength tensors. Differing from existing quadratic approximations of failure surfaces, the present theory satisfies the invariant requirements of coordinate transforma tion, treats interaction terms as independent components, takes into account the difference in strengths due to positive and negative stresses, and can be specialized to account for different material symmetries, multi-dimensional space, and multi-axial stresses. The measured off-axis uniaxial and pure shear data are shown to be in good agreement with the predicted values based on the present theory.
In trying to solve multiobjective optimization problems, many traditional methods scalarize the objective vector into a single objective. In those cases, the obtained solution is highly sensitive to the weight vector used in the scalarization process and demands that the user have knowledge about the underlying problem. Moreover, in solving multiobjective problems, designers may be interested in a set of Pareto-optimal points, instead of a single point. Since genetic algorithms (GAs) work with a population of points, it seems natural to use GAs in multiobjective optimization problems to capture a number of solutions simultaneously. Although a vector evaluated GA (VEGA) has been implemented by Schaffer and has been tried to solve a number of multiobjective problems, the algorithm seems to have bias toward some regions. In this paper, we investigate Goldberg's notion of nondominated sorting in GAs along with a niche and speciation method to find multiple Pareto-optimal points simultaneously. The proof-of-principle results obtained on three problems used by Schaffer and others suggest that the proposed method can be extended to higher dimensional and more difficult multiobjective problems. A number of suggestions for extension and application of the algorithm are also discussed.
The present investigation aims at developing a few guidelines for the design of tapered laminated composites. The tapering in laminated composites is introduced by terminating (dropping-off) plies at different locations. The main objective in designing a drop-off is to reduce stress concentration. At present some thumb rules are used to design the drop-off. In this paper, guidelines have been developed by studying the effect of important parameters that determine the strength of the laminate. The numerical study shows that some of the thumb rules used at present are rather conservative and may be relaxed to an extent.
Two-dimensional tests of eight 6-percent-thick symmetrical airfoils of the supersonic and subsonic types were conducted in the Langley rectangular high-speed tunnel. Static pressures along the surfaces of each airfoil were measured over a Mach number range from 0.3 to the choking Mach number (about 0.92 at alpha = 0 deg) at angles of attack from 0 deg to 8 deg. Total-pressure surveys in the wake were obtained for the same Mach number range at angles of attack from 0 deg to 8 deg. Schlieren photographs of the air flow were also obtained for representative conditions. The aerodynamic characteristics of each of the airfoils have been determined from the measured pressure data. These results showed that the lift-curve slope of each of the airfoils decreased rapidly to a positive value approaching zero at angles of attack near 90 and roughly maintained this value up to the highest angle of attack tested. When the maximum thickness was located at the 0.3-chord station rather than at the 0.7-chord station, the circular-arc and wedge-type airfoils produced higher lift-curve slopes and maximum lift coefficients, lower drag coefficients for a given lift coefficient, and improved pitching-moment characteristics. The variations with Mach number of the lift, drag, and pitching-moment coefficients are generally similar for the various types of airfoils tested. There appeared to be no factors which would prohibit the use of the sharp-leading-edge type of profiles at the subsonic speeds tested.
This paper deals with identification of optimal fiber orientations and laminate thicknesses in maximum stiffness and minimum
weight design of laminated composite beams. The structural response is evaluated using beam finite elements which correctly
account for the influence of the fiber orientation and cross section geometry. The resulting finite element matrices are significantly
smaller than those obtained using equivalent finite element models. This modeling approach is therefore an attractive alternative
in computationally intensive applications at the conceptual design stage where the focus is on the global structural response.
An optimization strategy is presented which aims at enabling the use of fiber angles as continuous design variables albeit
the problems may have many local minima. A sequence of closely related problems with an increasing number of design variables
is treated. The design found for a problem in the sequence is projected to generate the starting point for the next problem
in the sequence. Numerical results are presented for cantilever beams with different geometries and load cases. The results
indicate that the devised strategy is well suited for finding optimal fiber orientations and laminate thicknesses in the design
of slender laminated composite structures.
KeywordsCompliance and weight optimization–Beams–Laminated composites
We present a methodology for the multi-objective optimization of laminated composite materials that is based on an integer-coded genetic algorithm. The fiber orientations and fiber volume fractions of the laminae are chosen as the primary optimization variables. Simplified micromechanics equations are used to estimate the stiffnesses and strength of each lamina using the fiber volume fraction and material properties of the matrix and fibers. The lamina stresses for thin composite coupons subjected to force and/or moment resultants are determined using the classical lamination theory and the first-ply failure strength is computed using the Tsai–Wu failure criterion. A multi-objective genetic algorithm is used to obtain Pareto-optimal designs for two model problems having multiple, conflicting, objectives. The objectives of the first model problem are to maximize the load carrying capacity and minimize the mass of a graphite/epoxy laminate that is subjected to biaxial moments. In the second model problem, the objectives are to maximize the axial and hoop rigidities and minimize the mass of a graphite/epoxy cylindrical pressure vessel subject to the constraint that the failure pressure be greater than a prescribed value.
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Composite materials design and testing, unlocking the mystery with invarients
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A unit circle failure criterion for carbon fiber reinforced polymer composites
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Multiobjective optimization of laminated composites plate using a non-dominated sorting genetic algorithm
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