Features of mathematical models construction for processes of hyperelastic shells of revolution deforming investigation

Аuthors

Dmitriev V. G.^1*, Korovaytseva E. A.^2**, Popova A. R.^1***

1. Moscow Aviation Institute (National Research University), 4, Volokolamskoe shosse, Moscow, А-80, GSP-3, 125993, Russia
2. Institute of Mechanics Lomonosov Moscow State University, 1, Michurinsky prospect, Moscow, 119192, Russia

*e-mail: vgd2105@mail.ru
**e-mail: katrell@mail.ru
***e-mail: Popova.ar@1566.ru

Abstract

The work represents mathematical models and numerical algorithms for investigation of hyperelastic thin-walled shells of revolution deforming at arbitrary generalized displacements and strains processes features. Two approaches to mathematical models construction are considered: a) the shell is considered in actual (deformed) state; b) equations are formulated for initial undeformed shell state. In the first case quasi-dynamic form of relaxation method with constructing explicit two-layer difference scheme in time of second order of accuracy is used. At this mesh analogues of equilibrium equations are replaced by the equations, coinciding in form with motion in viscous media equations. At follow load action for convergence acceleration iteration process is built in displacements of local basis u,w with the following recalculation in coordinate system referring to actual shell state. Iteration process parameters are determined from the condition of convergence and stability of difference scheme. When using the second approach solution of nonlinear boundary value problem is obtained on the basis of parameter differentiation method. In this case relations of the given boundary value problem are differentiated with respect to some preselected solution continuation parameter, in result of which a set of interconnected quasilinear boundary value and nonlinear initial problems is formed. Their solution is constructed in sequence using iterative approach. By means of numerical experiment features of hyperelastic shell of revolution stress-strain state are investigated using relations of neohookean model for cases of hinged and fixed edges. A good coincidence of the results obtained on the basis of two considered approaches is shown.

Keywords:

shells, hyperelastic materials, finite differences, nonlinear problems, relaxation method, parameter continuation method, approximation, boundary conditions

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