Postcritical behavior of hyperelastic cylindrical shell


DOI: 10.34759/trd-2023-131-06

Аuthors

Korovaytseva E. A.

Institute of Mechanics Lomonosov Moscow State University, 1, Michurinsky prospect, Moscow, 119192, Russia

e-mail: katrell@mail.ru

Abstract

The work studies the process of local inflation of cylindrical shell made of hyperelastic materials of different types under the action of uniformly distributed pressure and axial force. Mathematical statement of the problem includes 4 quasilinear differential equations and 9 nonlinear algebraic equations. Geometrical relations of thin shells nonlinear theory are used, and for nonlinear physical relations formulation elastic potentials of different types are involved. The problem is solved using parameter differentiation method algorithm. According to this algorithm, resolving nonlinear equation system is differentiated with respect to solution continuation parameter, which leads to forming interconnected quasilinear boundary and nonlinear initial problems. These problems are solved in steps using iteration method until reaching required proximity of prognosed and corrected solutions at each parameter step. At given loading type and boundary conditions for the shell of constant thickness components of its stress-strain state will be constant along the meridian at any value of internal pressure. However it is known that at uniform inflation of cylindrical shell after reaching load critical value bulging can occur under certain conditions. For obtaining corresponding numerical result an assumption of small local thinning of shell wall was introduced. Two types of shell material were considered — neohookean and Yeoh. The diagram «pressure — relative volume change» for the case of neohookean cylinder inflation has only one maximum. Postcritical deforming of a shell with local thinning in this case differs fundamentally from the one of a shell with constant thickness. Differences are observed both in loading diagrams and character of stress-strain state components distribution along the whole meridian. Meridian of the shell with local thinning buckles at the largest part of its length. The diagram «pressure — relative volume change» for the problem of inflation of a cylinder made of Yeoh material has a local maximum and a local minimum. Distribution of stress-strain state components along the meridian remains constant both for the shell of constant and variable thickness, in the last case changing insignificantly only along the segment with local thinning. Meridian of the shell with local thinning remains straight. Thus introduction of an assumption of hyperelastic cylindrical shell local thinning for the case of loading by uniform pressure and axial force allows investigating theoretically the character of its postcritical behavior corresponding to experimentally observed one.

Keywords:

soft shell, nonlinear deforming, hyperelastic material, large deformations, postcritical behavior, parameter differentiation method

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