Optimal Laminate Research Articles

Acquiring Optimal Laminate Veneer Preparation by Using Special Software

Acquiring Optimal Laminate Veneer Preparation by Using Special Software

Optimal lamination angles via exact and efficient differentiation of the geometrically nonlinear finite element solution

Laminates allow tailoring the fiber orientations in the layers to obtain the desired mechanical response. The optimal layup design is a challenging task in the case of finite deformations and buckling. For an assigned design, an incremental-iterative finite element analysis is needed to compute the structural response. Gradient-based methods are very often the most efficient optimization tools. Their bottleneck is the gradient evaluation, generally possible only approximately by finite differences. This article shows how to compute the exact gradient of the geometrically nonlinear finite element solution with respect to the stacking sequence. The strategy relies on the implicit differentiation of the nonlinear discrete equations of a control equilibrium point corresponding to an assigned displacement. This provides the load factor gradient by a single fast-solution linear system with the already factorized tangent stiffness matrix, regardless of the number of design variables, and scalar products involving the partial derivatives of the discrete internal force vector, calculated in an exact and efficient way. Several applications demonstrate the efficiency and robustness of the approach.

A novel spectral element method with a higher-order coarse quad meshing approach to design laminated composite panels with arbitrarily shaped cutouts

Laminated panels are widely used in various industries due to their distinct advantages. The design of laminated composites requires efficient methodologies due to the vast design space. This study proposes a new spectral element modeling approach for accurate and computationally efficient analysis of laminated composites with arbitrarily shaped cutouts. The method employs a coarse quad meshing approach and a spectral Chebyshev method to determine the element matrices. The presented method enables obtaining high-fidelity models by applying h- and p-refinements following a non-dimensional approach, aiming to yield a model with the fewest degrees of freedom to achieve a desired convergence level. Benefiting from the advantages of both meshless methods (in terms of computational efficiency) and finite element methods (in terms of geometric capabilities), we performed several case studies for laminated panels with cutouts and it is shown that the presented spectral element method (SEM) enables calculating the natural frequencies and the mode shapes as accurate as FEM, yet decreases the analysis duration by 13 folds. Furthermore, the developed approach was employed with a gradient-based optimizer or genetic algorithm to demonstrate the design of (sandwich) laminated composites for obtaining optimal lamination parameters and 2D Pareto fronts.

Experimental Investigation to Optimize the Manufacturing Parameters of Ankle–Foot Orthoses Using Composite and Titanium Nanoparticles

The optimum structural characteristics of lamination materials used in the fabrication of prosthetic and orthotic parts were investigated in this work. Optimization was chosen based on high yields, ultimate stresses, and bending stress properties. The ideal materials were determined through the use of an RSM (response surface methodology) which considers three factors: Perlon reinforcement, a layer of glass fiber, and the percentage of titanium nanoparticles combined with the matrix laminating resin. The RSM approach suggests thirteen samples by manipulating two variables: the Ti nano percentage and the number of Perlon layers. Laminating materials, defined by RSM methods and treated with a vacuum system, were submitted to a series of tests. The ideal lamination material was compared with the laminations from the initial study through the use of tensile, flexural, and fatigue testing according to ASTM standards. Tests carried out using version 10.0.2 of Design Expert software showed that, compared with the 12 other laminations, the one with 10 Perlon layers and 0.75 percent Ti nano had the highest overall yield and ultimate and bending loads. Fatigue eventually showed that stamina tension constraints were applied for optimal lamination, compared to ten Perlon lamination layers. We additionally tested the fatigue life of the best material and compared it with the available materials used at prosthetics and orthotics centers.

