Airframe Structural Modeling and Design Optimization Ramana V. Grandhi Distinguished Professor Department of Mechanical and Materials Engineering Wright State University

VIM/ITRI Relevance Computational Mechanics is a field of study in which numerical tools are developed for predicting the multi-physics behavior, without actually conducting physical experiments Study the behavior of -- materials -- environmental effects -- strength/service life -- signature, radar cross-section -- etc. Experiments are conducted mainly for validation and verification

Modeling of individual components Vertical Tail Fuselage Missile Elevator Nose Wing

Simulation Based Design Physical Modeling Simulations Cost Functions Design Variables Performance Limits Design Optimization Forging Extrusion Rolling Sheet Drawing Manufacturing Schemes Simulations Database Generation Experiments Rapid Access/Decision Making

Create a Parametric definition, Airframe Design Create a Parametric definition, Structural Model Generate a Finite Element Model of the structure Perform a Finite Element Analysis Optimize the design for improved performance and reliability

Structural model Tip chord Leading edge Trailing Edge Root chord

Simulation Based Design - Goals Study the complex multi-physics behavior of the warfighter at hypersonic speeds and in combat environment Study the behavior of shocks in transonic region due to flow non-linearities – vehicle response and control Develop high fidelity models for accurate performance measures Analyze wing structures with attached missiles. Reduce the modern vehicle development costs by performing simulations rather than costly physical experiments. --quickly and accurately analyze anything we can imagine

Development Challenges High fidelity simulation of integrated system behavior -- structures/aerodynamics/control/signature/plasma Design of lightweight high performance affordable vehicles Increase the structural safety, reliability and predictability Design critical components such as wing structures by including non-linear behavior models. Facilitate simulation of large-scale airframe structures in interdisciplinary design environment. Develop analysis procedures which are reliable for reaching the goal of “certification by analysis” instead of expensive trial-and-error component test procedures.

Material Characteristics Exceptional strength and stiffness are essential features of airframe parts. Low airframe weight boosts aircraft performance in pivotal areas, such as, range, payload, acceleration, and turn-rate. Advanced composite materials and high temperature materials offer reduced life-cycle costs – but manufacturability challenges

Generating a Finite Element Model Finite element model is a discretized representation of a continuum into several elements. where is the elemental stiffness matrix is the elemental displacement matrix is the elemental load matrix Quadrilateral element Triangular element θ

Finite Element Analysis Equations describing the behavior of the individual elements are joined into an extremely large set of equations that describe the behavior of the whole system where assembled stiffness matrix assembled displacement matrix assembled load matrix Finite Element model is used to study deflection, stress, strain, vibration, and buckling behavior in structural analysis Assembly of finite elements

Finite Element Analysis (FEA) It is one of the techniques to study the behavior of an Airframe structure by performing: Stress Analysis Frequency Analysis Buckling Analysis Flutter Analysis Missiles and their influence Multidisciplinary design Optimization

Stress Analysis A structure can be subjected to air loads, pressure loads, thermal loads, and dynamic loads from shock or random vibration excitation and the airframe responses can be analyzed using FEA techniques. FEA takes into account any combination of these loads. A detailed finite element analysis, shows the stress distribution on a F -16 aircraft wing.

Forces acting on the wing Leading edge Tip chord Trailing Edge Root chord

Stress distributions along the wing Minimum Stress at tip chord Maximum Stress at root chord

Finite Element Analysis (FEA) It is one of the techniques to study the behavior of an Airframe structure by performing: Stress Analysis Frequency Analysis Buckling Analysis Flutter Analysis Missiles and their influence Multidisciplinary design Optimization

Frequency Analysis The dynamic response of a structure which is subjected to time varying forces can be predicted using finite element analysis. Frequency Analysis is performed to determine the eigenvalues (resonant frequencies) and mode shapes (eigenvectors) of the structure. An eigenvalue problem is represented as: where is an eigenvalue (natural frequencies) is an eigenvector (mode shapes) The model can be subjected to transient dynamic loads and/or displacements to determine the time histories of nodal displacements, velocities, accelerations, stresses, and reaction forces.

