Didactical Tool for Wing Weight Estimation in a Preliminary Aircraft Design Stage

Aircraft preliminary design requires a lot of complex evaluations and assumptions related to design variables that are not completely known at a very initial stage. Didactical activity becomes unclear since students ask for precise values in the starting point. A tentative in providing a simple tool for wing weight estimation is presented for overcoming these common difficulties and explaining the following points: a) the intrinsic iterative nature of the preliminary design stage, b) provide useful and realistic calculation for the wing weight with very simple assumption not covered by cumbersome calculations and formulas. The purpose of the paper is to provide a didactic tool to facilitate the understanding of some steps in estimating wing weight at the preliminary design level. The problems of identifying the main variables for the initial estimation is dealt with and specifi aspects that are usually hidden by the complexity of the involved disciplines and by the usual calculation methods applied in structural design are pointed out. The procedure is addressed to highlight main steps in wing weight estimation for straight wing weight to highlight the main steps in estimating the wing weight for a general aviation straight wing aircraft at the preliminary design stage. The effect of the main variables on the wing weight variation is also presented confirming well-known results from literature and design manuals

Aeroelastic Analysis through Non-Linear Beam Finite Elements with Bending-Torsion Coupling Formulation

This research paper presents a procedure for static aeroelastic analysis of high aspect-ratio composite wings. The structural analysis is performed through the finite element method coupled with an aerodynamic analysis based on the vortex lattice method. The finite element model is obtained with beam finite elements with bending-torsion coupling formulation, which allows to consider the material coupling given by oriented anisotropic material. An advanced formulation of the same beam element can be used to consider geometric non-linearities. An iterative procedure computes the aerodynamic loads acting on the initially undeformed structures, then the obtained deformation is used to compute the aerodynamic loads for the deformed configuration until convergence. The aeroelastic analysis can be repeated for different speeds to find the divergence speed. This procedure has been tested on previously published analytical and experimental results on composite structures with different layups showing good accordance. Moreover, curvilinear lamination has been considered for the analysis to show the effects on the static aeroelastic performance

Finite Element Modal Analysis for Composite and Stiffened Beam Structures with Geometric Non-Linearities

Predicting the vibrations of wing-box structures is a crucial aspect of the aeronautic design to avoid aeroelastic effects during normal flight operations. The deformed configuration of a wing structure during flight can induce non-linear couplings which results in a different dynamic behavior from the linear counterpart, for this reason, it is necessary to include non-linear loaded configurations to perform more realistic simulations. Moreover, with the advent of composite materials and aeroelastic tailoring, new simulation tools are needed to include the coupling effects caused by these materials and technologies. In this research, a beam finite element with bending-torsion coupling formulation has been used to investigate the effects of the self-weight of beam structures with different aspect ratios. The nonlinear effects induced by the load have been included in the finite element formulation with Hamilton’s Principle and a linearization approach and performing modal analysis on an equilibrium configuration. The results obtained with the beam finite element model have been compared with numerical and experimental evidence

A Beam Finite Element for Static and Dynamic Analysis of Composite and Stiffened Structures with Bending-Torsion Coupling

This research presents a new beam finite element capable of predicting static and dynamic behavior of beam structures with bending-torsion coupling. The model here derived establishes a relation between the bending and torsional nodal degree of freedom of a two node beam element. The equilibrium equations are derived neglecting the non-linear terms while the stiffness and mass matrices are derived with Galerkin’s method. The shape functions are obtained considering Timoshenko’s hypothesis and the torsional moment constant along the element. The model has been validated through numerical and experimental results for static and dynamic simulation. The comparison revealed a relative difference mostly lower than 5% for static deformations and natural frequency prediction, while the Modal Assurance Criterion (MAC) confirmed the consistency with numerical and experimental results in terms of mode shape similarity

Optimization of Curvilinear Stiffener Beam Structures Simulated by Beam Finite Elements with Coupled Bending–Torsion Formulation

