Design Of Aerospace Structures Research Articles

Concurrent multi-scale design optimization of fiber-reinforced composite material based on an adaptive normal distribution fiber optimization scheme for minimum structural compliance and additive manufacturing

Structural lightweight is a core technical requirement for the structural design of aerospace and new energy power equipment structures. For multi-scale variable stiffness design optimization of discrete fiber-reinforced composite laminates, one of the challenges is how to avoid the explosion of design variable combinations caused by the increase in the number of candidate discrete fiber laying angles. The Normal Distribution Fiber Optimization (NDFO) interpolation scheme has the numerical advantage that the number of design variables does not increase with an increase in the number of candidate discrete fiber laying angles. However, the traditional NDFO interpolation scheme uses uniform penalty parameters across all elements, which means that normalizing the penalty parameters for all the elements ignores the convergence differences of discrete fiber laying angles in different elements within the macro-scale structure topology. This leads to time-consuming and unstable optimization iteration of the macro-scale structural topology and micro-scale discrete fiber laying angle selection. Especially, it easily causes the micro-scale discrete fiber laying angle selection to fall into the local optimum prematurely. Therefore, considering the difficulties and challenges of the traditional NDFO interpolation scheme in the multi-scale variable stiffness design optimization of fiber-reinforced composites. This paper proposes an Adaptive Normal Distribution Fiber Optimization (ANDFO) interpolation scheme, and the feedback mechanism of the convergence rate of the element design variable and the objective function is introduced to achieve the adaptive reduction of the penalty parameters. Based on the proposed ANDFO interpolation scheme, a multi-scale design optimization model of fiber-reinforced composite laminates is established, considering the macro-scale structure topology and micro-scale discrete fiber laying angel selection. The explicit sensitivity of the objective function of minimizing structural compliance to the macro-scale topological design variables and the micro-scale fiber laying angle design variables is derived. Considering the manufacturability of additive manufacturing based on the optimized design results, a multi-scale nonlinear continuous filtering strategy for discrete fiber laying angle is adopted to improve the continuity of the local fiber laying path. Numerical examples systematically present the coupling effects of macro-scale structural topology and micro-scale fiber laying path, multi-scale nonlinear discrete fiber continuous filtering laying path structure, and continuous fiber additive manufacturing multi-scale optimized structure. The proposed ANDFO scheme provides a new theoretical and methodological approach for the lightweight and integrated multi-scale design and manufacturing of fiber-reinforced composite laminates through additive manufacturing technology.

Optimization of Composite Wheel Fender for Manned Lunar Vehicle

Abstract Weight reduction is the eternal theme of aerospace optimization. In the process of weight reduction, the main ways are material change, structural change, and processing method change. In the process of aerospace structure design, the boundary and load conditions are more complicated, which restricts the development of optimization technology in the aerospace field to some extent. At present, the research object of optimization technology in the aerospace field is mainly the large parts of the aerospace craft, and the structural optimization of small aerospace parts is rarely involved. Therefore, the research of structural optimization design method has important theoretical and engineering significance. A complete optimization design process is proposed, the structural performance of aviation products is simulated by finite element software, and the feasibility of the optimization theory is verified. This article mainly compares several schemes for weight reduction design of composite material wheel fenders in the process of design.

Free vibration and supersonic flutter analyses of a sandwich cylindrical shell with CNT-reinforced honeycomb core integrated with piezoelectric layers

In this research, the free vibration and supersonic flutter analyses of a cylindrical sandwich shell with a reinforced honeycomb core (RHC) integrated with piezoelectric face sheets are investigated. The core is a honeycomb structure enriched with fibers and carbon nanotubes (CNTs). The layers of the shell are modeled based on the Cooper-Naghdi shell theory and the continuity conditions between the layers are considered. The aerodynamic pressure of the supersonic flow is modeled using the linear piston theory. Hamilton’s principle is used to derive the governing equations. A semi-analytical solution is presented including an exact solution in the circumferential direction followed by a numerical solution in the longitudinal direction via the differential quadrature method (DQM). The effects of several parameters on the frequencies, the corresponding damping coefficients, and the critical aerodynamic pressure are investigated. It is concluded that improving the stiffness of the honeycomb core with the CNTs does not necessarily improve the aeroelastic stability of the shell. The presented results can be used in the design and analysis of aerospace structures.

