Comparative study of soft shells of canonical meridian forms static deforming at inflation
DOI: 10.34759/trd-2022-123-02
Аuthors
Institute of Mechanics Lomonosov Moscow State University, 1, Michurinsky prospect, Moscow, 119192, Russia
e-mail: katrell@mail.ru
Abstract
The presented work compares behavior of the soft shells of revolution with various canonical shapes of meridian (semi-sphere, cylinder, torus, cone) from the non-Hookian material at large deformations under the impact of the pressure uniformly distributed along the meridian. The shells’ sizes are being selected from the condition of the geometric sizes equity in the in terms of non-deformed shells surfaces areas.
The shells deforming is being described by the unified system of equations, applicable for any meridian construction form considered at arbitrary displacements and strains. Boundary conditions are being considered equal as well. Resulting relations of the nonlinear problem, being considered physically and geometrically, are formulated in the vector-matrix form. The problem is solved using parameter differentiation method algorithm. The initial nonlinear equation system herewith is being differentiated with respect to solution continuation parameter, which leads to interconnected quasilinear boundary and nonlinear initial problems forming. These problems are solved in steps using iteration method.
A number of features of the considered problem solution is established. In particular, for the hemispherical shell, the solution can be considered verifiable only until reaching some minimal value of pressure in supercritical area. However, from the calculations viewpoint, this problem solution possesses the highest iteration convergence rate. An ability of bearing the smallest magnitude of pressure among all the considered variants of shell meridian is characteristic for the conical shell.
For subcritical area, increasing of meridian and decreasing of circumferential strains is characteristic while approaching the fixed boundary of the shell, and for cylindrical shell, it is more intensive. Meridian and circumferential stresses in cylindrical shell exceed the ones in the spherical shell on the largest part of the meridian. In the toroid shell, stresses as well as strains remain minimal.
In supercritical area, the meridian strains in cylindrical and spherical shells decrease while the fixed boundary approaching. Strains in cylindrical shell become the smallest ones, and meridian strains in the toroid shell are the largest. Similar behavior is being observed for the stresses distribution along the meridian.
Keywords:
soft shell, hyperelastic material, large deformations, parameter differentiation methodDownload