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Estimation of elastic coefficients for a multiple beam structure


In this paper, we consider the estimation of spatially dependent elastic parameters in a static distributed model of a simple structure composed of two beams at a fixed angle to one another. We formulate the potential energy functional of the system and obtain existence of optimal estimators to a regularized-output least-squares estimation problem. We discuss regularity and approximation results for the basic problem and penalized problem in which nonconforming elements are used to model the junction of the beams. Numerical examples are presented and generalizations to multiple-beam systems are discussed.

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  1. 1.

    Ciarlet, P.,The Finite Element Method for Elliptic Problems, North-Holland Publishing Company, New York, New York, 1978.

  2. 2.

    Lions, J. L.,Control of Systems Governed by Partial Differential Equations, Springer-Verlag, New York, New York, 1972.

  3. 3.

    Kunisch, K., andWhite, L.,Regularity Properties in Elliptic Equations, Applicable Analysis, Vol. 21, pp. 71–88, 1986.

  4. 4.

    White, L. W.,Estimation of Higher-Order Damping Terms in Linear Plate Models, Applications in Mathematics and Computers, Vol. 33, pp. 89–122, 1989.

  5. 5.

    Luenberger, D. G.,Optimization by Vector Space Methods, Wiley, New York, New York, 1968.

  6. 6.

    Maurer, H., andZowe, J.,First and Second-Order Necessary and Sufficient Optimality Conditions for Infinite-Dimensional Programming Problems, Mathematical Programming, Vol. 16, pp. 98–110, 1979.

  7. 7.

    Schultz, M.,Spline Analysis, Prentice-Hall, Englewood Cliffs, New Jersey, 1973.

  8. 8.

    Schumaker, L.,Spline Functions Basic Theory, Wiley, New York, New York, 1981.

  9. 9.

    Lions, J. L., andMagenes, E.,Nonhomogeneous Boundary-Values Problems and Applications, Vol. 1, Springer-Verlag, New York, New York, 1969.

  10. 10.

    White, L. W.,Stability of Optimal Output Least-Squares Estimators of Elliptic Coefficients in Beam and Plate Models, Applications in Analysis, Vol. 39, pp. 15–34, 1990.

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This work was supported in part by AFOSR Grant 91-0017.

Communicated by L. D. Berkovitz

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White, L.W., Feng, Y.S. Estimation of elastic coefficients for a multiple beam structure. J Optim Theory Appl 79, 611–640 (1993).

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Key Words

  • Connected beams
  • identification
  • nonconforming finite elements