2. Discretization of Partial Differential Equations [chapter]

2003 Iterative Methods for Sparse Linear Systems  
The flexible elastic rotationally symmetric round plate with constant thickness h, which is being under the shearing distributed load along the circle, is examined. The obtaining of the analytical solution regarding the rotationally symmetric bending flexure of the round flexible elastic plate described by the non-linear system of differential equations is mathematically difficult. Thereupon the use of the method of partial discretization of differential equations, developed by one of the
more » ... s of the article, was found to be appropriate. At the same time in the class of aggregated functions the solution of the concerned task is obtained and the curve of the plate's bending flexure is depicted. The comparison of curves built using the relatively simple differential equations showed their almost full coincidence. Also the expressions of the rotation angle, stress, bending moments and discontinuous forces are found. The solutions for different rules on distribution of shearing load and boundary conditions are demonstrated. The obtained results are new in the theory of the bending flexure of the thin elastic plates.
doi:10.1137/1.9780898718003.ch2 fatcat:vlx2cxq4gvekrlmxh7tjrxabt4