Polyaniline was chemically synthesized at three different temperatures of 25, 0, and -25oC, by oxidative polymerization with ammonium peroxidisulfate at equimolar of aniline to oxidant ratio and 1M HCl. The resulted polyaniline was in a powder form which was characterized by several techniques such as: electrical conductivity, elemental analysis, thermal analysis, wide-angle X-Ray diffraction, and scanning electron microscope. The solution properties of the reduced polymer were studied by viscometry, static and dynamic light scattering. It was found that as the polymerization temperature decreased, the molecular weight, crystallinity, and thermal stability of polyaniline increased, while the electrical conductivity was independent of the polymerization temperature. Moreover, the morphology of the polymer was changed from granular to tubular with reducing polymerization temperature. Viscometry and static light scattering showed that polyaniline has a flexible random coil conformation when dissolved in N-methyl-2-pyrrolidinone which proved to be a good solvent for this polymer. Dynamic light scattering indicated that the polymer solution is a polyelectrolyte with high hydrodynamic radius at low polymer concentrations. All mechanical features except Young&#039 / s modulus of polyaniline-filled low density polyethylene composites became poorer as polyaniline content increased. Moreover, a sudden increase in the electrical conductivity with increasing polyaniline contents was also observed. The conductivity of the tubular composites of multi wall nanotubes (MWNTs)-filled polyaniline increased with increasing MWNTs loading, and became weakly temperature dependent. The morphological analysis indicated that the MWNTs were well dispersed and isolated, and the tubes became crowded proportionally to MWNTs weight percent used in the composites.

Condition monitoring of critical machinery has many economic benefits. The primary objective is to detect faults, for example on rolling element bearings, at an early stage to take corrective action prior to the catastrophic failure of a component. In this context, it is important to be able to discriminate between stable and deteriorating fault conditions. A number of conventional vibration analysis techniques exist by which certain faults in rotating machinery may be identified. However, under circumstances involving multiple fault conditions conventional condition monitoring techniques may fail, e.g. by indicating deteriorating fault conditions for stable fault situations or vice versa. Condition monitoring of rotating machinery that may have multiple, possibly simultaneous, fault conditions is investigated in this thesis. Different combinations of interacting fault conditions are studied both through experimental methods and simulated models. Novel signal processing techniques (such as cepstral analysis and equidistant Fourier transforms) and pattern recognition techniques (based on the nearest neighbour algorithm) are applied to vibration problems of this nature. A set of signal processing and pattern recognition techniques is developed for the detection of small incipient mechanical faults in the presence of noise and dynamic load (imbalance). In the case investigated the dynamic loading consisted of varying degrees of imbalance. It is demonstrated that the proposed techniques may be applied successfully to the detection of multiple fault conditions. / Thesis (Ph.D. (Electronical Engineering))--North-West University, Potchefstroom Campus, 2004.

Tyrimo objektas: pacientų, persirgusių galvos smegenų insultu pusiausvyra. Problema: Lietuvoje klinikinėje praktikoje nėra plačiai taikomi pusiausvyrą vertinantys testai ar skalės. Darbo tikslas: įvertinti pusiausvyros testų informatyvumą pacientams, persirgusiems galvos smegenų insultu. Uždaviniai: įvertinti pacientų pusiausvyros sutrikimus Bergo, Brunelio pusiausvyros bei liemens kontrolės įvertinimo skalėmis praėjus 2, 4, 6 savaitėm po insulto bei palyginti šių skalių rodiklius. Tyrimo metodika: naudojant Bergo ir Brunelio pusiausvyros bei liemens kontrolės įvertinimo skales buvo vertinama pacientų, persirgusių išeminiu smegenų insultu, pusiausvyros sutrikimai ir jos pokyčiai reabilitacijos eigoje. Tyrimo duomenys statistiškai buvo apdoroti naudojantis kompiuterine programa SPSS 13,0 for Windows. Rezultatai: testuojant ligonius liemens kontrolės įvertinimo skale po 2 savaičių nagrinėjamos funkcijos vidutiniškai sudarė 48,2%, po 4 savaičių 76,8%, o po 6 – 91,8% maksimalios balų sumos (p<0,05). Bergo skalės rezultatai po 2 savaičių tesudarė 17,8%, po 4 savaičių nagrinėjamo rodiklio