Abstract
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 < R/r < 1) in problems of trans-verse bending, free oscillations and stability of plates.
Highlights
For the past 20 ... 25 years, the scientific school in Orel technical university
Several effective engineering methods for solving these problems have been developed, among them: the isoperimetric method (ISPM) [1, 2], the method of interpolation by the form factor (MIFF) [3, ..., 6], the method of interpolation with respect to the conformal radii (MIRCR) [7, 8]. Developing these methods, a functional relationship was established between the integral physical characteristics in the problems under consideration with integral geometric parameters of the plates
We investigate another geometric parameter – the ratio R / r (R is the maximum radius of the circle inscribed in the given region of the plate, r is the minimum radius of the circle circumscribed around it)
Summary
For the past 20 ... 25 years, the scientific school in Orel technical university Several effective engineering methods for solving these problems have been developed, among them: the isoperimetric method (ISPM) [1, 2], the method of interpolation by the form factor (MIFF) [3, ..., 6], the method of interpolation with respect to the conformal radii (MIRCR) [7, 8] Developing these methods, a functional relationship was established between the integral physical characteristics in the problems under consideration (maximal deflection w0, fundamental oscillation frequency ω, critical force with loss of stability N0 plates, the geometric stiffness given of the cross section of the twisting rod) with integral geometric parameters of the plates (form factor Кf, the ratio of conformal radii r r ). The magnitude of the integral physical characteristics, their behavior under various geometric transformations of the contour of the given plates (sections) are judged by the magnitude and behavior of the integral geometric characteristics, which are described by elementary analytical dependences
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