Mode 1: Bending mode (9.73 Hz) Mode shapes of the Wing 48’’ Shear Elements Quadrilateral Elements 26.5’’ 108’’ Rod Element Structural model Mode 1: Bending mode (9.73 Hz) This shows the structural and aerodynamic model of the wing. The structure is made up of CQUAD4 elements which represents the top and bottom skin. The CQUAD4 element is used with bending stiffness capability. The CSHEAR elements represent the spars and the rib. The CROD represent the posts. There are in all 120 elements. The aerodynamic root chord is 90 inch. tip chord is 48 inch. the semi-span is 108 inch both for structure and aerodynamic model. There are 400 panels have been used to represent the aerodynamic model. There 20 chordwise panels and 20 spanwise panels.

Mode 2: Torsion mode (34.73 Hz) Wing Mode Shapes 48’’ Shear Elements Quadrilateral Elements 26.5’’ 108’’ Rod Element Structural model Mode 2: Torsion mode (34.73 Hz) This shows the structural and aerodynamic model of the wing. The structure is made up of CQUAD4 elements which represent the top and bottom skin. The CQUAD4 element is used with bending stiffness capability. The CSHEAR elements represent the spars and the rib. The CROD represent the posts. There are in all 120 elements. The aerodynamic root chord is 90 inch. tip chord is 48 inch. the semi-span is 108 inch both for structure and aerodynamic model. There are 400 panels have been used to represent the aerodynamic model. There 20 chordwise panels and 20 spanwise panels.

Fluid- Structure Interaction Fluid structure interaction plays an important role in predicting the effect of a flow field upon a structure and vice-versa. This interaction helps in accurately capturing the various aerodynamic effects such as angle of attack/deflections/ shocks. .. . M x + C x + Kx = A(t) = Aerodynamic forces Structure Flow Field

Occurrence of Shocks Wing Model Shock on the wing Tip chord Root chord Trailing Edge Leading edge Tip chord

Shock transmission on the wing

Finite Element Analysis (FEA) It is one of the techniques to study the behavior of an Airframe structure by performing: Stress Analysis Frequency Analysis Buckling Analysis Flutter Analysis Missiles and their influence Multidisciplinary design Optimization

Buckling Analysis Buckling means loss of stability of an equilibrium configuration, without fracture or separation of material. Buckling mainly occurs in long and slender members that are subjected to compressive loads. Long Slender member F = compressive load Before Buckling After Buckling

Buckling Phenomena in a Sensorcraft AFRL/VA Sensorcraft Concept Finite Element Model Buckling Phenomenon 1562 grid pts 3013 elements Next

Finite Element Analysis (FEA) It is one of the techniques to study the behavior of an Airframe structure by performing: Stress Analysis Frequency Analysis Buckling Analysis Flutter Analysis Missiles and their influence Multidisciplinary design Optimization

Flutter Analysis Flutter is an aerodynamically induced instability of a wing, tail, or control surface that can result in total structural failure. Flutter occurs when the frequency of bending and torsional modes coalesce. It occurs at the natural frequency of the structure.

Finite Element Analysis (FEA) It is one of the techniques to study the behavior of an Airframe structure by performing: Stress Analysis Frequency Analysis Buckling Analysis Flutter Analysis Missiles and their influence Multidisciplinary design Optimization

Missiles and their influence Wing Tip Missile Under wing Missile

Structural dynamic effect Influence of a Missile Missile Influence Structural dynamic effect Aerodynamic effect Flutter speed of the wing increases/decreases depending on missile placement. As the center of gravity moves towards the leading edge the flutter speed increases. Design optimization is performed to place the missile at an optimal position. The natural frequency of the wing reduces due to increased mass This shows that frequency is inversely proportional to mass.

