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Mathematical and numerical modelling of piezoelectric sensors

Sebastien Imperiale, Patrick Joly (2012)

ESAIM: Mathematical Modelling and Numerical Analysis

The present work aims at proposing a rigorous analysis of the mathematical and numerical modelling of ultrasonic piezoelectric sensors. This includes the well-posedness of the final model, the rigorous justification of the underlying approximation and the design and analysis of numerical methods. More precisely, we first justify mathematically the classical quasi-static approximation that reduces the electric unknowns to a scalar electric potential. We next justify the reduction of the computation...

Mathematical and numerical modelling of piezoelectric sensors

Sebastien Imperiale, Patrick Joly (2012)

ESAIM: Mathematical Modelling and Numerical Analysis

The present work aims at proposing a rigorous analysis of the mathematical and numerical modelling of ultrasonic piezoelectric sensors. This includes the well-posedness of the final model, the rigorous justification of the underlying approximation and the design and analysis of numerical methods. More precisely, we first justify mathematically the classical quasi-static approximation that reduces the electric unknowns to a scalar electric potential. We next justify the reduction of the computation...

Mathematical modeling and simulation of flow in domains separated by leaky semipermeable membrane including osmotic effect

Jaroslav Hron, Maria Neuss-Radu, Petra Pustějovská (2011)

Applications of Mathematics

In this paper, we propose a mathematical model for flow and transport processes of diluted solutions in domains separated by a leaky semipermeable membrane. We formulate transmission conditions for the flow and the solute concentration across the membrane which take into account the property of the membrane to partly reject the solute, the accumulation of rejected solute at the membrane, and the influence of the solute concentration on the volume flow, known as osmotic effect. The model is solved...

Mathematical modeling of delamination and nonmonotone friction problems by hemivariational inequalities

Charalambos C. Baniotopoulos, Jaroslav Haslinger, Zuzana Morávková (2005)

Applications of Mathematics

The paper deals with approximations and the numerical realization of a class of hemivariational inequalities used for modeling of delamination and nonmonotone friction problems. Assumptions guaranteeing convergence of discrete models are verified and numerical results of several model examples computed by a nonsmooth variant of Newton method are presented.

Mathematical modelling and numerical solution of swelling of cartilaginous tissues. Part I: Modelling of incompressible charged porous media

Kamyar Malakpoor, Enrique F. Kaasschieter, Jacques M. Huyghe (2007)

ESAIM: Mathematical Modelling and Numerical Analysis

The swelling and shrinkage of biological tissues are modelled by a four-component mixture theory in which a deformable and charged porous medium is saturated with a fluid with dissolved ions. Four components are defined: solid, liquid, cations and anions. The aim of this paper is the construction of the Lagrangian model of the four-component system. It is shown that, with the choice of Lagrangian description of the solid skeleton, the motion of the other components can be described in terms of...

Mathematical modelling of cable stayed bridges: existence, uniqueness, continuous dependence on data, homogenization of cable systems

Josef Malík (2004)

Applications of Mathematics

A model of a cable stayed bridge is proposed. This model describes the behaviour of the center span, the part between pylons, hung on one row of cable stays. The existence, the uniqueness of a solution of a time independent problem and the continuous dependence on data are proved. The existence and the uniqueness of a solution of a linearized dynamic problem are proved. A homogenizing procedure making it possible to replace cables by a continuous system is proposed. A nonlinear dynamic problem connected...

Mathematical modelling of rock bolt reinforcement

Runt, David, Novotný, Jaroslav, Pruška, Jan (2017)

Programs and Algorithms of Numerical Mathematics

Rock bolts as construction elements are often used in underground civil engineering projects. This work deals with their numerical modelling. Aydan special finite elements for the description of rock bolts and hexahedral quadratic finite elements for the description of rock massif were used. A code for the computation of stiffness matrices and right hand sides of these elements was developed. The code was tested on several simple test examples and their results were compared with the analytical...

Mathematical modelling of rock bolt systems. I

Josef Malík (1998)

Applications of Mathematics

The main goal of the paper is to give a variational formulation of the behaviour of bolt systems in rock mass. The problem arises in geomechanics where bolt systems are applied to reinforce underground openings by inserting steel bars or cables. After giving a variational formulation, we prove the existence and uniqueness and some other properties.

Mathematical modelling of rock bolt systems. II

Josef Malík (2000)

Applications of Mathematics

The main goal of the paper is to describe a reinforcement consisting of fully grouted bolts, which is applied to stabilizing underground openings and tunnels. After a variational formulation is given, the existence and uniqueness is proved. Some asymptotic results that make it possible to replace the real system with a continuous one more suitable for discretization are presented. Some other types of reinforcements and properties are studied.

Mathematical models of suspension bridges

Gabriela Tajčová (1997)

Applications of Mathematics

In this work we try to explain various mathematical models describing the dynamical behaviour of suspension bridges such as the Tacoma Narrows bridge. Our attention is concentrated on the derivation of these models, an interpretation of particular parameters and on a discussion of their advantages and disadvantages. Our work should be a starting point for a qualitative study of dynamical structures of this type and that is why we have a closer look at the models, which have not been studied in literature...

Mathematical study of an evolution problem describing the thermomechanical process in shape memory alloys

Pierluigi Colli (1991)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

In this paper we prove existence, uniqueness, and continuous dependence for a one-dimensional time-dependent problem related to a thermo-mechanical model of structural phase transitions in solids. This model assumes the free energy depending on temperature, macroscopic deformation and also on the proportions of the phases. Here we neglect regularizing terms in the momentum balance equation and in the constitutive laws for the phase proportions.

Mathematical treatment for thermoelastic plate with a curvilinear hole in S-plane

Alaa A. El-Bary (2006)

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

The Cauchy integral method has been applied to derive exact and closed expressions for Goursat's functions for the first and second fundamental problems for an infinite thermoelastic plate weakened by a hole having arbitrary shape. The plate considered is conformally mapped to the area of the right half-plane. Many previous discussions of various authors can be considered as special cases of this work. The shape of the hole being an ellipse, a crescent, a triangle, or a cut having the shape of a...

Mathematically Modelling The Dissolution Of Solid Dispersions

Meere, Martin, McGinty, Sean, Pontrelli, Giuseppe (2017)

Proceedings of Equadiff 14

A solid dispersion is a dosage form in which an active ingredient (a drug) is mixed with at least one inert solid component. The purpose of the inert component is usually to improve the bioavailability of the drug. In particular, the inert component is frequently chosen to improve the dissolution rate of a drug that is poorly soluble in water. The construction of reliable mathematical models that accurately describe the dissolution of solid dispersions would clearly assist with their rational design....

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