On computing the forces from the noisy displacement data of an elastic body

International Journal for Numerical Methods in Engineering

Volumn 76, Issue 11, 2008, Pages 1645-1677

  Reddy, A Narayana ^a   Ananthasuresh, G K ^a  

^a INDIAN INSTITUTE OF SCIENCE   (India)

Author keywords

Cauchy's problem; Geometric non linearity; Inverse problems; Vision based force sensor

Indexed keywords

DIFFERENTIAL EQUATIONS; INVERSE PROBLEMS; LINEARIZATION; NUMERICAL METHODS; SENSORS;

APPLIED FORCES; CAUCHY'S PROBLEM; DISPLACEMENT MEASUREMENTS; ELASTIC BODIES; ELASTICITY PROBLEMS; FINITE ELEMENT MODELLING; FORCE-SENSING; FRAME ELEMENTS; GEOMETRIC NON-LINEARITY; ILL-POSED PROBLEMS; LARGE DISPLACEMENTS; MEASUREMENT TECHNIQUES; NON-LINEAR MODELLING; NUMERICAL EXAMPLES; OVER-CONSTRAINED SYSTEMS; PSEUDO INVERSE; REASONABLE ACCURACIES; VISION-BASED FORCE SENSOR;

ELASTICITY;

EID: 60849139642     PISSN: 00295981     EISSN: 10970207     Source Type: Journal    
DOI: 10.1002/nme.2373     Document Type: Article

References (29)

1. Wang X, Ananthasuresh GK, Ostrowski JP. Vision-based sensing of forces in elastic objects. Sensors and Actuators A: Physical 2001; 94(3):142-156.
2. Greminger MA, Nelson BJ. Vision-based forces measurement. IEEE Transactions on Pattern Analysis and Machine Intelligence 2004; 26(3):290-298.
3. Kamiyama K, Vlack K, Mizota T, Kajimoto H, Kawakami N, Tachi S. Vision-based sensor for real time measuring of surface traction. IEEE Computer Graphics and Applications 2005; 25(1):68-75.
4. Vendroux G, Knauss WG. Submicron deformation field measurements. Part 2. Improved digital image correlation. Experimental Mechanics 1998; 38(2):86-92.
5. Charette PG, Hunter IW, Hunter PJ. Large deformation mechanical testing of biological membranes using speckle interferometry in transmission. I: experimental apparatus. Applied Optics 1997; 36(10).
6. Zhang R, Shilo D, Ravichandran G, Bhattacharya K. Mechanical characterization of released thin films by contact loading. ASME Journal of Applied Mechanics 2006; 73:730-736.
7. Schnur DS, Zabaras N. Finite element solution of two-dimensional inverse elastic problems using spatial smoothing. International Journal for Numerical Methods in Engineering 1990; 30(1):57-75.
8. Bonnet M, Constantinescu A. Inverse problems in elasticity. Inverse Problems 2005; 21:R1-R50.
9. Tikhonov AN, Arsenin VY. Solution of Ill-posed Problems. V.H. Winston: Washington, DC, 1977.
10. Belgacem FB. Why is the Cauchy problem severely ill-posed? Inverse Problems 2007; 23:823-826.
11. Krishnan G, Ananthasuresh GK. An objective evaluation of displacement-amplifying compliant mechanisms for sensor applications. CD-ROM Proceedings of the ASME International Design Engineering and Technical Conferences, Philadelphia, U.S.A., 10-13 September 2006; Paper#DETC2006-99345 (Also to appear in the Journal of Mechanical Design 2008).
12. Oda J, Moto S. On inverse analytical technique to obtain contact stress distributions-technique using measurement values with errors (in Japanese but with an abstract in English). Transactions of the Japan Society of Mechanical Engineers, Series A 1980; 55:827-877.
13. Maniatty A, Zabaras N, Stelson K. Finite-element analysis of some inverse elasticity problems. Journal of Engineering Mechanics (ASCE) 1989; 115(11):1303-1317.
14. Zabaras N, Morellas V, Schnur D. Spatially regularized solution of inverse elasticity problems using the BEM. Communications in Applied Numerical Methods 1989; 5(3):547-553.
15. Maniatty AM, Zabaras NJ. Investigation of regularization parameters and error estimating in inverse elasticity problems. International Journal for Numerical Methods in Engineering 1994; 37(6):1039-1052.
16. Bezerra LM, Saigal S. Inverse boundary traction reconstruction with the BEM. International Journal of Solids and Structures 1995; 32(10):1417-1431.
17. Martin TJ, Halderman JD, Dulikravich GS. An inverse method to finding unknown surface tractions and deformations in elastostatics. Computers and Structures 1995; 56(5):825-835.
18. Zhang F, Kassab AJ, Nicholson DW. A 3-D traction reconstruction method using BEM and internal strain data. AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference and Exhibit, 38th, and AIAA/ASME/AHS Adaptive Structures Forum, Kissimmee, FL, U.S.A., 7-10 April 1997; 1873-1883.
19. Lu S, Rizzo FJ. A boundary element strategy for elastostatic inverse problems involving uncertain boundary conditions. International Journal for Numerical Methods in Engineering 1999; 46:957-972.
20. Turco E. An effective algorithm for reconstructing boundary conditions in elastic solids. Computer Methods in Applied Mechanics and Engineering 2001; 190(29-30):3819-3829.
21. Nakagiri S, Suzuki K. Finite element interval analysis of external loads identified by displacement input with uncertainty. Computer Methods in Applied Mechanics and Engineering 1999; 168:63-72.
22. Turco E. Is the statistical approach suitable for identifying actions on structures? Computers and Structures 2005; 83:2112-2120.
23. Marine L. A meshless method for solving the Cauchy problem three-dimensional elastostatics. Computers and Mathematics with Applications 2005; 50:73-92.
24. Kozlov VA, Maz'ya VG, Fomin AV. An iterative method for solving the Cauchy problem for elliptic equations. Computational Mathematics and Mathematical Physics 1991; 31(1):45-52.
25. Baranger TN, Andrieux A. An optimization approach for the Cauchy problem in linear elasticity. Structural and Multidisciplinary Optimization 2008; 35:141-152.
26. Belgacem FB, Feikh HE. On Cauchy's problem: I. A variational Steklov-Poincaré theory. Inverse Problems 2005; 21:1915-1936.
27. Azazïez M, Belgacem FB, Fekih HE. On Cauchy's problem: II. Completion, regularization and approximation. Inverse Problems 2006; 22:1307-1336.
28. Howell LL. Compliant Mechanisms. Wiley: New York, 2001.
29. Crisfield MA. Non-Linear Finite Element Analysis of Solids and Structures. Wiley: New York, 1997.