This research presents the application of a beam finite element, specifically derived for simulating bending–torsion coupling in equivalent box-beam structures with curvilinear stiffeners. The stiffener path was simulated and optimized to obtain an expected coupling effect with respect to four typical static load cases, including geometric constraints related to the additive manufacturing production method. The selected load condition was applied to the centroid of the beam section, and the structure performance was consequently determined. A variation in load position up to onefourth of the beam width was considered for investigating the stiffener path variation corresponding to a minimum bending–torsion coupling effect. The results demonstrated the capability of such a beam finite element to correctly represent the static behavior of beam structures with curvilinear stiffeners and show the possibility to uncouple its bending–torsion behavior using a specific stiffener orientation. The simulation of a laser powder bed fusion process showed new opportunities for the application of this technology to stiffened panel manufacturing

Experimental and Numerical Dynamic Behavior of Bending-Torsion Coupled Box-Beam

Purpose Structural configurations related to new green aircraft design require high efficiency and low weight. As a consequence, moderate-to-large deformation under operating loads arise and aeroelastic instabilities different with respect to rigid counterpart are possible. Coupled structural configurations can provide the right mean to overcome such a critical situations selecting the right coupling parameters and structural performance. In this work, the dynamic behaviour of stiffened box-beam architecture with selected optimal stiffener orientation to emphasize the bending-torsion coupling characteristics has been investigated. Methods An extensive experimental activity has been performed for a validation and confirmation of the numerical results. Two cantilever beams produced with different technologies and materials have been tested. Modal performance has been determined by means of a laser Doppler vibrometer (LDV), while Finite-Element Method (FEM) numerical simulation based on solid elements and equivalent single layer approach have been applied and compared. Experimental/numerical comparison have been presented pointing out the specific coupling performance of this architecture with respect to natural frequencies and modal shapes. Results The activity demonstrates a good correlation in natural frequencies that remains mostly under 4%. Modal assurance criterion (MAC) has been considered in comparing experimental and numerical modal shapes. Conclusion The proposed innovative configuration demonstrates its capability to be used in aeroelastic critical problem as a mean to reduce their influence in aircraft design. The numerical procedure used for equivalencing the stiffened parts of the box-beam has also been validated in dynamical response confirming the possibility to be used in design phase

Numerical/Experimental Validation of Thin-Walled Composite Box Beam Optimal Design

Thin-walled composite box beam structural configuration is representative of a specific high aspect ratio wing structure. The optimal design procedure and lay-up definition including appropriate coupling necessary for aerospace applications has been identified by means of “ad hoc” analytical formulation and by application of commercial code. The overall equivalent bending, torsional and coupled stiffness are derived and the accuracy of the simplified beam model is demonstrated by the application of Altair Optistruct. A simple case of a coupled cantilevered beam with load at one end is introduced to demonstrate that stiffness and torsion angle distribution does not always correspond to the trends that one would intuitively expect. The maximum of torsional stiffness is not obtained with fibers arranged at 45° and, at the maximum torsional stiffness, there is no minimum rotation angle. This observation becomes essential in any design process of composite structures where the constraints impose structural couplings. Furthermore, the presented theory is also extended to cases in which it is necessary to include composite/stiffened hybrid configurations. Good agreement has been found between the theoretical simplified beam model and numerical analysis. Finally, the selected composite configuration was compared to an experimental test case. The numerical and experimental validation is presented and discussed. A good correlation was found confirming the validity of the overall optimization for the optimal lay-up selection and structural configuration

