PSI - Issue 28

O. Pozhylenkov et al. / Procedia Structural Integrity 28 (2020) 458–463 Author name / Structural Integrity Procedia 00 (2019) 000–000

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Conclusions In the opposite with Pozhylenkov O. V. (2019) where the exact solution of the boundary problem with conditions of the ideal contact on the both lateral sides of the rectangular domain was found, the problem in presented paper is complicated with the mixed boundary conditions, which leads to the singular integral equation. The displacements and stress were investigated for the different domain sizes and types of external load. References Liew K. M., Yuming Cheng, Kitipornchai S. (2005) Boundary elemnt-free method (BEFM) and application to two dimensional elasticity problems. International journal for Numerical Methods in Engineering. Vulume 65, Issue 8 Oden J. T., Kikuchi N. (1982) Finite element methods for constrained problems in elasticity. International journal for Numerical Methods in Engineering. Volume 18, Issue 5. Dongyang Shi, Minghao Li, (2014) Superconvergence analysis of the stable conforming rectangular mixed nite elements for the linear elasticity problem Journal of Computational Mathematics. Volume 32, Number 2, pp. 205-214. Shyam N. Prasad, Sailendra N. Chatterjee (1973) Some mixed boundary value problems of elasticity in a rectangular domain. International journal of Solids and Structures. Volume 9, Issue 10, pp. 1193-1210. V. A. Kondrat`ev (1967) Boundary value problems for elliptic equations in domains with conical or angular points. Tr. Mosk. Mat. Obs. Volume 16, pp. 209-292. V. G. Maz`ya, B. A. Plamenevskii (1974) On the coefficients in the asymptotic of solutions of elliptic boundary- value problems near conical points. Dokl. Akad, Nauk SSSR. Volume 219, Number 2, pp. 286-289. Vihak V. M., Yuzvyak N. Y., Yasinskij A. V. (1998) The solution of the plane thermoelasticity problem for a rectangular domain. Journal of Thermal Stresses. Volume 21, Issue 5. Vihak V. M., Tokovyy Yu. (2002) Construction elementary solutions of the elasticity plane problem for the rectangular domain. International applied mechanics. Volume 32, Issue 7, pp. 79-87. El Dhaba, A. R.; Abou-Dina, M. S.; Ghaleb, A. F. (2015) Deformation for a Rectangle by a Finite Fourier Transform. Journal of Computational and Theoretical Nanoscience, Volume 12, Number 1, pp. 31-37(7). Popov G., (1982) The elastic stress concentration around dies, cuts, thin, inclusions and reinforcements (in Russian), Nauka, Moscow. Popov G. Ya., Protserov Yu. S. (2016) Axisymmetric problem for an elastic cylinder of infinite length with fixed lateral surface with regard for its weight. J. Math. Sci. Volume 212, No. 1., pp. 67-82. Popov G., Vaysfeld N., Zozulevich B. (2014) The exact solution of elasticity mixed plain boundary value problem in a rectangular domain. 20-th International Conference Engineering Mechanics. Srvatka, Czech Republic. Zhuravlova Z. Yu. (2018) The plane mixed problem for an elastic semi-strip under different load types at its short edge. International Journal of Mechanical Science. Volume 144, pp. 526-530. Popov G., Vaysfeld N. (2011) The steady-one oscillations of the elastic infinite come loaded at a vertex by a concentrated force. Acta Mechanica. 221, Issue 3-4, pp. 261-270 Pozhylenkov O. V. (2019) The stress state of the rectangular elastic domain. Researches in Mathematics and Mechanics . Volume 24, № 2(34). Popov G., Abdimanapov S., Efimov V. (1999) Grin’s functions and matrixes of the one-dimensional problems. Student manual for the physical and mathematical faculties. Almaty . Gantmakher F. R. (1998) The theory of matrices. AMS Chelsea Publishing, Providence, Rohde Island.