Title | Mathematical modeling of the stress-strain state of a thin isotropic plate |
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Authors | V. N. Popov^{1}, O. V. Germider^{1}^{1}Northern (Arctic) Federal University named after M.V. Lomonosov |

Annotation | A new modification of the collocation method is proposed and implemented for constructing a solution to an inhomogeneous biharmonic equation in the framework of modeling the stress-strain state of a thin isotropic plate. The proposed modification is based on the Chebyshev polynomial approximation of the mixed partial derivative of the desired function. Chebyshev polynomials of the first kind are used as basis functions. The proposed method is used to simulate the bending of an elastic isotropic plate under the action of a transverse load. An analysis is made of the results obtained by the collocation method using the integral approach and in its absence when using the zeros of Chebyshev polynomials of the first kind as collocation points. |

Keywords | Chebyshev polynomials of the first kind, collocation method, isotropic plate, stress-strain state |

Citation | Popov V. N., Germider O. V. ''Mathematical modeling of the stress-strain state of a thin isotropic plate'' [Electronic resource]. Proceedings of the XVI International scientific conference "Differential equations and their applications in mathematical modeling". (Saransk, July 17-20, 2023). Saransk: SVMO Publ, 2023. - pp. 193-197. Available at: https://conf.svmo.ru/files/2023/papers/paper31.pdf. - Date of access: 02.12.2023. |

**© SVMO, National Research Mordovia State University, 2023**

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