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The paper considers the dimensionless geometric characteristic  R /r ( R  is the maximum radius of a circle inscribed in a given region, r is the minimum radius of a circle circumscribed around it), which is used as a geometric analogue of integral characteristics in problems of the technical theory of plates and theory of elasticity. By numerical experiment the authors showed that using this characteristic as the only argument made it possible to approximate with one elementary function all the solutions for short plates, which satisfied the condition (0.5 &lt;  R /r &lt; 1) in problems of trans-verse bending, free oscillations and stability of plates.

The approximate method of determining the integral physical characteristics in some problems of technical theory of plates