vidutinė reikšmė ženkliai padidėjo ir tapo lygi 37,3%, o po 6 savaičių registruota reikšmė buvo didesnė (p<0,05) nei po 4 savaičių ir sudarė 59,2%. Brunelio skalės vertinimo rezultatų kaita po 2 savaičių buvo 26,3%, po 4 savaičių tiriamųjų pateiktų užduočių vertinimas siekė 54,2%, o tyrimo pabaigoje – 72,5% (p<0,05). Išvados: 1. Liemens kontrolės įvertinimo skalės didžiausias pusiausvyros... [toliau žr. visą tekstą] / Object of the study: balance of patients after stroke. Problem of the study: there are no widely used balance tests and scales in the clinical practice in Lithuania. Aim of the study: to evaluate informative of balance scales for patients after stroke. Objectives: to evaluate balance disability of patients after stroke during 2, 4, 6 weeks with Brunel, Berg balance and postural assessment scales and compare their indexes. Methods: balance disability was measured with the use of the trunk control and balance items of the Postural Assessment, Berg’s and Brunel’s balance scales for patients after stroke. Research data was analyzed using SPSS 13,0 for Windows. Results: the results of postural assessment scale for stroke patients after 2 weeks post stroke average makes 48,2%, after 4 weeks it was 76,8%, and the last – 91,8% of maximal total points (p<0,05). Evaluation of Berg balance scale after 2 weeks reach 17,8%, after 4 weeks indexes value improve a lot and makes 37,3%, after 6 weeks this value was bigger and makes 59,2% (p<0,05). The results fluctuation of Brunel balance scale after 2 weeks were 26,3%, after 4 weeks improve twice – 54,2% and 72,5% in the end of evaluation. Conclusions: 1. The biggest improvement of balance of postural assessment scale for stroke patients observed after 2 stroke weeks, between 2-6 weeks – gradually slow down, but approach maximal indexes in the end of the search. 2. Berg balance scale indexes during three evaluations improve gradually, though... [to full text]

This paper is the first to explicitly test for the presence of a trade-off between static and dynamic efficiency in a regulated industry, the electricity industry. We show for 16 European countries over the period 1998-2007 that higher electricity end-user prices in a country subsequently lead to higher investments in the capital stock, i.e. in generation, distribution and transmission assets. Moreover, there is a trade-off between vertical economies and competition. Ownership unbundling and forced access to the incumbent transmission grid increase competition but come at the cost of lost vertical economies. Generally, we find that regulation that affect only the market like the establishment of a wholesale market or free choice of suppliers increase investment activity via spurring competition. Regulation, however, that adversely affects the incumbent directly, like ownership unbundling, decreases aggregate investment spending. (author's abstract) / Series: Working Papers / Research Institute for Regulatory Economics

Condition monitoring of critical machinery has many economic benefits. The primary objective is to detect faults, for example on rolling element bearings, at an early stage to take corrective action prior to the catastrophic failure of a component. In this context, it is important to be able to discriminate between stable and deteriorating fault conditions. A number of conventional vibration analysis techniques exist by which certain faults in rotating machinery may be identified. However, under circumstances involving multiple fault conditions conventional condition monitoring techniques may fail, e.g. by indicating deteriorating fault conditions for stable fault situations or vice versa. Condition monitoring of rotating machinery that may have multiple, possibly simultaneous, fault conditions is investigated in this thesis. Different combinations of interacting fault conditions are studied both through experimental methods and simulated models. Novel signal processing techniques (such as cepstral analysis and equidistant Fourier transforms) and pattern recognition techniques (based on the nearest neighbour algorithm) are applied to vibration problems of this nature. A set of signal processing and pattern recognition techniques is developed for the detection of small incipient mechanical faults in the presence of noise and dynamic load (imbalance). In the case investigated the dynamic loading consisted of varying degrees of imbalance. It is demonstrated that the proposed techniques may be applied successfully to the detection of multiple fault conditions. / Thesis (Ph.D. (Electronical Engineering))--North-West University, Potchefstroom Campus, 2004.