Wing Model with Missile at the tip Structural Model Mode 1: Bending Mode (3.8 Hz) Missile This is a structural and aerodynamic representation of the wing with tip store. Here, the store has been attached @50% of the tip chord of the wing. This is one of the cases, which I am trying to demonstrate…I have also done the flutter analysis of wing with tip store @25% and 32.5% tip chord. Due to the shortage of time, I am presenting only one case. i.e.,50% tip chord. The second figure is a combination of structural model superimposed over the aerodynamic model. The aerodynamic center is 1/4th of the aerodynamic root chord. Frequency of the wing first mode without a missile : Bending mode (9.73 Hz)

Wing Model with Missile at the tip Structural Model Mode 2: Torsion mode (7.84 Hz) Frequency of the wing second mode without a missile : Torsion mode (34.73 Hz)

Finite Element Analysis (FEA) It is one of the techniques to study the behavior of an Airframe structure by performing: Stress Analysis Frequency Analysis Buckling Analysis Flutter Analysis Missiles and their influence Multidisciplinary design Optimization

Design Optimization Tools used for optimization are: Optimization is required for: Improved performance High reliability Manufacturability Higher strength Less weight Tools used for optimization are: Sensitivity Analysis Approximation Concepts Graphical Interactive Design Conceptual and Preliminary Design Design with Uncertain and Random Data

Sensitivity Analysis Sensitivity analysis measures the impact of changing a key parameter in system response. The plot shows that the elements near the root chord are the most sensitive, and change in these element parameters will effect the stress distribution -3.07E-02 -3.04E-02 -2.37E-02 -1.71E-02 -1.04E-02 -3.35E-03 2.91E-03 9.58E-02 -3.74E-02 -4.37E-02 1.62E-02 Sensitivity analysis plot

Optimization of design variables (Thickness) Optimum Thickness Distribution

Simulation Based Design Physical Modeling Simulations Cost functions Design variables Performance limits Design Optimization Forging Extrusion Rolling Sheet Drawing Manufacturing Schemes Simulations Database Generation Experiments Rapid Access/Decision Making

Forging Process

Forging Illustration

3-D view of a Mechanical part : Case study

Forging Simulation (Peanut Shaped Billet) Top die Billet Bottom die Conventional approach (Peanut Shaped Billet)

Challenges in Process Simulation Modeling of forging dies Collection of material flow-data Thermal expansion Heat conductivity Flow stresses Appropriate boundary conditions. Nonlinear material behavior Optimal forging process parameters Press velocity Die and Billet temperature Die Shape Optimization Preforming Stages Preform Shapes Infinite paths to reach the final shape

Optimal Design Objectives Design for manufacturability Reduce material waste, i.e. achieve a net shape forging process by optimizing material utilization and scrap minimization. Eliminate surface defects, i.e. laps and voids. Eliminate internal defects, i.e. shear cracks and poor microstructure. Minimize effective strain and strain-rate variance in workpiece. Design optimal process parameters such as forming rate (die velocity) and initial workpiece and die temperatures.

Preform Design Engineering Preform Design Methods: Empirical guidelines based on designer’s experience Computer aided design/geometric mapping Backward Deformation Optimization Method (BDOM) Current Design Methods: Backward tracing method Numerical optimization method

Preform Design of the billet Trimming the scrap Reducing the scrap Section After Die fill

Backward Simulation – Preform Design Optimization Approach

Scrap Comparison for different initial billets Peanut Shape 5 % Scrap Preform Shape

Crankshaft (Ford Motor Company)

Crankshaft Forging - Initial Stage Top Die Billet Bottom die

Crankshaft undergoing deformation

Forging Challenges Incomplete die fill

Database Development & Rapid access Computational Engineering Visualize complex dynamics in multi-physics behavior Understand system response Visualization Modeling Database Development & Rapid access Visualize product quality (shape, defects) Identify design limits High fidelity simulations for certification Defect detection Imaging Simulation Based Design Manufacturing process Features extraction Design under competing goals