Методика решения осесимметричных нелинейных задач для почти несжимаемых неоднородно трансверсально-изотропных гиперупругих тел вращения

Abstract

The numerical solution methodics of axisymmetric (with and without the torsion) physically and geometrically nonlinear problems for nearly incompressible piecewise-homogeneous nonhomogeneously transversely isotropic and isotropic hyperelastic bodies of revolution on the base of the variational principle of possible displacements in the increments which realized of the stepping algorithm of the finite element method was stated. The reliability of the results which received with the help of this methodics was confirmed by coincidence of numerical and analytic solutions of the linear (Lame) and nonlinear (A.I. Lurie) problems of deformation of the hollow cylinder and sphere loaded by the internal pressure. The proposed methodics was used for study of the stress-strain state of two types objects: the rubber-technical structures (armoured hose, different kinds of rubber support and shock-absorbers with restriction of the radial displacement of the rubber blocks) and mathematical model of the heart left ventricle