Tyrimo problema: Apie 2,5 mln. žmonių visame pasaulyje serga išsėtine skleroze. Lietuva priklauso didelio sergamumo išsėtine skleroze zonai (Kizlaitienė, 2008). Vienas iš pagrindinių simptomų, pasireiškiančių ankstyvoje šios ligos stadijoje, yra pusiausvyros sutrikimas (Prosperini et al., 2010; Cameron et al., 2008; Martin, Phillips, 2006). Darbo aktualumas: Kinezioteipas yra lengvai prieinama ir neivazinė priemonė, galinti pagerinti sergančiųjų išsėtine skleroze statinę ir dinaminę pusiausvyrą, gyvenimo kokybę, sumažinti griuvimų riziką. Tyrimo hipotezė: Kinezioteipas, užklijuotas ant dvilypio ir priekinio blauzdos raumens, gali pagerinti sergančiųjų išsėtine skleroze statinę ir dinaminę pusiausvyrą. Tyrimo tikslas: Nustatyti kinezioteipo poveikį sergančiųjų išsėtine skleroze statinei ir dinaminei pusiausvyrai. Tyrimo uždaviniai: 1. Įvertinti tiriamųjų statinę ir dinaminę pusiausvyrą su kinezioteipu, užklijuotu ant dvilypio ir priekinio blauzdos raumens funkcine korekcine technika. 2. Įvertinti tiriamųjų statinę ir dinaminę pusiausvyrą su kinezioteipu, užklijuotu placebo ant keturgalvio raumens. 3. Įvertinti skirtingų kinezioteipavimo technikų efektyvumą tiriamųjų statinei ir dinaminei pusiausvyrai. Tyrimo metodai: Tyrimas atliktas Lietuvos Sveikatos Mokslų Universiteto Reabilitacijos Klinikoje, 2014 kovo 21 – 28 dienomis, jame dalyvavo 48 darbingi asmenys, sergantys išsėtine skleroze. Atliktas aklas vienpusis tyrimas, tiriamieji atsitiktiniu atrankos būdu suskirstyti į... [toliau žr. visą tekstą] / Abaut 2,5 million people suffer from multiple sclerosis. Lithuania belongs to a zone of high rate of people suffering from this desease (Klizaitienė, 2008). On of the main symptoms, appearing in the early stage of this desease is imbalance (Prosperini et al., 2010; Cameron et al., 2008; Martin & Phillips, 2006). Relevance of the topic: Kinesio Tape is a available and non-invasive means which can improve static balance, quality of life and reduce coincidental risk of falls for those who have multiple sclerosis. Hypothesis: Kinesio Tape sticked to gastrocnemius and tibialis anterior muscle can improve the postural stability of those who have multiple sclerosis. The aim of the research: To establish the effect of the Kinesio Tape of those who suffer from multiple sclerosis and to estimate the postural stability. The task of the research: 1. Estimate the static and dynamic posture with Kinesio Tape sticked on the gastrocnemius and tibialis anterior muscle with the help of functional correctional technique. 2. Estimate the static and dynamic posture with Kinesio Tape sticked on the quadriceps muscle with the placebo technique. 3. Estimate the efficiency of Kinesio Tape on postural stability of those who were in the research. Methods of the research: The study was conducted in Lithuanian University of Health Sciences, in Rehabilitation clinic in March 21th – 28th. There were 48 patients with Multiple Sclerosis participating in the study. The patients were randomized into two... [to full text]

Sabe-se que materiais compostos laminados são, hoje em dia, geralmente usados nas indústrias aeronáutica, aeroespacial, naval e outras, principalmente por causa de suas atrativas propriedades se comparadas aos materiais isotrópicos, como alta rigidez/peso, alta resistência, alto amortecimento e boas propriedades relacionadas ao isolamento térmico e acústico, entre outras. Porém, o comportamento de estruturas feitas de materiais compostos pode ser aperfeiçoado através da utilização de materiais inteligentes. Dentre os diferentes tipos comercialmente disponíveis de materiais inteligentes, os materiais piezelétricos são amplamente usados como sensores e atuadores para o monitoramento e controle de estruturas. O efeito piezelétrico direto define que uma deformação mecânica aplicada ao material é