Damage detection of Kevlar woven fabric using optical fiber multimode interferometer

Kevlar woven fabric is crucial for the lightweight design of aerospace structures due to its unique advantages. However, it is susceptible to damage during operation, making effective damage detection essential for ensuring structural reliability. Nevertheless, conventional sensors used for damage detection have limitations such as complex manufacturing processes and weight. To address this issue, this paper proposed a simple singlemode-multimode-singlemode (SMS) optical fiber sensor to collect vibration signals and construct a damage recognition model based on natural frequency in order to identify the size of damages in Kevlar woven fabrics. To achieve a highly linear and accurate sensor, a length determination criterion for multimode optical fiber segments based on quasi-image, notch, and transmission spectrum loss was proposed. An optical sensor was fabricated based on this criterion. The feasibility and sensitivity of the sensor for vibration signal measurement were verified by constructing a vibration signal measurement device. An experimental study was conducted to detect damage in Kevlar tapes, where the natural frequency changes measured by the SMS sensor were integrated with an optimized multi-variable gray model for damage size detection. The experimental results indicate that the estimated error in damage size is 0.71%. The damage identification system proposed in this paper offers a simple and cost-effective solution for measuring damage in flexible structures using fiber optic sensors.

Adaptive-Quadratic-Neural-Network-Based Multifidelity Modeling Approach for Buckling of Stiffened Panels

This paper presents a method for predicting the buckling load of stiffened panels using multifidelity modeling based on quadratic neural networks (QNNs) with adaptive activation functions. The effectiveness of the proposed approach is demonstrated through a series of simulations on a range of stiffened panel configurations, and the results are compared to those obtained from traditional multifidelity and high-fidelity models in terms of accuracy and computational efficiency. Numerical experiments demonstrate that the model can accurately and efficiently predict the buckling load of stiffened panels while significantly reducing the computational cost of evaluating the surrogate model. In particular, the proposed adaptive quadratic neural networks (AQNNs) model achieves convergence approximately three times faster and four times less trainable parameters compared to traditional artificial neural networks while maintaining the same validation loss. This approach can significantly improve the design and optimization of aerospace structures by easily and quickly exploring various design configurations and finding stable and efficient configurations. This study highlights the potential of a new multifidelity modeling framework for predicting the buckling load and collapse load of aerospace structures by enhancing convergence speed and prediction accuracy while reducing the computational complexity of neural networks.

Scaler nonlinear continuum damage models for ceramic matrix composites with and without in plane ply anisotropy at room temperature

Damage tolerant design of aerospace structures with continuous fiber reinforced ceramic matrix composites (CMCs) require progressive damage models that can predict the behavior at local stress concentrations. Here we introduce three versions of a continuum damage model including a two-variable damage model that considers damage formulation perpendicular and in line with the direction of the primary fiber reinforcement, a coupled two-variable damage model and a four-variable damage model that includes the previously mentioned modes along with two additional modes specific to shear damage. The model is demonstrated using data for two different SiC/SiC CMCs including one that consists of stacks of balanced woven plies and one that consists of stacks of unidirectional laminate-based plies. The behavior is well captured for the balanced woven ply-based materials, but required a more complex damage formulation to close the solution for the unidirectional based plies that exhibited a significant degree of anisotropy.

Experimental study on the influence of welding structure details of TC4 titanium alloy under thermo-vibration coupling environment on vibration fatigue life

The widespread application of titanium alloy materials in aerospace structural design makes them susceptible to thermo-vibration coupling fatigue failure in harsh vibration and thermal environments. Vibration fatigue issues significantly affect the safety and operational reliability of aircraft. In order to obtain optimal design details for titanium alloy welding structures under thermo-vibration coupling conditions, experimental specimens with different structural details of TC4 titanium alloy welding structures were designed to simulate actual structural designs. The structural details included skin with U-shaped supports at different angles, skin with L-shaped supports, and skin with T-shaped supports. A thermo-vibration coupling vibration fatigue test system was established, and vibration fatigue tests were conducted at a temperature of 150°C. All structural fatigue crack failures occurred at the welds. The experimental results were statistically analysed, and using the Chauvinet criterion, abnormal data points were removed. The influence of structural details on vibration fatigue life was determined through F-tests. It was found that for the skin with a U-shaped support structure, a support angle of 90° resulted in a longer vibration fatigue life. When comparing skin with T-shaped support and skin with L-shaped support structures, the T-shaped support structure exhibited a longer vibration fatigue life. Among the three structural types, the skin with a T-shaped support structure has the longest vibration fatigue life. These experimental conclusions serve as important references for the design of thin-walled structures in aircraft structural design.

