Numerical and analytical solution of the problem on deformation of the circular cylinder using the Bessel functions https://doi.org/10.33108/visnyk_tntu2018.02.079
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Abstract
The elastic deformation of the plate in the form of a circular cylinder under the action of a smooth stamp contacting with the plate along the entire surface of the upper base is considered. The work deals with the finding of the critical areas of a deformed circular cylinder, undergoing a constant axial deformation
under the action of the compressive load. The top of the cylinder is pressed by a smooth, absolutely rigid parabolic stamp that moves vertically and contacts with the entire top of the cylinder. Lower base is free of loads. As a criterion of strength the Mises energy hypothesis is taken. The Eri function is represented in a trigonometric form using the Bessel functions of zero and first order. The analytical formulas for components of the stress tensor for the investigated body of rotation are obtained, as well as the function of the potential energy of the form-change
in accordance with the Mises energy hypothesis. The adequacy of the constructed mathematical model is checked by the method of finite elements.
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