April 22, 2014
E.B. Voronkova (SPbSU)
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.
Eva B. Voronkova – PhD, Associate Professor (SPbSU).
Research interests – biomechanics, mechanics of solids.
March 25, 2014
V.V. Eliseev, E.A. Oborin (SPbSTU)
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.
Vladimir V. Eliseev – Dr. Sci. , Professor Polytechnic
University (SPbSTU). Research interests – mechanics of deformable solids.
Evgeniy A. Oborin – master student of the
Institute of metallurgy, engineering and transport SPbSTU.
Area of research interests – mechanics of rods.
March 11, 2014
O.V. Shchepilina (SPbEU "LETI")
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.
Shchepilina Olesya Valerievna – graduate student
of Applied Mechanics and Engineering Graphics Department at St. Petersburg
Electrotechnical University "LETI".
Research interests – biomechanics of the lower extremities.
The author of three published scientific papers.
Scientific director – Prof. P.I.Begun
February 25, 2014
Yu.M. Dahl (St. Petersburg State University)
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.
Yury M. Dahl – Doctor of Science (Math), Professor
of St. Petersburg State University, Honoured Scientist of Russia.
Area of research interests – mathematical methods in mechanics of solids,
linear and nonlinear theories of elasticity,
fracture mechanics.
February 11, 2014
B.V. Kostenko (PSTU)
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.
Bogdan V. Kostenko – student
of Petersburg State Transport University.
Area of research interests – mechanics of solids.
Supervisors – Asso.Prof. A.N. Bestuzheva and Prof. V.V. Egorov.
December 10, 2013
A.V. Ivchenkova (SPbSU)
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.
Alina V. Ivchenkova – Master student
of St.Petersburg State University, Faculty of Mathematics and Mechanics,
Department of Theoretical and Aplied Mechanics SPbSU.
Area of research interests – biomechanics.
Supervisor – Prof. S.M. Bauer.
November 26, 2013
E.A.Kosjakov (SPbSU)
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.
Evgeniy Kosjakov – Master student
of St.Petersburg State University, Faculty of Mathematics and Mechanics,
Department of Theoretical and Aplied Mechanics SPbSU.
Area of research interests – nonlinear mechanics
Supervisor – Prof. A.A. Tikhonov.
November 12, 2013
P.V. Trofimenko (SPbSU)
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).
Pavel Trofimenko – PhD student
of St.Petersburg State University, Faculty of Mathematics and Mechanics,
Department of Theoretical and Aplied Mechanics SPbSU.
Area of research interests – biomechanics, shell theory.
Author of 1 published paper.
Supervisor – Prof. S.M. Bauer.
October 29, 2013
A. V. Kuzmin (SPbSU)
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.
Andrey V. Kuzmin – master student
of St.Petersburg State University,
Faculty of Mathematics and Mechanics,
Department of Theoretical and Applied Mechanics.
Supervisor – Prof. S.B. Filipov.
October 15, 2013
M.V. Zaitseva (SPbSU)
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.
Marima V. Zaitseva – master student
of St.Petersburg State University,
Faculty of Mathematics and Mechanics,
Department of Theoretical and Applied Mechanics.
Supervisor – Asso.Prof. N.V. Naumova
October 1, 2013
D.V. Alchibaev (SPbSU)
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.
Daniil V. Alchibaev – master student
of St.Petersburg State University,
Faculty of Mathematics and Mechanics,
Department of Theoretical and Applied Mechanics.
Supervisor – Prof. P. E. Tovstik.
September 17, 2013
Ye. V. Pesterev (SPbSUCA)
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.
Yegor V. Pesterev – second year
PhD student at the Department of Applied Mathematics
of St. Petersburg State University of Civil Aviation (SPbSUCA)
on a specialty "Mechanics of liquid, gas and plasma". Author of
25 published papers on the filtration theory and thermodynamics.
Supervisor – Prof. E.N. Bereslavsky.
September 3, 2013
A.L. Smirnov and E.S. Pomytkina
Vibrations of a beam with variable parameters.
Evgenia S. Pomytkina
– MSc. (Math), graduated from SPbSU in 2013. Author of 1 published paper.
Supervisor – Asso. Prof. A.L. Smirnov.
Andrei L. Smirnov
– PhD, Associate Prof. at the Department of Theoretical
and Applied Mechanics SPbSU. Author papers on mechanics of thin-walled structures.