Design, simulation, and additive manufacturing performance of three lightweight FBG acceleration sensors

Low-weight, high-performance accelerometers are sought-after objectives in aerospace structural design. This paper presents three design schemes for lightweight FBG accelerometers: lattice-based (FBGL), reinforced (FBGR), and lattice-reinforced (FBGL-R) accelerometers. The influence of the design’s filling factor ( F d ) on the first-order frequency and sensitivity in three directions of the accelerometers is investigated. Additionally, the Additive Manufacturing (AM) performance of the designed accelerometers is explored and compared with the original model. The results demonstrate that the first-order natural frequencies of the three design models decrease linearly with increasing F d , with FBGL-R exhibiting a larger adjustable range of low-frequency response under the same mass. FBGL shows the greatest sensitivity variation with F d in all three directions, while FBGR exhibits the least sensitivity variation. Under the same mass fraction, FBGR demonstrates higher sensitivities in all three directions, with FBGL-R's performance falling between the other two designs. AM simulations indicate that the porous structures can reduce the deformation amplitude during the AM of FBG accelerometers. FBGL, FBGR, and FBGL-R exhibit approximately 7% lower deformations compared to the original sensor. The deformation distribution is similar among the four models, with larger residual deformations occurring at the outer edges of the components, while differences in deformation distribution exist within the porous regions.

Acoustic vibration analysis of high-temperature thin-walled structures

Advanced aerospace structures are subjected to extremely harsh working environment, including of mechanical, acoustic, thermal, and aerodynamic loads. These combined loads can make the structures exhibit complex response, which has already attracted increasing concern in the design of advanced aerospace structures. To tackle the problem, a finite element model (FEM) by discretizing the theoretical differential equation is established to calculate the dynamic response of thin-walled structures under combined thermal and acoustic loads. The numerical analysis indicates that three types of nonlinear responses of the thin plate under combined thermal-acoustic loads are obtained, and the mechanism of snap-through is revealed through two ways: thermal buckling analysis and thermal modal analysis. which can be used to explain the nonlinear response characteristics.

Analyzing the backbone curve of piecewise-linear non-smooth systems using a generalized bilinear frequency approximation method

Estimating the resonant frequency of non-smooth systems with contacting elements is critical for the design, control, and health monitoring of various mechanical and aerospace structures. The nonlinearity caused by the intermittent contact excludes the use of efficient linear methods; hence, predicting vibration characteristics of these systems becomes computationally challenging. Furthermore, several numerical and analytical approaches that have been developed for analyzing smooth nonlinear systems cannot be applied to analyze non-smooth oscillators. To understand the dynamic properties of non-smooth dynamical systems, the bilinear frequency approximation (BFA) method, a classical analytical tool, was developed to estimate the nonlinear natural frequency of bilinear oscillators by using the linear characteristics of underlying linear subsystems to construct a closed-form analytical solution. However, the traditional BFA method is only applicable to systems in which the gap size between the contacting element is zero, which limits the capability of this efficient analytical technique. In this paper, a generalized BFA method is proposed to extend the capability of the method to capture the nonlinear natural frequency of high-dimensional non-smooth systems where either gaps or prestress exist. The generalized BFA method employs the natural frequencies, mode shapes, and modal amplitudes of the linear subsystems as well as the gap size at the contacting degrees of freedom (DOF) to estimate the nonlinear natural frequencies at different amplitude levels. The backbone curve of non-smooth oscillators can be efficiently constructed using the proposed analytical method. The generalized BFA method is demonstrated on a single-DOF system, a three-DOF system, and a finite element model (FEM) of a cantilever plate with contacting elements. The results show that the proposed method provides an accurate approximation of the backbone curve for the first resonance, which has the most dominant vibration response, with very low computational effort, but a rather poor approximation for higher resonances. The proposed technique can be integrated with high-dimensional FEMs to analyze the nonlinear resonance of complex structures. The performance of the method is validated both numerically and experimentally in this work.

