All you need is Love (and Kirchhoff).

Biomechanical simulations using COMSOL Multiphysics software.

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.

Theory and calculation of large elastic deformations
of flat rods with tension and shear.

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 dynamic analysis of the state of the
«thighbone-bone graft-implant» in rehabilitation period

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.

About Kolovos’s formulas in the plane theory of elasticity .

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.

Development of the method of analysis of the combined truss rod systems.

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.

Deformation of a spherical segment under dynamic loading
(the elementary model of a pneumotonometer)

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.

Differential equations for librational
motion of gravity-oriented rigid body.

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.

Nonclassical shell theories for the analysis of
transversally isotropic spherical
layers under normal pressure.

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).

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).

Large deformations of membranes under action of internal pressure.

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.

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.

Mathematical Modelling of cylindrical
shell vibrations under the internal pressure of fluid flow.

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 cylindrical anisotropic shell under
normal pressure.

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 construction pits fenced with rabbets.

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.

Vibrations of a beam with variable parameters.