Abstract:
Modern technologies allow creating functionally graded materials whose material properties usually vary according to power laws. Therefore, an urgent problem of mechanics of deformable solids is the identification of material characteristics of such materials. In this case, the general approach leads to a rather complex procedure. Therefore, in this paper, the search for the desired functions is implemented in the class of polynomials. A study is carried out of the problem of identifying variable properties of an oscillating inhomogeneous thermoelastic rod using additional information measured in the load region. The direct problem is solved by the finite element method in the FlexPDE package. The solution to the direct problem for a homogeneous rod is verified, and the sensitivity of additional information to the material functions included in the model is inves-tigated. A projection-iteration approach is proposed to find thermomechanical characteristics in the form of polynomial functions. During the iteration process, the coefficients of the polynomials were refined by solving a system of algebraic equations that arose as a result of discretization of the operator equations of the first kind. The initial approximation was set among the constants as the average value of the maximum and minimum values of the material characteristics, which were considered known from a priori information about the reconstructed characteristic. Then, a step-by-step refinement was performed in the class of constants, linear functions, quadratic functions. The proposed approach has the advantages of fast convergence of the iterative scheme at each stage of reconstruction, speed of solution of the direct problem, and high accuracy of reconstruction.
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