On applications of distributions to analysis of circular plate design elements

Abstract eng:
The mathematical model of a circular plate according to Kirchhoff’s theory contains classical derivatives of internal forces, moments, slopes of a middle surface and deflection. However these derivatives are not defined at such internal points of middle plane where a line lateral loading, a line moment loading, a line support, or a rotational coupling between plate segments is situated. We have used the distributional derivatives for the unknown discontinuous functions, and developed a generalized mathematical model in the form of a system of ordinary differential equations in order that the mathematical model of the circular plate subjected to axisymmetric loading may be valid also along the lines of discontinuity mentioned, which are common in calculating experience. We have found a general solution to the generalized system of differential equations by means of a symbolic programming approach using Maple.

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