Analytical and numerical solutions of pressurized thick-walled FGM spheres

Das, Prodip Kumer; Islam, Md. Ariful; Somadder, Somnath; Hasib, M. A.

doi:10.1007/s00419-023-02406-3

Cited by 6 publications

(2 citation statements)

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“…There are a number of works that are devoted to the study of direct problems for given laws of properties of an inhomogeneous material [5][6][7]. In a number of cases, solutions were obtained numerically using the finite element method [8][9][10], and for some special cases, analytical solutions were obtained (see, for example [11][12][13]). Onedimensional or two-dimensional power functions described by one or two parameters are usually used as variation laws.…”

Section: Introductionmentioning

confidence: 99%

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Efficient Numerical Methods of Inverse Coefficient Problem Solution for One Inhomogeneous Body

Vatulyan,

Uglich,

Dudarev

et al. 2023

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In the present paper, the problems of longitudinal and flexural vibrations of an inhomogeneous rod are considered. The Young’s modulus and density are variable in longitudinal coordinate. Vibrations are caused by a load applied at the right end. The proposed method allows us to consider a wider class of inhomogeneity laws in comparison with other numerical solutions. Sensitivity analysis is carried out. A new inverse problem related to the simultaneous identification of the variation laws of Young’s modulus and density from amplitude–frequency data, which are measured in given frequency ranges, is considered. Its solution is based on an iterative process: at each step, a system of two Fredholm integral equations of the first kind with smooth kernels is solved numerically. The analysis of the kernels is carried out for different frequency values. To find the initial approximation, several approaches are proposed: a genetic algorithm, minimization of the residual functional on a compact set, and additional information about the values of the sought-for functions at the ends of the rod. The Tikhonov regularization and the LSQR method are proposed. Examples of reconstruction of monotonic and non-monotonic functions are presented.

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Section: Introductionmentioning

confidence: 99%

“…1], and similarly for η(ξ). Graphs of δ(ξ) for increasing, decreasing and non-monotonic laws g(ξ) and η(ξ) are shown inFigures 8,11 and 14, respectively. In Figures 9, 12 and 15 the AFC |u(1, λ)| and |v(1, λ)| are plotted in the frequency ranges in which the identification of the sought-for variation laws is carried out.…”

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confidence: 99%