Bending of a Clamped Thin Circular Plate Having a Rigid Square Column on Its Center

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In spite of the practical importance, the solutions for the title problem under the action of various loadings have not been obtained. In this paper, based on the classical theory, and changing the geometry of plate, the following three cases are treated. The plate is bent under the action of (a) the vertical force by the column, (b) the moment by the column, and (c) a uniformly distributed load respectively. The construction of solution is based on the principle of superposition. The boundary conditions are satisfied by the Lekhnitski-Muskhelishvili's method on the internal contour and by the point matching method on the external. The following conclusions are obtained. (1) The point matching method is sufficiently effective. (2) Using the values nondimensionalized with respect to a side length of the square, the influence of the geometry on the stress concentration is the largest in (c) and the smallest in (b), and so on.
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