convertida em uma carga elétrica. Por outro lado, o efeito piezelétrico inverso define que um potencial elétrico aplicado ao material é convertido em deformação mecânica. Estes efeitos governam a interação eletromecânica nos materiais piezelétricos. O Método dos Elementos Finitos, uma ferramenta amplamente reconhecida e poderosa para a análise de estruturas complexas, é capaz de realizar a integração dos componentes inteligentes e das partes estruturais clássicas. Sendo assim, o comportamento estático e dinâmico, linear e geometricamente não-linear, de estruturas compostas laminadas delgadas com lâminas piezelétricas incorporadas é analisado neste trabalho usando o Método dos Elementos Finitos (MEF). Elementos triangulares, chamados GPL-T9, com três nós e seis graus de liberdade por nó (três componentes de deslocamento e três de rotação) e um grau de liberdade por camada piezelétrica (potencial elétrico) são usados. Para a análise estática não-linear as equações de equilíbrio são solucionadas usando o Método do Controle de Deslocamentos Generalizados (MCDG) enquanto a solução dinâmica é obtida usando o Método de Newmark com Formulação Lagrangeana Atualizada (FLA). O sistema de equações é resolvido usando o Método dos Gradientes Conjugados (MGC) e nos casos não-lineares um esquema iterativo-incremental é empregado. Diversos exemplos numéricos são apresentados e comparados com resultados obtidos por outros autores com diferentes tipos de elementos e diferentes formulações. A concordância entre estes resultados demonstra a validade e a eficácia dos modelos desenvolvidos. / It is well known that laminate composite materials are nowadays commonly used in the aeronautical, aerospace, naval and other industries mainly because their attractive properties as compared to isotropic materials, such as higher stiffness/weight, higher strength, higher damping and good properties related to thermal or acoustic isolation, among others. However, the behavior of structures made of composite materials can be improved using smart materials. Among several kinds of commercially available smart materials, the piezoelectric materials are widely used as sensors and actuators for the monitoring and control of structures. The direct piezoelectric effect states that a mechanical strain applied to the material is converted to an electric charge. On the other hand, the converse piezoelectric effect states that an electric potential applied to the material is converted to mechanical strain. These effects govern the electromechanical interaction in piezoelectric materials. The finite element method, a widely accepted and powerful tool for analyzing complex structures, is capable of dealing with the integration of smart components and classic structural parts. So, linear and geometrically nonlinear static and dynamic behavior of thin laminate composite structures embedded with piezoelectric layers are analyzed in this work using the Finite Element Method (FEM). Triangular elements, called GPL-T9, with three nodes and six degrees of freedom per node (three displacement and three rotation components) and one degree of freedom per piezoelectric layer (electrical potential) are used. For static analysis the nonlinear equilibrium equations are solved using the Generalized Displacement Control Method (GDCM) while the dynamic solution is performed using the classical Newmark Method with an Updated Lagrangean Formulation (ULF). The system of equations is solved using the Gradient Cojugate Method (GCM) and in nonlinear cases an iterative-incremental scheme is employed. Several numerical examples are presented and compared with results obtained by other authors with different kind of elements and different schemes. The agreement among these results demonstrates the validity and effectiveness of the developed models.

