Numerical Modeling of Thin Plate Bending using a Discrete Version of the Pre-Integration Method
DOI:
https://doi.org/10.71310/pcam.4_68.2025.04Keywords:
plate bending, load distribution, Chebyshev polynomials, discrete version of the preliminary integration method, high accuracy, efficiencyAbstract
Many applied problems are described by the Dirichlet problem for the Poisson equa tions. This problem is used in the following practical situations: membrane or plate deflection, electric potential, gravitational and magnetic potential, stationary tempera ture distribution (diffusion), and electron-optical systems. Although there are both direct and iterative methods for numerically solving the Poisson equation, the question of the effectiveness of using these methods remains relevant. In this work, the bending of a thin plate is studied using a discrete version of the method of preliminary integration over Chebyshev polynomials of the first kind. The proposed method is used to determine the bending of the plate. Numerical calculations are performed to demonstrate the depen dence of the bending of the plate on the distributed load, and the proposed method is shown to be highly accurate.
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