Shape sensitivity analysis of flutter response of a laminated wing

A method is presented for calculating the shape sensitivity of a wing aeroelastic response with respect to changes in geometric shape. Yates' modified strip method is used in conjunction with Giles' equivalent plate analysis to predict the flutter speed, frequency, and reduced frequency of the wing. Three methods are used to calculate the sensitivity of the eigenvalue. The first method is purely a finite difference calculation of the eigenvalue derivative directly from the solution of the flutter problem corresponding to the two different values of the shape parameters. The second method uses an analytic expression for the eigenvalue sensitivities of a general complex matrix, where the derivatives of the aerodynamic, mass, and stiffness matrices are computed using a finite difference approximation. The third method also uses an analytic expression for the eigenvalue sensitivities, but the aerodynamic matrix is computed analytically. All three methods are found to be in good agreement with each other. The sensitivities of the eigenvalues were used to predict the flutter speed, frequency, and reduced frequency. These approximations were found to be in good agreement with those obtained using a complete reanalysis

Interference Drag Associated with Engine Locations for Multidisciplinary Design Optimization

This research aims to quantify the interference drag for various engine locations on a traditional tube and wing, 150-passenger commercial aircraft flying at 35,000 ft and Mach 0.8. Engine locations are varied in the chord wise, span wise, and vertical directions near the wing, both under and above the wing, as well as along the fuselage. Euler simulations are performed with representative powered modern engines. The results are intended to supplement empirical drag estimates suitable for multidisciplinary design environments. Large interference drag increases, as compared to the isolated air frame and engine geometry, are found to occur when the engine is placed directly above or below the wing. Interference effects are significantly reduced, and in some instances result in benefits compared to the isolated bodies, when the engines are placed fore or aft of the wing. Interference drag increases are partially explained by flow channels leading to choked flow and shock interactions between bodies

Skin-stringer assembly using radial basis functions for curvilinearly stiffened panels

This is a preprint of an article whose final version has been published in the American Institute of Aeronautics and Astronautics (AIAA) Journal, AIAA, March 2021.Mechanical and Aerospace Engineerin

Finite Element Analysis of Geodesically Stiffened Cylindrical Composite Shells Using a Layerwise Theory

Layerwise finite element analyses of geodesically stiffened cylindrical shells are presented. The layerwise laminate theory of Reddy (LWTR) is developed and adapted to circular cylindrical shells. The Ritz variational method is used to develop an analytical approach for studying the buckling of simply supported geodesically stiffened shells with discrete stiffeners. This method utilizes a Lagrange multiplier technique to attach the stiffeners to the shell. The development of the layerwise shells couples a one-dimensional finite element through the thickness with a Navier solution that satisfies the boundary conditions. The buckling results from the Ritz discrete analytical method are compared with smeared buckling results and with NASA Testbed finite element results. The development of layerwise shell and beam finite elements is presented and these elements are used to perform the displacement field, stress, and first-ply failure analyses. The layerwise shell elements are used to model the shell skin and the layerwise beam elements are used to model the stiffeners. This arrangement allows the beam stiffeners to be assembled directly into the global stiffness matrix. A series of analytical studies are made to compare the response of geodesically stiffened shells as a function of loading, shell geometry, shell radii, shell laminate thickness, stiffener height, and geometric nonlinearity. Comparisons of the structural response of geodesically stiffened shells, axial and ring stiffened shells, and unstiffened shells are provided. In addition, interlaminar stress results near the stiffener intersection are presented. First-ply failure analyses for geodesically stiffened shells utilizing the Tsai-Wu failure criterion are presented for a few selected cases