La robotique mobile autonome est un axe de recherche qui vise à donner à une machine la capacité de se mouvoir dans un environnement sans assistance ni intervention humaine. Cette thèse s’intéresse à la partie décisionnelle de la navigation robotique à savoir la planification de mouvement pour un robot mobile non-holonome, pour lequel, la prise en compte des contraintes cinématiques et non-holonomes est primordiale. Aussi, la nécessité de considérer la géométrie propre du robot et la bonne maîtrise de l’environnement dans lequel il évolue constituent des contraintes à assurer. En effet la planification de mouvement consiste à calculer un mouvement réalisable que doit accomplir le robot entre une position initiale et une position finale données. Selon la nature de l’environnement, notamment les obstacles qui s’y présentent, deux instances du problème se distinguent : la planification de chemin et la planification de trajectoire. L’objectif de cette thèse est de proposer de nouveaux algorithmes pour contribuer aux deux instances du problème de planification de mouvement. La méthodologie suivie repose sur des solutions génériques qui s’appliquent à une classe de systèmes robotiques plutôt qu’à une architecture particulière. Les approches proposées intègrent les B-splines Rationnelles non uniformes (NURBS) dans le processus de modélisation des solutions générées tout en s’appuyant sur la propriété de contrôle local, et utilisent les algorithmes génétiques pour une meilleure exploration de l’espace de recherche. / The mobile robotics is an area of research that aims to give a machine the ability to move in an environment without assistance or human intervention. This thesis focuses on the decisional part of robotic navigation, namely motion planning for a non-holonomic mobile robot, for which, the consideration of kinematic and non-holonomic constraints is paramount. Also, the need to consider the specific geometry of the robot and the good control of the environment in which it operates are constraints to insure. Indeed, motion planning is to calculate a feasible movement to be performed by the robot between an initial and a final given position. Depending on the nature of the environment, two instances of the problem stand out: the path planning and the trajectory planning. The objective of this thesis is to propose new algorithms to contribute to the two instances of motion planning problem. The followed methodology is based on generic solutions that are applicable to a class of robotic systems rather than a particular architecture. The proposed approaches include the Non-Uniform Rational B-Spline (NURBS) in the modeling process of the generated solutions while relying on the local control property. Also, they use genetic algorithms for better exploration of the search space.

Sabe-se que materiais compostos laminados são, hoje em dia, geralmente usados nas indústrias aeronáutica, aeroespacial, naval e outras, principalmente por causa de suas atrativas propriedades se comparadas aos materiais isotrópicos, como alta rigidez/peso, alta resistência, alto amortecimento e boas propriedades relacionadas ao isolamento térmico e acústico, entre outras. Porém, o comportamento de estruturas feitas de materiais compostos pode ser aperfeiçoado através da utilização de materiais inteligentes. Dentre os diferentes tipos comercialmente disponíveis de materiais inteligentes, os materiais piezelétricos são amplamente usados como sensores e atuadores para o monitoramento e controle de estruturas. O efeito piezelétrico direto define que uma deformação mecânica aplicada ao material é convertida em uma carga elétrica. Por outro lado, o efeito piezelétrico inverso define que um potencial elétrico aplicado ao material é convertido em deformação mecânica. Estes efeitos governam a interação eletromecânica nos materiais piezelétricos. O Método dos Elementos Finitos, uma ferramenta amplamente reconhecida e poderosa para a análise de estruturas complexas, é capaz de realizar a integração dos componentes inteligentes e das partes estruturais clássicas. Sendo assim, o comportamento estático e dinâmico, linear e geometricamente não-linear, de estruturas compostas laminadas delgadas com lâminas piezelétricas incorporadas é analisado neste trabalho usando o Método dos Elementos Finitos (MEF). Elementos triangulares, chamados GPL-T9, com três nós e seis graus de liberdade por nó (três componentes de deslocamento e três de rotação) e um grau de liberdade por camada piezelétrica (potencial elétrico) são usados. Para a análise estática não-linear as equações de equilíbrio são solucionadas usando o Método do Controle de Deslocamentos Generalizados (MCDG) enquanto a solução dinâmica é obtida usando o Método de Newmark com Formulação Lagrangeana Atualizada (FLA). O sistema de equações é resolvido usando o Método dos Gradientes Conjugados (MGC) e nos casos não-lineares um esquema iterativo-incremental é empregado. Diversos exemplos numéricos são apresentados e comparados com resultados obtidos por outros autores com diferentes tipos de elementos e diferentes