Investigation into tensile behavior of 3D printed nylon-based low and high-volume fraction carbon fiber composite

PurposeThe tensile behavior of additively manufactured nylon-based carbon fiber-reinforced composites (CFRP) is an important criterion in aerospace and automobile structural design. So, this study aims to evaluate and validate the tensile stiffness of printed CFRP composites (low- and high-volume fraction fiber) using the volume average stiffness (VAS) model in consonance with experimental results. In specific, the tensile characterization of printed laminate composites is studied under the influence of raster orientations and process-induced defects.Design/methodology/approachCFRP composite laminates of low- and high-volume fraction carbon fiber of different raster orientations (0°, ± 45° and 0/90°) were fabricated using the continuous fiber 3D printing technique, and tensile characteristics of laminates were done on a universal testing machine with the crosshead speed of 2 mm/min. The induced fracture surface of laminates due to tensile load was examined using the scanning electron microscopy technique.FindingsThe VAS model can predict the tensile stiffness of printed CFRP composites with different raster orientations at an average prediction error of 5.94% and 10.58% for low- and high-volume fiber fractions, respectively. The unidirectional CFRP laminate composite with a high-volume fraction (50%) of carbon fiber showed 50.79% more tensile stiffness and 63.12% more tensile strength than the low-volume fraction (26%) unidirectional composite. Fiber pullout, fiber fracture and ply delamination are the major failure appearances observed in fracture surfaces of laminates under tensile load using scanning electron microscopy.Originality/valueThis investigation demonstrates the novel methodology to study specific tensile characteristics of low- and high-volume fraction 3D printed CFRP composite.

Isogeometric-based mapping modeling and buckling analysis of stiffened panels

Modeling and analysis of stiffened panels are two key technologies in the design of aerospace thin-walled structures. For the stiffened panels with complex geometry, classical finite element analysis (FEA) and conventional isogeometric analysis (IGA) based on explicit geometry usually require time-consuming and labor-intensive geometric processing, and additional coupling matrices to be ready for analysis. In this study, a new method for modeling and buckling analysis of stiffened panels is proposed, which provides a more efficient and simpler way. During the modeling process, the stiffeners are treated as curves on surfaces, which is not explicitly defined using the control-point-based representation of curves, but implicitly defined using parameter curves in the parametric space of the surface. Mapping modeling provides more accurate geometric description and transfer the complex modeling problems (three-dimensional space) of stiffeners on free-form surface into simple modeling problems in the regular parametric space (two-dimensional space). During the buckling analysis process, a new mapped stiffener element based on mapping modeling is proposed, which can model the section of the eccentric stiffener without changing the geometry. The precise normal information of the Non-Uniform Rational B-Splines (NURBS) surface can ensure that the stiffeners are perpendicular to the skin. In addition, the coupling of the stiffener and the skin is automatic, without any additional coupling matrix. This buckling analysis framework realizes the complete integration of modeling and analysis. Furthermore, for the stiffened panels with cutouts, the trimmed surface analysis (TSA) method is extended to be used for the numerical integration of the trimmed stiffeners, which means that no additional geometric process is required. Finally, four numerical examples of different types of stiffened panels are constructed, involving metal, trimmed surface, classical grid-stiffener, free-form surface, variable-stiffness composites, and curvilinear grid-stiffener. Several numerical examples of static and buckling analysis of stiffened panels with high fidelity demonstrate the effectiveness of the proposed framework.

A NURBS-based degenerated stiffener element for isogeometric static and buckling analysis

Complex shells and curvilinear stiffeners are promising for the lightweight design of aerospace structures. Along with the increasing of structural size and geometric characteristics, traditional finite element analysis (FEA) requires fine grids to content the analysis accuracy, which is extremely time-consuming. In this study, a novel NURBS-based degenerated stiffener element is proposed. Based on the 6 degree of freedom (DOF) degenerated beam element, the proposed stiffener element solves the issue of direct coupling between the beam element and 5 DOF degenerated shell element. Skin and stiffener are characterized by NURBS surface and curve, respectively. Meanwhile, the buckling behavior of stiffened panels is investigated based on isogeometric analysis (IGA), which reduces the geometric discrete error and realizes the integration of modeling and analysis. In addition, since the grids of skin and stiffeners are always unmatched, a strong coupling method based on NURBS interpolation and projection algorithm is constructed to merge non-conforming grids. The degrees-of-freedom (DOFs) of stiffeners is eliminated in the equilibrium equation, which greatly reduces the calculation scale. Furthermore, an improved point-to-surface projection algorithm is proposed, which improves the computational efficiency and solves the problem of unstable convergence of Newton iteration. Finally, the static and buckling analyses are performed for different types of stiffened plates and shells. Displacement solutions, von Mises stress solutions and buckling modes are discussed in detail. The prediction accuracy and meshes are compared with the shell-type model and beam-shell-type model in ABAQUS software, which indicates the high applicability and efficiency of the proposed analysis method for various types of stiffened panels.