Novel Control Effectors for Truss Braced Wing

At cruise flight conditions very high aspect ratio/low sweep truss braced wings (TBW) may be subject to design requirements that distinguish them from more highly swept cantilevered wings. High aspect ratio, short chord length and relative thinness of the airfoil sections all contribute to relatively low wing torsional stiffness. This may lead to aeroelastic issues such as aileron reversal and low flutter margins. In order to counteract these issues, high aspect ratio/low sweep wings may need to carry additional high speed control effectors to operate when outboard ailerons are in reversal and/or must carry additional structural weight to enhance torsional stiffness. The novel control effector evaluated in this study is a variable sweep raked wing tip with an aileron control surface. Forward sweep of the tip allows the aileron to align closely with the torsional axis of the wing and operate in a conventional fashion. Aft sweep of the tip creates a large moment arm from the aileron to the wing torsional axis greatly enhancing aileron reversal. The novelty comes from using this enhanced and controllable aileron reversal effect to provide roll control authority by acting as a servo tab and providing roll control through intentional twist of the wing. In this case the reduced torsional stiffness of the wing becomes an advantage to be exploited. The study results show that the novel control effector concept does provide roll control as described, but only for a restricted class of TBW aircraft configurations. For the configuration studied (long range, dual aisle, Mach 0.85 cruise) the novel control effector provides significant benefits including up to 12% reduction in fuel burn

Interlaminar Stresses by Refined Beam Theories and the Sinc Method Based on Interpolation of Highest Derivative

Computation of interlaminar stresses from the higher-order shear and normal deformable beam theory and the refined zigzag theory was performed using the Sinc method based on Interpolation of Highest Derivative. The Sinc method based on Interpolation of Highest Derivative was proposed as an efficient method for determining through-the-thickness variations of interlaminar stresses from one- and two-dimensional analysis by integration of the equilibrium equations of three-dimensional elasticity. However, the use of traditional equivalent single layer theories often results in inaccuracies near the boundaries and when the lamina have extremely large differences in material properties. Interlaminar stresses in symmetric cross-ply laminated beams were obtained by solving the higher-order shear and normal deformable beam theory and the refined zigzag theory with the Sinc method based on Interpolation of Highest Derivative. Interlaminar stresses and bending stresses from the present approach were compared with a detailed finite element solution obtained by ABAQUS/Standard. The results illustrate the ease with which the Sinc method based on Interpolation of Highest Derivative can be used to obtain the through-the-thickness distributions of interlaminar stresses from the beam theories. Moreover, the results indicate that the refined zigzag theory is a substantial improvement over the Timoshenko beam theory due to the piecewise continuous displacement field which more accurately represents interlaminar discontinuities in the strain field. The higher-order shear and normal deformable beam theory more accurately captures the interlaminar stresses at the ends of the beam because it allows transverse normal strain. However, the continuous nature of the displacement field requires a large number of monomial terms before the interlaminar stresses are computed as accurately as the refined zigzag theory

Wing Weight Optimization Under Aeroelastic Loads Subject to Stress Constraints

A minimum weight optimization of the wing under aeroelastic loads subject to stress constraints is carried out. The loads for the optimization are based on aeroelastic trim. The design variables are the thickness of the wing skins and planform variables. The composite plate structural model incorporates first-order shear deformation theory, the wing deflections are expressed using Chebyshev polynomials and a Rayleigh-Ritz procedure is adopted for the structural formulation. The aerodynamic pressures provided by the aerodynamic code at a discrete number of grid points is represented as a bilinear distribution on the composite plate code to solve for the deflections and stresses in the wing. The lifting-surface aerodynamic code FAST is presently being used to generate the pressure distribution over the wing. The envisioned ENSAERO/Plate is an aeroelastic analysis code which combines ENSAERO version 3.0 (for analysis of wing-body configurations) with the composite plate code

Response of Honeycomb Core Sandwich Panel with Minimum Gage GFRP Face-Sheets to Compression Loading After Impact

A compression after impact study has been conducted to determine the residual strength of three sandwich panel constructions with two types of thin glass fiber reinforced polymer face-sheets and two hexagonal honeycomb Nomex core densities. Impact testing is conducted to first determine the characteristics of damage resulting from various impact energy levels. Two modes of failure are found during compression after impact tests with the density of the core precipitating the failure mode present for a given specimen. A finite element analysis is presented for prediction of the residual compressive strength of the impacted specimens. The analysis includes progressive damage modeling in the face-sheets. Preliminary analysis results were similar to the experimental results; however, a higher fidelity core material model is expected to improve the correlation

