Sessions 2013-2014

The talk is concerned with FEM modeling using COMSOL Multiphysics (c) software. Notably, the effect of the intraocular volume (IOV) changes on intraocular pressure (IOP) is discussed. The eyeball is simulated as an ellipsoidal shell of one (representing the sclera) or two (representing the sclera and the cornea) segments. The impact of mechanical properties of the sclera and the cornea on IOP-IOV relationship is studied. Certain characteristics of COMSOL Multiphysics, like parameterized material properties and the interaction of mechanical structures with fluid flow is showed.

A general nonlinear theory of rods as material lines Cosserat and equations in the components for the plane problem are presented. A method for the numerical solution with the help of computer maths is proposed. Models of rods with tension and shear flexibility are considered. Among them there are straight rod and curved rod, which form is described analytically and by points.

The object of the research is to develop thighbone diagnostic technique after osteosynthesis with muscle activity and elasticity module (E, MPa) taken into account at every bone graft remodeling stage. The algorithm has been developed, the calculations have been carried out and the analysis and the research have been undertaken for the “thighbone-bone graft-implant” system stress and stain behavior at various rehabilitation stages. Femur model system "thighbone-bone graft-implant" when introduced assumptions built using the software Mimics, SolidWorks software package and includes bone, represented by two homogeneous isotropic layers, regenerate and implant titanium screws. According to the research, the dependences of deformation in the elements of the system from time to time under dynamic loading of the femoral head in the appropriate clinical experiment and formulated recommendations on making corrections to existing rehabilitation technologies.

Solutions of plane theory of elasticity in terms of complex functions Phi(z) and Psi(z) (two Kolosov’s formulas) were examined. The right part of the first of these formulas is the integral of equation of indissolubility, and the right part of the second formula is the integral of two equations of equilibrium. Besides classical form two different new versions of Kolosov’s relations were found. The exact solution for a periodical problem for the elastic plane with infinite cracks along a straight line are found. It is assumed that the stresses vanish at infinity and the opposite crack edges are loaded with normal concentrated forces. The existence conditions for such solution were formulated.

The statement of the initial static problem, peculiarities of the structure design, derivation of equations and methods of solution are discussed in the first part of the report. The numerical-analytical solution of the initial static problem, in which deflections and strengths depend nonlinearly on the external load, is obtained. The methods for improving the structure design and the effect of these improvements on the mathematical formulation of the problem are considered. The second part is devoted to the dynamic problem, in which the external load varies in time and space.

The simple mathematical model to study the mechanics of a pneumotonometer is developed. The problem of dynamic loading of the hollow spherical segment is analyzed.

A gravity-oriented rigid body on a circular Keplerian orbit in a central gravitational field is considered. The attitude motion of the body is affected by a perturbation torque that lends itself to a cubic approximation. With inclusion of third infinitesimal terms a new notation is obtained for the differential equations of disturbed motion which is generalization of familiar equations in canonical variations extending them to the case where both potential and nonpotential disturbing forces are operative. The form is convenient for the analysis of quasi-linear oscillations of a body about its center of mass with the use of asymptotic methods of nonlinear mechanics.

The stress strain states of transversally isotropic two-layered spherical shell under normal pressure are studied.

Solutions are obtained by using the exact 3D theory of elasticity and two approximate theories for orthotropic plates: the theory of shells of moderate thicknesses by Paliy-Spiro (PS) and the refined theory developed by Rodinova-Titaev-Chernykh (RTC).

Infinite cylindrical membrane squeezed by two planes is considered. The membrane is filled with ideal incompressible liquid. The formulas for the deformations and pressure in liquid vs. distance between the planes are obtained.

Secondly, axisymmetric deformation of the soft toroidal membrane under internal pressure is considered. The system of nonlinear differential equations describing deformation of a membrane is integrated numerically. Numerical and asymptotic results are compared.

Eigenvalues and eigenmodes of a cylindrical tank filled with liquid are calculated numerically with the FEM program complex ANSYS Workbench13. Axisymmetric vibrations of thin elastic cylindrical shell under the internal pressure of fluid flow are analyzed. Analytical formulas for calculating the components of normal and tangential deflections of the shell middle surface are obtained.

Buckling of a thin cylindrical shell of medium length made of an anisotropic material described by 21 elastic modules under normal pressure is considered. First two components of the asymptotic expansion for the buckling mode are obtained.

The filtration from the pits, which are fenced with rabbets of Zhukovsky through a soil layer consider. At the bottom of the soil is highly permeable pressure aquifer with nonpermeable site. Mixed multiparametric boundary value problem of the theory of analytic functions is formulated to study the infiltration of the free surface. The problem is solved using the Polubarinova-Cochina's method. The limiting cases are considered. They associated with the lack of one of the factors which characterize the simulated process.