PROGRAM

2006 IASME / WSEAS International Conference on
CONTINUUM MECHANICS (CM'06)

Chalkida, Evia Island, Greece

co-organized by WSEAS and Technological Educational Institute of Chalkida

Sponsored by WSEAS and WSEAS Transactions

May 11-13, 2006

Thursday, May 11, 2006

Plenary Lecture I

Mathematical modelling and simulation of blood circulation

Prof. Adelia Sequeira

Department of Mathematics and CEMAT/IST

Lisbon, Portugal

adelia.sequeira@math.ist.utl.pt

Abstract: Mathematical and numerical models together with computer simulations are playing an increasingly relevant role in biology and medicine. Applications to blood flow in the human circulatory system, in normal or pathological conditions are certainly one of the major mathematical challenges of the coming decades.

Relevant features have already been addressed but many fundamental issues have still to be fully understood. Blood is a multi-component mixture of plasma (Newtonian fluid), cells (elastic membranes filled with a Newtonian fluid), platelets (elastic solids) and other matter, like inorganic and organic salts, proteins and transported substances, that is homogenized and can be modeled as a single component fluid. Blood interacts both mechanically and chemically with vessel walls producing complex fluid-structure interactions whose mathematical analysis is still incomplete and which are practically impossible to simulate in its entirety.

In large and medium vessels, blood can be considered as a Navier-Stokes liquid, at a first level of approximation. However, blood can shear-thin considerably and also exhibits viscoelastic properties that cannot be neglected, at least in small arteries where the vessel diameters are comparable with the one of blood cells. In particular the high viscosity behaviour of blood at low shear rates is due to red blood cells aggregation (into rouleaux) and low viscosity at high shear rates is a consequence of deformability of red blood cells. Also stretching of the elastic red blood cells and their consequent storage of elastic energy account for the memory effects in blood.

In this talk we address some mathematical issues arising from the modelling of the cardiovascular system through problems of different complexity. Several reduced models have been developed which may give a reasonable approximation of averaged quantities, such as mean flow rate and pressure, in different sections of the cardiovascular system. They are, however, unable to provide the details often needed for understanding a local behaviour, such as the effect on the shear stress distribution due to a modification in the blood flow consequent to a partial vessel stenosis. In particular we will specifically consider the fluid-structure interaction problem of an incompressible generalized Newtonian shear-thinning fluid flowing inside a thin compliant vessel whose walls undergo small deformations under the action of the fluid. The numerical approach is based on a finite element method for the coupling of the fluid equations in a moving domain, described in an Arbitrary Lagrangian Eulerian (ALE) frame, with a simple structural model for the vessel wall. A review of various continuum (differential and rate type) constitutive models proposed for blood flow and their numerical simulations in different geometries will also be presented in this talk.

Plenary Lecture II

On the Mathematical Problems Arising from the Motion of a Viscous Fluid Around a Rotating Body

Professor Sarka Necasova

Mathematical Institute

Academy of Sciences

Prague, Czech Republic

matus@math.cas.cz

Abstract: The motion of one or several rigid bodies in a viscous incompressible fluid has been a topic of numerous theoretical and numerical studies. Over the last 40 years the study of the motion of small particles in a viscous liquid has become one of the main focuses of the applied research. The presence of the particles affects the flow of the liquid, and in term, affects the motion of the particles, so that the problem of determining the flow characteristics is highly coupled. It is just the latter feature that makes any fundamental mathematical problem related to the liquid-particle interaction particularly challenging.

One of the mathematical aspects is the orientation of the particles in a viscous liquid. The orientation of long bodies in liquids of different nature is a fundamental issue in many problems of practical interest, for example, composite materials, separation of macromolecules of electrophoresis, ow induced microstructures. The second very interesting problem is the motion of a self-propelled body in a liquid. Typical examples are motions performed by birds, fish, rockets, submarines.

