Advances in Structural Analysis Methods for Structural Health - PowerPoint PPT Presentation

National Aeronautics and Space Administration Advances in Structural Analysis Methods for Structural Health Management of NextGen Aerospace Vehicles Dr. Alex Tessler NASA Langley Research Center 2011 Annual Technical Meeting May 10 – 12, 2011 St. Louis, MO www.nasa.gov

Outline • Motivation • Vehicle Health Management • Shape-sensing • Shape-sensing (NASA Dryden) • Full-field reconstruction (NASA LaRC) • Collaborations • Summary 2

Motivation: Sensing of wing deformations FBG strain sensing – wing deformation (inverse reconstruction, ill-posed problem) Conforming antenna on AEW&C (airborne radar system) Strain-displacement relations   ε Lu h h h on 3

Shape sensing: from in-situ strains to deformed shape Hat-stiffened panel: full-field solution FBG sensor 4

Vehicle Health Management Objectives • Affordable, safe and reliable technologies for aeronautic and long-duration space structures – Provide real-time vehicle health information via sensors, software and design by monitoring critical structural, propulsion, and thermal protection systems – Provide valuable information to adaptive control systems to mitigate accidents due to failure and achieve safe landing – Provide detection and localization of impact events on key structural and flight control surfaces – Utilize decision-making mechanisms using intelligent reasoning based on safe- outcome probability – Maximize performance and service life of vehicle or space structure 5

Continuous Monitoring and Assessement of Structural Response in Real Time • Diagnosis and prognosis of structural integrity – Deformation – Temperature – Strains and stresses (internal loads) – Damage and failure 6

Maximize Performance: Provide Active Structural Control via Shape Sensing Wing control systems – Helios class of aircraft (solar panel) • Control of wing dihedral – Unmanned Aerial Vehicles (UAV) – Morphing capability aircraft • Shape changes of aircraft wing – Embedded antenna performance – Shape control of large space structures • Solar sails • Membrane antennas Shape Control of Space Structures 7

Implementation & enabling capabilities • Diverse arrays of distributed in-situ sensors – Process, communicate, and store massive amounts of SHM data – Perform on-board structural analysis based on SHM sensing data • Determine deformed shape of structure continuously • Perform diagnosis and prognosis of structural integrity – Provide information of structural integrity to cockpit displays and remote monitoring locations to enable safe and effective operational vehicle management and mission control – Provide valuable information to improve future designs

NASA Dryden Shape-Sensing Analysis • 1-D integration of classical beam Eqs for cantilevered, non-uniform cross-section View from above the left wing beams (no shear deformation) (Optical fiber is glued on top of wing)      x w ( u ( , ) x z z w )  , xx x , x c x ( )   z [ , c c ] • Piecewise linear approximation of strain and taper between regularly spaced “nodes” where strains are measured • Neutral axis is computed from detailed FEM (SPAR code) • Incorporates cross-sectional geometry of a wing in a beam-type approximation Method for Real-Time Structure Shape-Sensing, U.S. Patent No. 7,520,176, issued April 21, 2009. 9

NASA Dryden Shape-Sensing Analysis

NASA LaRC High-Fidelity, Full-Field Inverse FEM From strains measured at discrete    locations, determine full-field ε σ f ε σ F u , , , ( , ) 0 ext continuous displacements, strains, and stresses that represent the measured Wing data with sufficient accuracy Composite and sandwich Frame structures Aircraft 11

Conceptual Framework of Inverse FEM: Discretized, high-fidelity solution 1. Discretization with iFEM: – beam, plate, shell or solid  h 2. Elements defined by a continuous displacement field h u x ( ) 3. Strains defined by strain-displacement relations   ε Lu h h h on 4. Experimental strain-gauge data and iFE strains match up in a least-squares sense   2  2    ε ε ε h  ε xi strain at 5. Displacement B.C.’s prescribed  h h u u x ( ) sensor   u u on  ε Lu h h 6. Linear algebraic Eqs determine nodal  σ Cε h h  displacements h 7. Element-level substitutions yield full-field 3-node inverse strains, stresses (internal loads), and failure   shell element σ Cε criteria h h h on