Elastic buckling analysis and optimization of thin-walled bamboo-like pipe beam subjected to pure bending

In this paper, a stiffening design imitating the bamboo node is proposed for weight reduction of the long composite pipe beam subjected to bending load. The distribution of bamboo nodes can efficiently suppress the ovalization of the section, thus significantly improving the bending resistance of the bamboo. Based on this principle, ring stiffeners are proposed to be fixed to the pipe beam, making the long beam equivalent to the combination of a series of short pipes that suffered less section ovalization. A database of the optimal laminate orientations for different normalized lengths is obtained through optimizations, where the discreteness of the ply count is considered. Based on this database, weight optimizations are conducted, and the optimal designs of beams with and without stiffeners are obtained and compared. The comparison results show that the proposed bamboo-like stiffened beam not only regains a near-linear load–displacement relationship, but also reduces the weight by up to 16% under the same buckling load. In addition, it is found that for the pipe beams with radius-to-thickness ratios of more than 18, increasing the radius leads to a decrease in elastic buckling resistance when the weight remains a constant, which is opposite to the design for strength and stiffness. The model and database developed in this paper can provide a reference for weight reduction design and weight estimation for composite pipe beams.

Towards composite suspension control arm: Conceptual design, structural analysis, laminate optimization, manufacturing, and experimental testing

The automotive industry needs composite materials to decrease the weight of new-generation vehicles whilst increasing their strength. In this study, one of the critical (load bearing) components of automobiles, i.e., the suspension control arm made of steel, is fully redesigned for its suitable manufacturing using composite materials. To this end, innovative mechanical simulation methods are developed and coupled to perform the design, analysis, and optimization of the automotive suspension control arm. The main design/optimization criteria are set to reduce no less than 75% weight of the metal control arm and increase its safety by at least 60% by using composite materials and a new geometry suitable for mass production. To predict the deformation-stress state of the control arm, a four-node quadrilateral shell element is implemented based on the kinematics of refined zigzag theory (RZT). Once verified numerically, the computer implementation of the RZT is combined with the optimization algorithm to achieve the optimum laminate stacking sequence of the control arm. Accordingly, prototypes of the composite control arms with optimum lamination plans are manufactured and then experimentally tested under the loading and constraint conditions defined at the conceptual design stage. The numerical and full-scale experimental results are compared, and the RZT models are comprehensively validated. Hence, the advantages of the overarching design-analysis-optimization strategy presented herein are revealed for redesigning and manufacturing automobile parts from composite materials.

Out-of-autoclave molding of carbon fiber laminates by consolidation with shape memory polymer foams

Carbon fiber reinforced (CFR) laminates have been manufactured by an innovative out-of-autoclave (OOA) process thanks to the use of smart materials. In this study, for the first time, a shape memory polymer (SMP) foam has been used into a pressure dome to apply the consolidation pressure to the laminate. Heat for resin curing was supplied by a thermal blanket between the laminate and the SMP foam. In order to test the OOA molding process, 24-ply CFR laminates were manufactured and tested. For comparison and reference, CFR laminates were also molded by traditional vacuum bagging and autoclave curing. Samples for bending tests were extracted from OOA and autoclave molded plates. Results show that the SMP-OOA process is able to provide optimal laminate consolidation, despite of the low applied pressure (about 1 bar). A comparable density and ply thickness was measured on samples by the innovative and the conventional molding process, whereas a higher bending strength (+5%) was found on OOA samples. A higher dispersion was also observed for the properties of SMP-OOA molded laminates in comparison with autoclave, probably due to the prototyping nature of the molding technique in comparison with the well-known autoclave practice. Nevertheless, the final quality of the molded laminates is very high, and the SMP-OOA process is a very promising candidate as a technology to repair CFR structures.

Minimum weight design of CNT/fiber reinforced laminates subject to a frequency constraint by optimal distribution of reinforcements across the thickness

Present work involves minimization of the weight of a three-phase, glass and carbon nanotubes (CNT) reinforced angle-ply laminate, subject to a fundamental frequency constraint. Design variables include the optimal (nonuniform) distributions of the fibers and the CNTs across the laminate thickness, the stacking sequence, ply angles and ply thicknesses. In order to assess the effect of different design variables on weight minimization, a sequence of five different optimization problems is solved with an increasing number of design variables. The present approach has the advantage of comparing and assessing the effectiveness of different sets of design variables on the design efficiency and identifying the ones which are more effective in minimizing the weight. Design efficiency is defined as the ratio of the weight of the optimal laminate to the weight of a plate which is not reinforced, but subject to the same frequency constraint. It is observed that fiber and CNT reinforcements are used most effectively if placed close to or in the outer layers. It is also observed that CNT reinforcement affects the optimal values of the ply angles due to the fact that the directional properties of the fibers become less pronounced as the matrix is reinforced by CNTs.

