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  Volume 5, Number 3, July 2020 , pages 305-321

Algorithm of solving the problem of small elastoplastic deformation of fiber composites by FEM
Askhad M. Polatov, Abduvali A. Khaldjigitov and Akhmat M. Ikramov

    In this paper is presented the solution method for three-dimensional problem of transversely isotropic body's elastoplastic deformation by the finite element method (FEM). The process of problem solution consists of: determining the effective parameters of a transversely isotropic medium; construction of the finite element mesh of the body configuration, including the determination of the local minimum value of the tape width of non-zero coefficients of equation systems by using of front method; constructing of the stiffness matrix coefficients and load vector node components of the equation for an individual finite element's state according to the theory of small elastoplastic deformations for a transversely isotropic medium; the formation of a resolving symmetric-tape system of equations by summing of all state equations coefficients summing of all finite elements; solution of the system of symmetric-tape equations systems by means of the square root method; calculation of the body's elastoplastic stress-strain state by performing the iterative process of the initial stress method. For each problem solution stage, effective computational algorithms have been developed that reduce computational operations number by modifying existing solution methods and taking into account the matrix coefficients structure. As an example it is given, the problem solution of fibrous composite straining in the form of a rectangle with a system of circular holes.
Key Words
    modeling; algorithm; grid; front; FEM; transversal isotropy; fiber; composite; hole; elastoplastic; strain, stress
Askhad M. Polatov, and Akhmat M. Ikramov: Department of Mathematics, National University of Uzbekistan, 4, University Street,Tashkent 100174, Uzbekistan
Abduvali A. Khaldjigitov : Samarkand branch of Tashkent University of Information Technologies, 47A,
Shohruh Mirzo Str., Samarkand, 140100, Uzbekistan

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