Exterior boundary value problems of elasticity in parabolic coordinates

What is it about?

The bodies bounded by the parabola are common in practice, for example, in building, mechanical engineering, biology, medicine, etc., and 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 from a practical view. The present work, by using the method of the separation of variables, states and analytically (exactly) solves the external boundary value problems of elastic equilibrium of the homogeneous isotropic body bounded by the parabola, when normal or tangential stresses are given on a parabolic border. Using MATLAB software, the numerical results and constructed graphs of the mentioned boundary value problems are obtained.

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Why is it important?

The statement and solution of boundary value problems and boundary-contact problems of elasticity are rather simplified if they examine the relevant curvilinear coordinate system. Therefore, in order to solve the boundary value problems and boundary-contact problems in areas with a curvilinear border, it is useful to consider these tasks in the corresponding curvilinear coordinate system. In the present paper the external boundary value problems are considered in a parabolic coordinate system.