Исследование НДС толстостенной гиперупругой эллипсоидальной оболочки с относительно жесткими включениями (модель левого желудочка сердца)

Abstract

The geometrically and physically nonlinear statical axisymmetric problem for the investigation of the stressstrain state of the hyper-elastic thick-wall ellipsoid loaded by the internal pressure (the model of a left ventricle heart in the diastole) was formulated. The model comprises two relatively hard inclusions (the base of the heart and the infarction zone). The problem was solved by developing the variational principle of possible displacements in the increments, which was used in the step-by-step algorithm of the finite element method. Influence of the kind and dimensions of the infarction zone on the stress intensity and also dependence of the end-diastolic volume of the left ventricle on the infarction zone volume was studied. It was determined that the maximum values of the stress intensity arises by the endocardial inclusion and increases with the angle of the infarction zone; increase of the angle of the infarction zone decreases the end-diastolic volume, the minimum volume arises by the endocardial inclusion.