Identifying a rigidity function distributed in static composite beam by the boundary functional method

Abstract

In many situations, it is important to recognize the bending performance of a newly received composite beam. With this in mind, this paper estimates unknown rigidity function of a static Euler–Bernoulli composite beam. To solve the inverse coefficient problem with the help of boundary data, a sequence of boundary functions are derived, which satisfy the homogeneous boundary conditions, and are at least the fourth-order polynomials. All boundary functions and zero element constitute a linear space. An energetic boundary functional is introduced in the linear space, of which the energy is preserved for each energetic boundary function. The linear system used to recover the unknown rigidity function of composite beam with energetic boundary functions as bases is derived and the iterative algorithm is developed, which is convergent very fast. The accuracy and robustness of boundary functional method (BFM) are confirmed by comparing the estimated results with exact rigidity functions of composite beams.