Determination of the stressed state of rectangular anisotropic plates in the space statement
We consider the problem of the stress-strain state of rectangular anisotropic plates in the space statement for one plane of elastic symmetry. The initial problem is described by a system of three partial differential equations of the second order. After separating variables and by using the spline-collocation method in two coordinate directions, we reduce the problem to a system of ordinary differential equations of high order with boundary conditions on edges. The obtained boundary-value problem is solved by the stable discrete-orthogonalization method. Results for the cases of rigid attachment and hinged support and for different geometries of plates are presented.
KeywordsEnglish Translation Elastic Symmetry Anisotropic Body Orthotropic Body Hinge Support
Unable to display preview. Download preview PDF.
- 1.A. Ya. Grigorenko, T. L. Efimova, and L. V. Sokolova, “On the investigation of free vibrations of nonthin cylindrical shells of variable thickness by the spline-collocation method,” Mat. Met. Fiz.-Mekh. Polya, 53, No. 4, 169–179 (2010); English translation: J. Math. Sci., 53, No. 4, 506–519 (2012).CrossRefGoogle Scholar
- 3.S. G. Lekhnitskii, Theory of Elasticity of an Anisotropic Body [in Russian], Nauka, Moscow (1977).Google Scholar
- 4.A. K. Malmaister, V. P. Tamuzh, and G. A. Teters, Strength of Polymeric and Composite Materials [in Russian], Zinatne, Riga (1980).Google Scholar
- 5.B. E. Pobedrya and S V. Sheshenin, “Some problems of the equilibrium of an elastic parallelepiped,” Izv. Akad. Nauk SSSR, Ser. Mekh. Tverd. Tela, No. 1, 74–86 (1981).Google Scholar
- 6.N. N. Suslova, “Methods for solving the space problem of the theory of elasticity for a body in the form of parallelepiped,” Itogi Nauki Tekhn., Ser. Mekh. Tverd. Deform. Tela, 13, 187–296 (1980).Google Scholar
- 11.A. Ya. Grigorenko, T. L. Efimova, and I. A. Loza, “Solution of an axisymmetric problem of free vibrations of piezoceramic hollow cylinders of finite length by the spline collocation method,” Mat. Met. Fiz.-Mekh. Polya, 51, No. 3, 112–120 (2008); English translation: J. Math. Sci., 165, No. 2, 290–300 (2010).CrossRefGoogle Scholar
- 13.A. Ya. Grigorenko, W. H. Müller, R. Wille, and S. N. Yaremchenko, “Numerical solution of the problem of the stress-strain state in hollow cylinders by means of spline approximations,” Mat. Met. Fiz.-Mekh. Polya, 53, No. 3, 127–134 (2010); English translation: J. Math. Sci., 180, No. 2, 135–145 (2012).MathSciNetCrossRefGoogle Scholar
- 15.Ya. M. Grigorenko, A. Ya. Grigorenko, and G. G. Vlaikov, Problems of Mechanics for Anisotropic Inhomogeneous Shells on the Basis of Different Models [in Russian], Akademperiodika, Kiev (2009).Google Scholar