On One Problem of Plate Bending in the Case of a Rectangle Weakened by a Hole and Notches at the Vertices

We consider the problem of finding an equal strength contour of the bending theory plates for a rectangle weakened by a hole and notches at the vertices (unknown part of the boundary) provided that on each linear segment of the boundary a rigid bar is attached and the plate is bent by normal moments, applied to the slats in such a way that the angles of rotation of the middle surface the plates take piecewise constant values, and the unknown part of the boundary free from external efforts. The condition of the equal strength of the desired contour (the set the boundaries of holes and cutouts) is that the acting on it the tangential normal moment takes on a constant value.
By the methods of complex analysis, complex potentials expressing the deflection the mean surface of the plate and the equation of the desired equal-strength contour are constructed efficiently (analytically). The analysis of the above results in the case of square.

The authors declare no conflict of interest.

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The datasets used in this study are openly available at [repository link] and the source code is available on GitHub at [GitHub link].

This work did not receive any external funding.