First-Order Shear Deformation Theory: Flat inverse-shell element • Kinematic assumptions account for deformations due to z, w – Membrane – Bending – Transverse shear  y y, v x, u     x u ( , ) x t u z x y     h u ( , ) x t v z y x 2h  u ( , ) x t w z  x ( , , ) x y z   z [ h h , ] 13

Experimental in-situ strains Experimental strains via FSDT formalism In-situ surface strains                 xx   top   xx 1 4           yy            z rosette   yy 2 5          xy       z       xy 3 6 2 h     xx     bottom     yy ฀    rosette    xy    Evaluate   x z ; h at i                               4 xx xx         1 xx xx       1 1                           k         e i 5 yy yy i 2 yy yy 2 h         2                                   6 xy xy 3 xy xy 14 ฀  ฀ 

Full-Field Reconstruction using iFEM • Least-Squares variational formulation – Plate formulation based on first-order shear deformation theory    2   2   2 p h ( u ) p e p k p g 1 2 3 – Strain compatibility equations fulfilled e p : Positive valued weighting constants – Strains treated as tensor quantities i – put different importance on the – No dependency on material, inertial or satisfaction of the individual strain components and their adherence to the damping properties measured data – Efficient elements for – Beams and frames Strain sensor Displ. – Plates and shells u h @ x i vector: – Application to metal, multilayer composite, and sandwich structures ฀  Element A e area: ฀ 

Discretization using iMIN3 elements • Variational principle A ( x i ) symmetric, positive definite matrix (B.C.’s imposed) N   d   h min : ( u ) 0 Nodal displacement vector e  e 1 r.h.s. vector, function of b ฀  measured strain values • Linear Eqs Ad  b ฀  Coarse discretization sufficient ฀  (more efficient than direct FEM) • Efficient solution   1 d A b ฀  strain rosette

Attributes of Inverse FEM • Theory • Computational efficiency, architecture – Strain-displacement relations fulfilled and modeling – Least-squares compatibility with – Architecture as in standard FEM measured strain data (e.g., user routine in ABAQUS) – Integrability conditions fulfilled – Superior accuracy on coarse meshes (advantage of integration) – Independent of material properties – Beam, frame, plate, shell and built- – Stable solutions under small changes in up structures input strain data (random error in measured strain data) – Thin and moderately thick regime – Geometrically linear and nonlinear (co- – Low and higher-order elements rotational formulation) response – Use of partial strain data (over part of structure, or incomplete strain – Dynamic regime tensor data) • Studies performed • Beam, frame, plate, and built-up shell structures • Experimental studies using FBG strains and strain rosettes • Transient dynamic response and strain data

iFEM applied to Plate Bending • Strain rosette data • FBG sensors • Incomplete strain data

Cantilevered Plate: iFEM using experimental strains • Aluminum 2024-T3 alloy - Elastic modulus: 10.6 Msi - Poisson’s ratio: 1/3 - Thickness: 1/8 in • Weight loaded at (9 in,1.5 in) - P = 5.784 lb (2623 g ) y Strain rosette Clamped Applied force Edge 3/8 in 3/8 in 3/8 in 3/4 in 3/2 in 3 in x 3 in 1 in 9 in * A. Tessler & J. Spangler. EWSHM (2004); P. Bogert et al., AIAA (2003)

Deflection comparison Measured deflection, W = 6.81 mm, W (in) at (214.3 mm, 38.1 mm) 0.000 -2.455-02 FEM (ABAQUS) iFE Rossette strains -4.911-02 -7.366-02 -9.821-02 Clamped -1.228-01 edge -1.473-01 -1.719-01 -1.964-01 -2.210-01 -2.455-01 -2.701-01 Max. deflection Max. deflection W = 6.860 mm W = 6.855 mm 20