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The Impliсit Finite Difference Method in the Deformation Mechanics of Homogeneous and Piecewise Homogeneous Bodies

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Mechanics of Composite Materials Aims and scope

The implicit finite difference method for solving deformation problems of mechanics of piecewise-homogeneous bodies is presented. The method is based on approximating the sought-for quantities by polynomials with indeterminate coefficients. It allows one to approximate the derivatives in resolving equations based on a grid with an irregular, in general, arrangement of nodal points. Relations were given for one-, two-, and three-dimensional approximations of the second-order of accuracy. This method was applied to studying the deformation of an elastic rotating cylinder whose matrix is reinforced in the circumferential directions with one layer of round fibers. The material configuration of the cylinder at large displacements and deformations are presented together with the stresses of contact interaction between the matrix and fibers. Its deformation characteristic, which reflects the continuation of the solution of the problem in terms of rotation speed, is determined. The results obtained are compared with the solution of the problem for a cylinder with square fibers at the same filling found by the methods of implicit finite differences and the traditional method of finite differences. Boundary-value problems for a thick-walled cylinder made of an isotropic material are also solved in nonlinear and linear formulations with uniform and nonuniform distributions of nodal points across the cylinder thickness, and the results obtained are compared with the exact solution of the corresponding linear problem.

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Authors and Affiliations

  1. National Metallurgical Academy of Ukraine, Dnepropetrovsk, Ukraine

    V. M. Akhundov

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  1. V. M. Akhundov
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Correspondence to V. M. Akhundov.

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Translated from Mekhanika Kompozitnykh Materialov, Vol. 57, No. 6, pp. 1129-1154, November-December, 2021. Russian DOI: 10.22364/mkm.57.6.07.

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Akhundov, V.M. The Impliсit Finite Difference Method in the Deformation Mechanics of Homogeneous and Piecewise Homogeneous Bodies. Mech Compos Mater 57, 795–812 (2022). https://doi.org/10.1007/s11029-022-10000-x

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  • DOI: https://doi.org/10.1007/s11029-022-10000-x

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