Full-strength contour finding problems

Author: Konstantin Demurchev
Co-authors: d.tskhondia, i.sukhishvili
Keywords: Full-strength, Contour, Elasticity, Stress
Annotation:

Abstract The paper addresses partially unknown boundary problems (full-strength contours finding problems) of plane elasticity theory and plate bending. Tangential normal stresses whose values depend on external loads and hole shapes play an important role in the plasticity zone formation in the plates with the holes and also in the plate destruction in the neighborhood to the plate's hole boundary. Proceeding from the above -mentioned, the following tasks were assigned: in conditions of provided external loads the shapes of the holes in plates should be chosen so that on the boundaries tangential normal stresses module's maximal value will be the same and minimal in the same body in all other possible holes tangential normal stresses maximal value of module. It's proven that for infinite domains tangential normal stresses the minimum of maximal value will be obtained on such contours, where this value maintains the constant value. These contours are named full-strength contours.The solvability of these problems provides controlling stress optimal distribution selecting the appropriate hole boundary. Using the methods of complex analysis the unknown full-strength contour and stressed state of the body are determined. Numerical analysis are performed and the corresponding graphs are constructed by Java and Wolfram Mathematica. The project involves reflection in the virtual world of body deformation which happened under the force action, and a service creation that provide with information on the characteristics of this event and also on the outcome.

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