Multi-objective optimization of snap-through instability of helicoidal composite imperfect beams using Bernstein polynomials method

This paper deals with the multi-objective optimization problems of snap-through instability of geometrically imperfect simply supported helicoidal composite beam with nonlinear orientation schemes. The objective function is to maximize the load required to initiate snap-through and minimize the instability region. It is assumed that the curved bioinspired beam is embedded on nonlinear elastic foundation and is subjected to different types of lateral loads. The presented formulation is based on Euler-Bernoulli theory, nonlinear higher order strain, and imperfect curvature. Bernstein polynomials (BPs) method is employed to solve the nonlinear nonhomogeneous fourth order integro-differential governing equation. Developed model can considered the effect of imperfection, lamination scheme, and elastic foundation on the nonlinear deflection and snap-through behaviors of helicoidal composite structures. Analytical closed form formula of the nonlinear load-deflection relationship is developed. The analytical relation is validated by comparing it with exact solution and numerical results available in literature. Multi-objective particle swarm optimization (MOPSO) algorithm is employed to determine Pareto-optimal set for limiting load and region of instability. In these analyses, optimal lamination parameter, amplitude of imperfection and elastic foundation constants are found for helicoidal composite beam, and the results are presented as 2D Pareto-optimal design points.

Static Aeroelastic Optimization of High-Aspect-Ratio Composite Aircraft Wings via Surrogate Modeling

The race towards cleaner and more efficient commercial aviation demands novel designs featuring improved aerodynamic and structural characteristics, the main pillars that drive aircraft efficiency. Among the many proposed and introduced, the increase in the aspect ratio of the wings enables greater fuel efficiency by reducing induced drag. Nevertheless, such structures are characterised by elevated flexibility, aggravating static and dynamic aeroelastic phenomena. Consequently, the preliminary and conceptual design and optimization stages using high-fidelity numerical tools is rendered extremely intricate and prohibitive in terms of computational cost. Low-fidelity tools, contrastingly, enable computational-burden alleviation. In our approach, a computational framework for the low-fidelity steady-state static aeroelastic optimization of a composite high-aspect-ratio commercial aircraft wing via surrogate modelling is proposed. The methodology starts with the development of the 3D panel method as well of the elements of the surrogate model. The design variables, objective function and constraints which formulate the optimization problem are then provided. Moreover, comparison against rigid aerodynamics indicate the significant load-alleviation capabilities of the present case study. The effect of structural nonlinearities is also explored. The optimization framework is executed and optimal laminates for the structural members are obtained. The optimal structure was deemed critical in panel buckling.

An aeroelastic optimisation framework for manufacturable variable stiffness composite wings including critical gust loads

This work presents a new aeroelastic optimisation framework for the preliminary design of variable stiffness composite wing structures. The framework is constructed by sequentially and iteratively solving two sub-problems: aeroelastic tailoring and lay-up retrieval, using gradient-based algorithms with full-analytical sensitivities provided. During aeroelastic tailoring, the wing mass is minimised by optimising the lamination parameters and thickness of wing laminates together with wing jig twist distribution. The load cases cover not only static loads, but also the critical gust loads that are identified across the entire flight envelop at every iteration of optimisation. Further, a cruise shape constraint is included in addition to other aerostructural constraints, so that the optimal aircraft performance can be ensured. During lay-up retrieval, the manufacturable stacking sequence is retrieved according to the optimal lamination parameters with the consideration of minimal steering radius constraint. Moreover, to fix the possible constraint violations caused by lay-up retrieval, a correction strategy is incorporated to tighten the violated constraints for repeating aeroelastic tailoring. Finally, several case studies on the design of NASA common research model wing are carried out and investigated. The results indicate that the critical gust loads and cruise shape constraint have a large influence on the design of tow-steered composite wing structures, which therefore demonstrate the usefulness and benefits of the proposed optimisation framework.

