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Analysis of coefficient identification problems associated to the inverse Euler-Bernoulli beam theory. (English) Zbl 0954.74025

Summary: We investigate the identification of a heterogeneous flexural rigidity coefficient in the steady-state Euler-Bernoulli beam theory in the presence of a prescribed load. Mathematically, this study is an extension to higher-order differential equations of the coefficient identification problem analysed by P. Marcellini [Ric. Mat. 31, 223-243 (1982; Zbl 0529.34018)] for the one-dimensional Poisson equation. In addition, we discuss various boundary conditions and establish the well-posedness of these inverse problems. We also present numerical results obtained by using a regularization algorithm.

MSC:

74G75 Inverse problems in equilibrium solid mechanics
74K10 Rods (beams, columns, shafts, arches, rings, etc.)

Citations:

Zbl 0529.34018
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