A variable-fidelity multi-objective optimization method for aerospace structural design optimization

Variable-fidelity (VF) surrogate models have been widespreadly applied to aerospace structural design and optimization problems with multiple objectives to alleviate the optimization cost. To enhance the performance of the existing multi-objective optimization algorithms based on VF surrogate model, a variable-fidelity hypervolume expected improvement (VF-HVEI) method is proposed. Co-Kriging model is utilized to replace computational expensive objective functions in the proposed method, and it is sequentially updated with the VF-HEVI method during the optimization process. The proposed infilling criterion effectively considers the prediction uncertainty of the VF surrogate model, the contribution of sample points of different fidelity on the improvement of the current Pareto front and the computation cost of different simulation models at the same time. The test results in analytical and engineering examples indicate that the proposed method obtains more accurate and robust Pareto front under the same simulation cost.

An efficient method for postbuckling optimization of composite laminated plates with holes under compression and shear loading

Laminated composite plates with hole are commonly used in aeronautic and aerospace structure design, subjecting to the in-plane compression and shear loading. The existing of hole reduces both the in-plane and out-of-plane stiffness and influences the postbuckling behavior of the plate. The structural lightweight design can be further explored when the external load is allowed entering into the postbuckling regime. However, the lamination optimizations to maximize the postbuckling stiffness have high computational burden when the standard nonlinear finite element method is applied in each function call for postbuckling analysis. Thus, we propose a reduced-order modeling method based on the improved Koiter perturbation theory for buckling and postbuckling analysis. The low-scale reduced order model, instead of the full-scale FE model, is constructed and solved to obtain the initial postbuckling response. The postbuckling stiffness is defined to be the slope of the load-end shortening relation curve at the bifurcation point. A multi-start searching strategy based on the gradient-based algorithm is developed to maximize the postbuckling stiffness, efficiently and accurately. Laminated composite plates with different hole sizes, loading conditions and ply numbers, are considered to validate the excellent performance of proposed method.

Rear Fuselage Structural Optimization Using Genetic Algorithm

Structural optimization is one of the most important tasks during the airplane structural design and yet there is a lack of well established procedures to determine the optimum design of aerospace structures. This paper represents development of structural optimization code based on genetic algorithm, and results for light aircraft aft fuselage optimal design using the optimization code. We have developed a MATLAB code according to the genetic algorithm and FE model for the composite light aircraft aft fuselage using MSC PATRAN to generate NASTRAN input file; the MATLAB code was coupled with MSC NASTRAN which used to perform linear static and buckling analysis. we obtained the minimum weight of the aft fuselage with a linear static and buckling constraints; the minimum weight is 21.6 kg; it has been obtained after 43 iterations; the margin of safety is of the optimum design is 1.22 and the buckling factor is 1.24 and hence the structure is free of static failure and buckling. The code is efficient in the conceptual and preliminary structural design phases to obtain the optimal aft fuselage weight.

Identify the spatially-correlated random fluctuating pressure on structure from strain data

Distributed load information is essential for the design and monitoring of aerospace structures. A frequency domain method for the identification of correlated random fluctuating pressure is proposed in which structural responses acquired from limited strain sensors are used. The spatially-correlated power spectral density function of the random fluctuating pressure on the structure is firstly represented by Legendre polynomials w.r.t. the spatial distance multiplying their corresponding frequency-dependent coefficients. Secondly, the transfer matrix is obtained by the stochastic response analysis using distributed load in the form of Legendre polynomials. Then, the coefficients in the power spectral density function model of the pressure are identified by inversion of the transfer matrix together with a modified regularization technique. Finally, the random fluctuating pressure load is reconstructed by the superposition of the identified coefficients multiplying with Legendre polynomials. Numerical simulations on a simply-supported plate subjected to correlated stochastic distributed loads are conducted to verify the proposed method. Factors that may influence the accuracy of identification results are also discussed. To test the performance of the proposed method on complex structures, the gust-induced pressure load on a 3D wing structure is further identified using the proposed method. Results show that the proposed method is capable of identifying the correlated random fluctuating pressure on aircraft structures.

