Research automation of fibrous composite materials elastic-plastic deformation

Authors

  • A. M. Polatov Национальный университет Узбекистана им.М.Улугбека, Республика Узбекистан, г. Ташкент
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Keywords:

computer model, algorithm, software, computer experiment, fiber composite, elastic-plastic state, toughness

Abstract

This paper describes the computer simulation of unidirectional fiber composite materials elastic- plastic deformation. To this end, developed efficient algorithms: formation of finite element mesh of elementary sub-areas; association sub-areas; determining the initial front and ordering numbers of nodes based on a modified front method; constructing the coefficients of the stiffness matrix of finite elements; forming resolving a system of equations on the basis of the progressive training data for each node individually; solving systems of equations by method of square roots with the symmetrically-band structure of the coefficient matrix; display on the screen a picture of the stress-strain state of the object. A set of tools to automate the process of designing new fiber composite materials and structures with predetermined mechanical properties is developed. To achieve this goal developed Computer Aided Engineering: building a finite element mesh areas (pre-processing); solving the problem of elastic-plastic deformation of composites (processing); visualization of calculation results (post-processing). This structure allows: to conduct computational experiments in the design of new composite materials and structures; investigate the effect of structural features on the structural strength of the material; to make recommendations to improve the bearing capacity and reduction of material structural elements. Technology calculation,computational algorithms and specialized software package together form the concept of predicting the structural parameters of the designed fiber composite materials and the strength of structural elements. Described the structure and functioning of specialized software. Composite materials elastic-plastic analysis results are presented.

References

[1] Tikhonov A.N. On independence of the solutions of differential equations froma small parameter, Matem.sb., Vol. 22 (64) No. 2 (1948) 193-204.
[2] Tikhonov A.N. O granichnykh skachkakh lineynykh differentsialnykh uravneny s malym parametrom pri starshikh proizvodnykh // Vestnik ZhGU im. I. Zhansugurova. 2012. № 4. p. 17-21.Systems of differential equations containing a small parameter within derivatives, Matem.sb., Vol.31 (73) No. 31 (1952) 575-586.
[3] Vishik M.I., Lyusternik L.A. Regular extinction and boundary layer for linear differential equations with a small parameter, UMN, Vol.212, No. 5. (1957) 3-122.
[4] Vasilyeva A.B. Asymptotics of the solutions of some boundary value problems for quasilinear equations within a small parameter and a senior derivative, RCS USSR, Vol. 123 No.4 (1958) 583-586.
[5] Imanaliev M.I. Asymptotic methods in the theory of singular perturbed integer-differential systems//Researches on the integer-differential equations.// -Frunze : Ilim, 1962. -Ò 2. -P. 21-39.
[6] Vishik M.I., Lyusternik L.A. On initial jump for non-linear differential equations containing a small parameter, RCS USSR, Vol. 132 No. 6. (1960) 1242-1245.
[7] Kasymov K.A. On asymptotic of the solutions of Cauchy problem with boundary conditions for non-linear ordinary differential equations containing a small parameter, UMN, Vol. 17 No. 5 (1962) 187-188.
[8] Dauylbaev M.K. Asymptotic estimates of solutions of the integro-differential equations with small parameter // Mathematical Journal. Vol.8. No4 (2008).
[9] Kasymov K.A., Nurgabyl D.N. Asymptotic estimates of the solution of a singularly perturbed boundary value problem with initial jump for linear differential equations, Differential equations, Vol. 40 No. 4 (2004). pp. 597-607.
[10] Nurgabyl D.N. Construction of solution of the singularly perturbed boundary problem with initial jump // Vestnik of Kirghiz State National University. - 2001. - Vol.3., №6. - C.173-177.
[11] Nurgabyl D.N. Semidegenerate for singularly perturbed boundary value problems // Abstracts of the International Conference "Differential Equations and Their Applications."Almaty, 2001.-C. 51-52.
[12] Vasilyeva A.B., Butuzov V.F. Asymptotic decomposition of Solutions it is Singularly Perturbed equations, Moscow, Nauka (1973) -p.272.

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How to Cite

Polatov, A. M. (2018). Research automation of fibrous composite materials elastic-plastic deformation. Journal of Mathematics, Mechanics and Computer Science, 84(1), 107–119. Retrieved from https://bm.kaznu.kz/index.php/kaznu/article/view/429