Multidisciplinary Design Optimization and Cruise Mach Number Study of Truss-Braced Wing Aircraft

The Subsonic Ultra Green Aircraft Research (SUGAR) Phase III was led by Dr. Rakesh K. Kapania and Dr. Joseph A. Schetz at the Multidisciplinary Analysis and Design Center for Advanced Vehicles, Department of Aerospace and Ocean Engineering, Virginia Tech, Blacksburg VA. The research was performed from December 2014 to December 2015. Three major areas were investigated: Multidisciplinary Design Optimization (MDO) studies of truss braced wing (TBW) and strut braced wing (SBW) vehicles at cruise Mach numbers of 0.7 and 0.8 for a flight mission similar to current market single aisle configurations. The performance and the characteristics of the optimized vehicles were compared to the SUGAR Phase II TBW vehicle. These results were obtained without applying any of the extended transonic aerodynamic and aeroelastic tools that will be discussed later. It was found that the cruise Mach number has a large effect on the best truss configuration. At Mach 0.7, an SBW has a better fuel consumption and better take-off gross weight (TOGW). However, at Mach 0.8, the TBW is superior because the jury strut aids in satisfying the flutter constraint; Two-dimensional, steady, transonic aerodynamic analysis of the Boeing Airfoil J (BACJ) airfoil was performed for a range of thickness ratios, Mach numbers and lift coefficients. Reynolds-averaged Navier-Stokes (RANS) equations were solved to obtain the lift-curve slope, wave drag coefficient, the location of the center of pressure and to predict the separation at the trailing edge, which may lead to buffeting. One of the goals was to develop a database of lift-curve slope and the location of center of pressure, which could be used in a transonic aeroelastic analysis. Another goal was to compare the wave drag coefficients to those predicted by Locks fourth-power law and also to compare the transonic effects obtained from RANS simulations to those predicted by the Korn equations. A third goal was to develop a buffet boundary, which can be integrated into the MDO framework to prevent the optimized designs from probable buffeting; A state-space transonic aeroelastic analysis tool was developed, which can incorporate the nonlinear transonic effects in the unsteady aerodynamics but is yet computationally cheap when used within the VT MDO framework. The aeroelastic analysis uses Leishman- Beddoes (LB) indicial functions, which generated a state-space representation of the aeroelastic system. The indicial functions allow the incorporation of data for steady lift-curve slope and location of the center of pressure. Thus, the steady transonic effects are included, and the unsteady aerodynamic responses are a linearization about the steady results. The aeroelastic approach discretizes the wing into numerous strips, which results in a large eigenvalue problem as each strip has eight augmented aerodynamic states as per the LB theory. Thus, to reduce the computation expense, a reduced order model (ROM) was developed. The approach was validated using a few examples

Supersonic Wing Optimization Using SpaRibs

This research investigates the advantages of using curvilinear spars and ribs, termed SpaRibs, to design a supersonic aircraft wing-box in comparison to the use of classic design concepts that employ straight spars and ribs. The objective is to achieve a more efficient load-bearing mechanism and to passively control the deformation of the structure under the flight loads. Moreover, the use of SpaRibs broadens the design space and allows for natural frequencies and natural mode shape tailoring. The SpaRibs concept is implemented in a new optimization MATLAB-based framework referred to as EBF3SSWingOpt. This optimization scheme performs both the sizing and the shaping of the internal structural elements, connecting the optimizer with the analysis software. The shape of the SpaRibs is parametrically defined using the so called Linked Shape method. Each set of SpaRibs is placed in a one by one square domain of the natural space. The set of curves is subsequently transformed in the physical space for creating the wing structure geometry layout. The shape of each curve of each set is unique; however, mathematical relations link the curvature in an effort to reduce the number of design variables. The internal structure of a High Speed Commercial Transport aircraft concept developed by Boeing is optimized subjected to stress, subsonic flutter and supersonic flutter constraints. The results show that the use of the SpaRibs allows for the reduction of the aircraft's primary structure weight without violating the constraints. A weight reduction of about 15 percent is observed