Study of deflected mode of ellipse and ellipse weakened with crack

What is it about?

The principal outcomes of the present paper can be summarized as follows: 1. Mathematical modeling of the boundary value problem of the theory of elasticity for the elliptic body with an internal crack by setting a problem in the elliptic coordinate system. 2. Reduction of the solution of the set problem to the solutions of the relevant, internal and external problems, which can be solved analytically quite simply by the method of separation of variables. 3. Obtaining the numerical values of the components of stress tensor and displacement vector at the points of the ellipse and the ellipse weakened by an internal crack; visualization and discussion of some obtained results.

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Why is it important?

As the bodies of an elliptic shape are common in practice, e.g. in building, mechanical engineering, biology, medicine, etc., the study of the deformed mode of such bodies is topical and consequently, in my opinion, setting the problems considered in the article and the method of their solution is interesting in a practical view.