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Analytical bending solutions of thin plates by two‐dimensional generalized integral transform method
Author(s) -
Qian Xu,
Jinghui Zhang,
Ullah Salamat,
Yang Zhong,
Litao Geng
Publication year - 2021
Publication title -
zamm ‐ journal of applied mathematics and mechanics / zeitschrift für angewandte mathematik und mechanik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 51
eISSN - 1521-4001
pISSN - 0044-2267
DOI - 10.1002/zamm.202000246
Subject(s) - integral transform , mathematical analysis , mathematics , superposition principle , integral equation , algebraic equation , partial differential equation , bending , boundary value problem , physics , nonlinear system , quantum mechanics , thermodynamics
Abstract In this paper, analytical bending solution of a rectangular thin plate with different boundary conditions was obtained by using the two‐dimensional generalized finite integral transform method. During the solution procedure, the vibrating beam functions satisfying different boundary conditions of the plate are taken as integral kernels to form the integral transform pairs. This two‐dimensional integral transform is used to the partial differential governing equations of the plate, to transform them to a system of linear algebraic equations from which the accurate analytical solution is obtained easily. The superiority of the present method is that it does not need to seek the deformation function in advance, and avoids the complex superposition processes. Thus, the proposed method is reasonable and feasible. The good agreement of present results and the analytical solution from the literature shows the validity of the method.