열영향을 받는 하이브리드 원통형 적층복합재의 최적화

In this study, a hybrid laminated composite comprising carbon/epoxy (C/E) and glass/epoxy(Gl/E) laminates was optimized. The optimal lamination angle must be calculated in the design of a cylindrical laminated composite that is subjected to both bending and torsion under a thermal stress environment. Generally, the composite material does not simply cause fracture owing to a stress component but exhibits fracture behavior according to the fracture theory owing to the combination of various stress components. The lamination angles of the hybrid cylindrical laminated composite were optimized using the four failure theories of Tsai-Wu, Tsai-Hill, Hoffman, and Hasin as the design criteria. The effect of thermal stress on the lamination angle was confirmed by comparatively examining the optimization results of the case where thermal stress was applied and the case where thermal stress did not act.

Optimal magnetoelectric coupling performance of Terfenol-D/PZT composites in resonance state under bias magnetic field

Laminated magnetoelectric (ME) composites with various thickness ratios were optimized, fabricated and experimentally investigated in this work. The Terfenal-D/PZT specimens with optimal thickness ratio between the magnetostrictive phase and piezoelectric phase, and two other values were tested for their ME coupling performance. The coupling voltage output increases linearly with the increase of DC bias magnetic field. The ME voltage coefficient increases more than 100 times in the resonance state for the optimal laminate. The DC bias magnetic field affects the ME voltage coefficient significantly, and also has little effect on the resonant frequency. The strength of AC magnetic field also slightly affects the ME voltage coefficient in resonance state, but does not affect the resonant state under which the same DC magnetic field is required. The experimental results can help understand the coupling performance of ME composite under bias magnetic field and prompt the application of ME devices.

The thermal-mechanical buckling and postbuckling design of composite laminated plate using a ROM-driven optimization method

The high temperature environment makes the buckling of composite laminated plate happen earlier. Further weight savings can be achieved once the plate has a favorable postbuckling stiffness. This study aims to address this issue by developing a ROM-driven lamination optimization to maximize the buckling and postbuckling performance of compressed plates under initial temperature field. The reduced-order model(ROM) constructed using the improved Koiter theory is reformulated to be suitable for thermal-mechanical buckling problems. A linear subspace of the force space is represented to be the span of the mechanical load, the thermal load and a set of predefined perturbation loads. The thermal load related to the initial temperature field is constant during the increase of in-plane compressive load. An independently additional degree of freedom corresponding to the thermal load is implemented into the construction of the reduced-order model. The buckling and postbuckling performance can be extracted from the solution of reduced-order model, and then subsequently selected as inputs to achieve the optimal laminate. The main novelty of this work is to achieve the thermal-mechanical buckling and postbuckling optimization, benefitting from the highly efficient single run of thermoelastic geometrically nonlinear analysis. Various numerical examples have been selected to validate the performance of the proposed method, considering the influences of length-to-width ratio, α 1/α 2, ply number and nonuniform temperature field.

Maximizing buckling load of elliptical composite cylinders using lamination parameters

Structural members made of fiber-reinforced polymers (FRP) attract increasing attention in the development of novel architectural systems that challenge the standard design methodologies. Cylindrical surfaces constitute one of the typical geometric sets obtained with the FRP component fabrication. This paper explores the influences of two geometric parameters on the buckling performance of elliptical cylinders: inverse slenderness (ratio of minimum diameter to height) and eccentricity (ratio of radii along semi-axes). The overall stiffness properties are defined using lamination parameters. This analysis method eliminates the dependency of optimal solutions on the initial assumptions regarding the laminate configuration, which needs to be explicitly described in multi-layer modeling. Finite element analyses are utilized to compute buckling loads of the cylinders under axial compression force and bi-axial bending moments. The optimal lamination parameters and buckling stresses are determined for various parameters, and the lamination parameters corresponding to the optimal and simple [±45°] angle-ply design points are presented in the lamination parameter plane via Miki's diagram. The results reveal the level of performance that can be achieved by a specific geometry and provide guidelines for the optimal design of elliptical laminated cylinders against buckling.