We would like to discuss the mathematical analysis of certain aspects of particle sedimentation. We assume that the liquid fills the whole space, in accordance with the fact that, as established by experiments: "wall effects" play no role on the preferred orientation of the particles. The mathematical analysis of particle sedimentation is based on the concept of free fall of a body B in a liquid L. To investigate the asymptotic behaviour of weak or strong solutions, the knowledge of the asymptotical structure of steady solutions is of the fundamental importance, and we will consider some properties of the linearized operators arising in this problem.

Plenary Lecture III

Flooding due to Sequential Dam Breaking

Professor C. D. Memos

School of Civil Engineering

National Technical University of Athens

GREECE

Abstract: The growing concern about the environmental impact due to eventual failure of civil engineering projects, encompasses cases where dam breaches can release enormous amount of water into natural watercourses. This could pose a serious threat to human life and property downstream of the failed dam. To assess the risk related to such situations a detailed description of the hydraulics of the resulting flood wave is required. However, in cases where more than one dams are present along the route of a watercourse, representation of the wave propagation is quite complex and realistic answers are difficult to be given by commercially available packages. Some of the complexities of the problem are discussed, especially those related to flood routing through a reservoir. Suggestions to overcome the difficulties are given along with a real life application to a Greek river with five dams constructed along its route.

SESSION: Applications and Computational Techniques on Continuum Mechanics

Chair: Nikolay Tutyshkin, Mihai Bugaru

SESSION: Experimental Techniques on Continuum Mechanics

Chair: Nikolay Tutyshkin, Adelia Sequeira

Friday, May 12, 2006

MINISYMPOSIUM: Mathematical Fluid Mechanics and Related Problems I

Organizer / Chair: Sarka Necasova

MINISYMPOSIUM: Mathematical Fluid Mechanics and Related Problems II

Organizer / Chair: Sarka Necasova

Saturday, May 13, 2006

Plenary Lecture III

Warping and Shear Deformation Effects in Static and Dynamic Analysis of 3-D Beam Elements

Evangelos Sapountzakis

National Technical University of Athens

Zografou Campus

Athens, GREECE

cvsapoun@central.ntua.gr

Abstract: In this speech, the static and dynamic analysis of 3-D beam elements restrained at their edges by the most general linear torsional, transverse or longitudinal boundary conditions and subjected in arbitrarily distributed static or dynamic twisting, bending, transverse or longitudinal loading is presented. For the solution of the problem at hand, a boundary element method is employed for the construction of the 14x14 stiffness matrix and the corresponding nodal load vector of a member of arbitrary homogeneous or composite cross section taking into account both warping and shear deformation effects, which together with the respective mass and damping matrices lead to the formulation of the equation of motion. To account for shear deformations, the concept of shear deformation coefficients is used, defining these factors using a strain energy approach, instead of Timoshenko’s and Cowper’s definitions, for which several authors have pointed out that one obtains unsatisfactory results or definitions given by other researchers, for which these factors take negative values. Eight boundary value problems with respect to the variable along the bar angle of twist, to the primary warping function, to a fictitious function, to the beam transverse and longitudinal displacements and to two stress functions are formulated and solved employing a pure BEM approach, that is only boundary discretization is used. Numerical results are presented to illustrate the method and demonstrate its efficiency and accuracy. The influence of the warping effect especially in composite members of open form cross section is analyzed through examples demonstrating the importance of the inclusion of the warping degrees of freedom in the analysis of a space frame. Moreover, the discrepancy of both the deflections and the internal forces of a member of a spatial structure arising from the ignorance of the shear deformation effect necessitates the inclusion of this additional effect, especially in thick walled cross section members. Moreover, free and forced transverse, longitudinal or torsional vibrations are considered, taking also into account effects of transverse, longitudinal, rotatory, torsional and warping inertia and damping resistance.

SESSION: Theoretical Methods on Continuum Mechanics

Chair: Evangelos Sapountzakis, George D. Verros