For citation:
Kaloerov S. A., Zanko A. I. Bending of Multiconnected Anisotropic Plates with the Curvilinear Holes. Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, 2016, vol. 16, iss. 4, pp. 456-464. DOI: 10.18500/1816-9791-2016-16-4-456-464, EDN: XHPYJL
Bending of Multiconnected Anisotropic Plates with the Curvilinear Holes
An approximate method for determination of the stress state of thin plates with curvilinear holes, consisting in the use of the complex potential theory of bending of anisotropic plates, approximating the contours of holes by ellipse arcs and straight sections, the use of conformal mapping, presentation of complex potentials by Laurent series and determining the unknown series coefficients of the generalized least squares method. Isotropic plates are considered as a special case of anisotropic plates. Numerical studies carried out for plates with square or triangular holes. Studies have established a high degree of accuracy of the results. Significant differences were noted in the literature known from the real results obtained by this approach.
- Lekhnitskii S. G. Anisotropic Plates. New York, Springer-Verlag, 1984, 546 p.
- Kosmodamianskii A. S. Napriazhennoe sostoianie anizotropnykh sred s otverstiiami ili polostiami [Stressed state of anisotropic media with holes or cavities]. Donetsk, Vishcha shk., 1976, 200 p. (in Russian).
- Meglinskii V. V. Nekotorye zadachi izgiba tonkikh mnogosviaznykh anizotropnykh plit [Some problems of bending of thin multi-connected anisotropic plates]. Nekotorye zadachi teorii uprugosti o kontsentratsii napriazhenii i deformatsii uprugikh tel : sb. nauch. tr. [Some problems of elasticity theory about stress concentration and deformation of elastic bodies. Collection of Papers], Saratov, Saratov Univ. Press, 1967, iss. 3, pp. 97–127 (in Russian).
- Savin G. N. Raspredelenie napriazhenii okolo otverstii [Stress distribution near the holes]. Kiev, Nauk. dumka, 1968, 887 p. (in Russian).
- Kaloerov S. A., Gorianskaia E. S. Dvumernoe napriazhenno-deformirovannoe sostoianie mnogosviaznogo anizotropnogo tela [Thфe twodimensional stress-strain state of a multi-connected anisotropic body]. Kontsentratsiia napriazhenii. Mekhanika kompozitov : v 12 t. [The mechanics of composites. Stress concentration]. Kiev, A. S. K., 1998, vol. 7, pp. 10–26 (in Russian).
- Kaloerov S. A., Dobriak D. A. Termouprugoe sostoianie kusochno-odnorodnoi anizotropnoi plastinki [Thermoelastic state of piecewise-homogeneous anisotropic plate]. Visn. Donets. un-tu, Ser. A, Prirod. nauki [Bulletin of Donetsk University, Series A, Natural Sciences], 2006, iss. 2, pp. 77–88 (in Russian).
- Kaloerov S. A. Kompleksnye potentsialy teorii izgiba mnogosviaznykh anizotropnykh plit [Complex potentials the theory of bending of multi-connected anisotropic plates].Teoret. i prikladnaia mekhanika [Theoretical and Applied Mechanics], 2012, no. 4 (50), pp. 115–136 (in Russian).
- Kaloerov S. A., Avdiushina E. V., Mironenko A. B. Kontsentratsiia napriazhenii v mnogosviaznykh izotropnykh plastinkakh [Stress concentration in multi-connected anisotropic plates]. Donetsk, DonNU Press, 2013, 440 p. (in Russian).
- Forsaythe G. E., Malcolm M. A., Moler C. B. Computer methods for mathematical computations. New Jersey, Prentice-Hall, 1977, 280 p.
- Kosmodamianskii A. S., Kaloerov S. A. Temperaturnye napriazheniia v mnogosvi-aznykh plastinkakh [Thermal stresses in multi-connected plates]. Kiev, Donetsk, Vishcha shk., 1983, 160 p. (in Russian).
- Kosmodamianskii A. S., Mitrakov V. A. Izgib konechnoi anizotropnoi plastinki s krivolineinym otverstiem [Bend of finite anisotropic plate with a curvilinear hole]. Prikladnaia mekhanika [Applied Mechanics], 1976, vol. 12, no. 12, pp. 96–99 (in Russian).
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