Innovative Aircraft Aeroelastic Modelling and Control

The aeroelastic design of innovative aircraft wing configurations imposes the designer to deal with specific phenomena, which are not usually considered in classical aircraft definition. The design process itself, though, gives the designer several indications on how to maintain the safety standards imposed by regulations. The investigation of the basic aeroelastic principles for unconventional wings with high aspect ratios can be extremely interesting as, once introduced in a multidisciplinary design, they can be very effective in giving an early determination of the static and dynamic behaviour of the aircraft, leading to significant improvements in the configuration weight, cost, and overall performance. The paper shows some preliminary results as part of the main objectives of the In.A.Team group (Innovative Aircraft Theoretical-Experimental Aeroelastic Modelling) at Politecnico di Torino, Italy. The In.A.Team Project has the following main objectives: 1) to develop multidisciplinary analysis methods appropriate to unconventional aircrafts (highly flexible, "morphing" vehicles); 2) to develop the capability of illustrating and understanding the effects of uncertainties on the behaviour of an aeroelastic system; 3) to apply the innovative adaptive L1 control techniques to highly flexible wings, 4) to integrate theoretical analysis with commercial structural (FEM) and aerodynamic tools (CFD). 5) to design and manufacture an aeroelastic experimental-test-model. 6) to validate theoretical/numerical results by vibration and aeroelastic wind tunnel test

Energy-absorbing origami structure for crashworthiness design

This paper presents experimental and numerical investigations on the origami-patterned tube which is acknowledged as a promising energy-absorption device. Its buckling mode leads to high performances in terms of specific energy absorption (SEA) and crush force efficiency (CFE). The polygonal tube is prefolded by following an origami pattern, which is designed to act as geometric imperfection and mode inducer. First, a series of quasi-static crushing tests are performed on origami tubes with different materials and geometrical features. Specimens in SUS316L and AlSi10Mg are produced through Additive Manufacturing (AM). It allows to conveniently produce few samples with a complex shape. Finite Element Analysis (FEA) and Direct Image Correlation (DIC) are employed for a better insight into the complex crushing behaviour. The Aluminum tube shows a brittle behaviour while SUS316L tubes have extremely promising performance until local crack happens. Limits stemming from the employment of AM are explored and a new geometry is designed to avoid cracking. Second, a numerical design exploration study is carried out to assess the sensitivity of origami pattern features over the energy-absorption performance. ANSYS Autodyn is utilized as FE solver and DesignXplorer for correlation and optimization. The benefits of new patterns are investigated through geometrical optimization, and an improved geometry is proposed. The pattern stiffness is tuned to account for the external boundary conditions, resulting in a more uniform crushing behaviour. A similar force trend is maintained with a SEA increment of 51.7% due to a drastic weight reduction in areas with lower influence on post-buckling stiffnes

Optimisation based analysis of the effect of particle spatial distribution on the elastic behaviour of PRMMC

A study of particle reinforced metal matrix composite (PRMMCs) by means of periodic multi-particle unit cells is presented. The inhomogeneous particle spatial distribution, as well as the effect of matrix/particles interface, strongly influences the heterogeneous material behaviour. The effect of both particle spatial distribution and particle size effect on the uniaxial elastic response of PRMMCs is addressed. The uniaxial tensile loading on cubicshaped cells with a different number of spherical particles (up to 50) and different fraction volumes (up to 25%) is studied by using Abaqus FEA [?], Matlab Global Optimisation Toolbox and the R Sequential Parameter Optimisation Toolbox SPOT [?]. Three different optimisation processes are used i.e. high-fidelity optimisation, low-fidelity optimisation and surrogate assisted optimisation that takes into account the uncertainty in particle spatial distribution. Accurate finite element analyses (FEA) on different representative volume elements (RVEs) have been conducted by means of Abaqus-optimizer coupling and computational homogenization. Numerical upper bound (UB) and lower bound (LB) of the homogenized uniaxial Young’s modulus Ex, based on high fidelity model based optimisation techniques (HFMBO), are reported. A memetic algorithm with adaptive parameter control optimisation process based on a model derived by sensitivities analysis is proposed. The results are compared to the ones using a surrogate assisted optimisation with Kriging. In the latter case, uncertainty in particle spatial distribution has been considered in regards to the current limited control in manufacturing techniques. The results show that the analytical upper bounds’ models overestimate predictions especially in configurations with a low number of particles per RVE. The results of the different optimisation processes have been compared and, the importance of the critical parameters on Ex has been addressed