COMPARISON OF ANALYTICAL AND NUMERICAL SOLUTIONS TO THE STRESSES PROBLEM IN A CYLINDRICAL SHELL WITH A CIRCULAR HOLE

• DOI: 10.37572/EdArt_2402237437

• Palavras-chave: Shell Theory, Cylindrical Shell, Circular Cutout

• Keywords: Shell Theory, Cylindrical Shell, Circular Cutout

• Abstract:

  In recent works, Kashtanova and Rzhonsnitskiy [1,2] reconsidered the classical approach to the solution of the problem of cylindrical shell a circular cutout under an axial tension. The protagonist of this problem is a certain geometric parameter that contains the ration between the radius of the hole, the radius of the cylindrical shell and the shell thickness. When this parameter is equal to zero, we have a plane problem (the Kirsch problem in case when the boundary condition is an axial tension). There were several reasons that forced us to look for a different approach: a very small range of applicability of the solution (close to Kirsch problem), a linear dependency in the system for finding coefficients for basis function, different results in the literature, a failure of the limit transition, no explicit formulas for the field of stresses and no opportunity to make an analytical analysis. The classical way was to decompose the solution and the coefficients into small parameter   , which immediately put restrictions on the range of applicability. The authors of the present paper offered to decompose the solution into Fourier series and to divide variables [1], then they found and exclude a linear-dependent equation and after some substitution of variables proofed the reducibility of the infinite system [2]. This method allows getting a model in range of    up to 4. In this paper this idea, in addition to axial tension, is applied to other boundary conditions: internal pressure and torsion. The comparison of analytical and numerical results by collocation method that were received by Van Dyke [4] is described.

• Número de páginas: 5