Artificial hail ice impact damage of laminated composite T-joint with stitching reinforcement

Hailstone impact has been one of the major concerns in the design and analysis of composite aerospace structures. Being key elements of such structures, T-joints with stitching reinforcement are investigated in this paper to understand its failure response in artificial hail ice impact loading conditions. Artificial hail ices are projected to the skin of composite T-joints at different energy levels with gas gun. High speed camera is used to capture the failure process of artificial hail ices. Quasi-static pull-off test is applied to assess the residual tensile strength of stitched and unstitched T-joint. Delamination damage has been observed on specimens after ice impact test, and the pull-off load capacity has been affected as well. It is found that hail ice impact can cause delamination damage to different regions and have influence on the failure mode and load capacity of T-joints in pull-off tests. Stitching has been found efficient in resisting the propagation of delamination, and can improve the ultimate displacement and load of T-joints remarkably.

Topology Optimization Design and Experimental Research of a 3D-Printed Metal Aerospace Bracket Considering Fatigue Performance

In the aerospace industry, spacecraft often serve in harsh operating environments, so the design of ultra-lightweight and high-performance structures is a major requirement in aerospace structure design. In this article, a lightweight aerospace bracket considering fatigue performance was designed by topology optimization and manufactured by 3D-printing. Considering the requirements of assembly with a fixture for fatigue testing and avoiding stress concentration, a reconstructed model was presented by CAD software before manufacturing. To improve the fatigue performance of the structure, this article proposes the design idea of abstracting the practiced working condition of the bracket subjected to cycle loads in the vertical direction via a multiple load-case topology optimization problem by minimizing compliance under a variety of asymmetric extreme loading conditions. Parameter sweeping was used to improve the computational efficiency. The mass of the new bracket was reduced by 37% compared to the original structure. Both numerical simulation and the fatigue test were implemented to support the validity of the new bracket. This work indicates that the integration of the proposed topology optimization design method and additive manufacturing can be a powerful tool for the design of lightweight structures considering fatigue performance.

УЗАГАЛЬНЕННЯ МОДЕЛІ ФОЛЬКЕРСЕНА НА ВИПАДОК ОСЬОВОЇ СИМЕТРІЇ

Thin-walled structures may contain defects as cracks and holes that are leftovers of the material the construction, is made of or they occur during the operation as a result of, for example, mechanical damage. The presence of holes in the plate causes a concentration of stresses at the boundary of the holes and ultimately leads to premature failure of the structural element. Repair of local damage of modern aircraft structures can be made by creating overlays that are glued to the main structure. The overlay takes on part of the load, unloading the damaged area. This method of repair provides tightness and aerodynamic efficiency to the structure. The calculation of the stress state of such glued structures is usually performed by using the finite element method. The classic models of the stress state of overlapped joints are one-dimensional. That is, the change of the stress state along only one coordinate is considered. At the same time, the connections of a rectangular form are also considered. The purpose of this work is to create a mathematical model of the stress state of circular axisymmetric adhesive joints and to build an appropriate analytical solution to the problem. It is assumed that the bending of the plates is absent; the deformation of the plates is even by thickness. The adhesive layer works only on the shift. The main plate and the overlay are considered isotropic. The solution is built on polar coordinates. The stress state of the connection depends only on the radial coordinate, i.e. one-dimensional. The solution is obtained in analytical form. This mathematical model is a generalization of the classical model of the adhesive connection of Volkersen to a circular or annular region and is considered for the first time. Boundary conditions are met exactly. The satisfaction of marginal conditions, as well as boundary conditions, leads to a system of linear equations with respect to the unknown coefficients of the obtained solutions. The model problem is solved and the numerical results are compared with the results of calculations performed by using the finite element method. It is shown that the proposed model has sufficient accuracy for engineering problems and can be used to solve problems of the design of aerospace structures.