Multi-objective optimization of composite sandwich panels using lamination parameters and spectral Chebyshev method

Composite materials are widely used in various industries because of their distinct properties. Hybridization is an efficient way of designing composite panels to decrease the cost and/or weight while maintaining stiffness properties. In this study, an accurate and efficient framework is developed to optimize laminated sandwich panels composed of high-stiffness face sheets and low-stiffness core. The stiffness properties of face sheets and core are represented using lamination parameters. The governing equations are derived following first-order shear deformation theory and solved using the spectral Chebyshev approach. In multi-objective optimization problems, genetic algorithm is used to determine Pareto-optimal solutions for fundamental frequency, frequency gap, buckling load, and cost metrics. In these analyses, optimal lamination parameters and thickness are found for face-sheets and core of sandwich panels, and the results are presented as 2D and 3D Pareto-optimal design points. When the individual performance metrics lead to different optimum points, a scattering behavior is observed in the 3D Pareto sets whose boundaries are defined by the 2-objective Pareto fronts. The results provide insights into the design requirements for improving the dynamic and load-carrying behavior of sandwich laminates while minimizing the cost that presents the usability of the presented approach in the multi-objective optimization.

Thermal Aeroelastic Tailoring for Laminated Panel with Lamination Parameters and JAYA Algorithm

This work investigates thermal aeroelastic tailoring of a laminated composite panel with a lamination parameter-based method. Equivalent membrane and bending coefficients of thermal expansions for symmetric laminated panel are derived and represented with lamination parameters using Classical Laminated Plate Theory. The relationship between thermal flutter behavior and lamination parameters is examined. The optimization process is split into two stages. In the first stage, lamination parameters and laminate thicknesses are as design variables to minimize the structure mass, subject to thermal flutter behavior and feasible region constraints of lamination parameters. In the second-stage, instead of using conventional genetic algorithm, the enhanced JAYA method is extended to search the laminate configuration to target the optimal lamination parameters. The effectiveness of the presented method is demonstrated through a thermal aeroelastic tailoring problem.

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.

Design of variable stiffness composites for maximum fundamental frequency considering manufacturing constraints of tow steering

In this study, an in-house finite element approach is developed to optimize fundamental frequency of variable stiffness composites considering manufacturing constraints of tow steering process. The method uses the lamination parameters as the design variables. Tow angles or fiber angles and their stacking sequence are computed from the optimum lamination parameters by direct search method. The Least-Squares and Continuity (LSC) method is applied to maintain the fiber or tow continuity within a prescribed curvature limit for manufacturability. Finally the discrete fiber angles or tow directions were converted into paths by using stream functions to have continuous manufacturable paths. The results of the method were compared to various literature findings for constant, balanced variable, and general variable stiffness designs for different boundary conditions, aspect ratios, and material properties. The optimum lamination parameter distributions were in good agreement with literature findings. The fundamental frequency improvements up to 11.9% and 10.2% were computed by the LSC method with respect to the optimum constant stiffness results for fully simply-supported and fully clamped cases, respectively.

Boosting Mechanical Properties of Orthoses - Foot Ankle by Adding Carbon Nanotube Particles

In this process, optimum laminating properties were used in producing prosthesis and orthoses were researched and selected based on high yield, ultimate stresses, stresses of bending and fatigue properties. The process of the optimal selection is the Response Surface Methodology (RSM), which has been used to reach two parameters: reinforcement perlon fiber and percent of multi-strand carbon MWCNT nanotube combined with the matrix resin. The response surface methodology is a combination of mathematician and statistic techniques which are used for experimental model building and analysis of problems. This technique revealed 13 separate laminations samples with a percentage of separate Perlon layers No. and MWCNT Wt %. Tests were conducted for all lamination materials as defined in RSM methods and rendered by vacuum system, including fatigue tests for the ideal laminating material as opposed to laminations developed in the prior study (three Tensile test, Bending test and Fatigue tests according to the ASTM D638 and D790 respectively). Tests from the system version 10.0.2 of Design Expert found lamination (10 perlon layers and 0.75% of MWCNTs) to be the best according to overall yield, ultimate and bending loads in the 12 other laminations. Fatigue eventually revealed that constraints were applied to the stamina tension (2,66, 1,66) for optimum lamination, relative to ten perlon lamination layers and 424 lamination respectively.