formulações. A concordância entre estes resultados demonstra a validade e a eficácia dos modelos desenvolvidos. / It is well known that laminate composite materials are nowadays commonly used in the aeronautical, aerospace, naval and other industries mainly because their attractive properties as compared to isotropic materials, such as higher stiffness/weight, higher strength, higher damping and good properties related to thermal or acoustic isolation, among others. However, the behavior of structures made of composite materials can be improved using smart materials. Among several kinds of commercially available smart materials, the piezoelectric materials are widely used as sensors and actuators for the monitoring and control of structures. The direct piezoelectric effect states that a mechanical strain applied to the material is converted to an electric charge. On the other hand, the converse piezoelectric effect states that an electric potential applied to the material is converted to mechanical strain. These effects govern the electromechanical interaction in piezoelectric materials. The finite element method, a widely accepted and powerful tool for analyzing complex structures, is capable of dealing with the integration of smart components and classic structural parts. So, linear and geometrically nonlinear static and dynamic behavior of thin laminate composite structures embedded with piezoelectric layers are analyzed in this work using the Finite Element Method (FEM). Triangular elements, called GPL-T9, with three nodes and six degrees of freedom per node (three displacement and three rotation components) and one degree of freedom per piezoelectric layer (electrical potential) are used. For static analysis the nonlinear equilibrium equations are solved using the Generalized Displacement Control Method (GDCM) while the dynamic solution is performed using the classical Newmark Method with an Updated Lagrangean Formulation (ULF). The system of equations is solved using the Gradient Cojugate Method (GCM) and in nonlinear cases an iterative-incremental scheme is employed. Several numerical examples are presented and compared with results obtained by other authors with different kind of elements and different schemes. The agreement among these results demonstrates the validity and effectiveness of the developed models.

Sabe-se que materiais compostos laminados são, hoje em dia, geralmente usados nas indústrias aeronáutica, aeroespacial, naval e outras, principalmente por causa de suas atrativas propriedades se comparadas aos materiais isotrópicos, como alta rigidez/peso, alta resistência, alto amortecimento e boas propriedades relacionadas ao isolamento térmico e acústico, entre outras. Porém, o comportamento de estruturas feitas de materiais compostos pode ser aperfeiçoado através da utilização de materiais inteligentes. Dentre os diferentes tipos comercialmente disponíveis de materiais inteligentes, os materiais piezelétricos são amplamente usados como sensores e atuadores para o monitoramento e controle de estruturas. O efeito piezelétrico direto define que uma deformação mecânica aplicada ao material é convertida em uma carga elétrica. Por outro lado, o efeito piezelétrico inverso define que um potencial elétrico aplicado ao material é convertido em deformação mecânica. Estes efeitos governam a interação eletromecânica nos materiais piezelétricos. O Método dos Elementos Finitos, uma ferramenta amplamente reconhecida e poderosa para a análise de estruturas complexas, é capaz de realizar a integração dos componentes inteligentes e das partes estruturais clássicas. Sendo assim, o comportamento estático e dinâmico, linear e geometricamente não-linear, de estruturas compostas laminadas delgadas com lâminas piezelétricas incorporadas é analisado neste trabalho usando o Método dos Elementos Finitos (MEF). Elementos triangulares, chamados GPL-T9, com três nós e seis graus de liberdade por nó (três componentes de deslocamento e três de rotação) e um grau de liberdade por camada piezelétrica (potencial elétrico) são usados. Para a análise estática não-linear as equações de equilíbrio são solucionadas usando o Método do Controle de Deslocamentos Generalizados (MCDG) enquanto a solução dinâmica é obtida usando o Método de Newmark com Formulação Lagrangeana Atualizada (FLA). O sistema de equações é resolvido usando o Método dos Gradientes Conjugados (MGC) e nos casos não-lineares um esquema iterativo-incremental é empregado. Diversos exemplos numéricos são apresentados e comparados com resultados obtidos por outros autores com diferentes tipos de elementos e diferentes formulações. A concordância entre estes resultados demonstra a validade e a eficácia dos modelos desenvolvidos. / It is well known that laminate composite materials are nowadays commonly used in the aeronautical, aerospace, naval and other industries mainly because their attractive properties as compared to isotropic materials, such as higher stiffness/weight, higher strength, higher damping and good properties related to thermal or acoustic isolation, among others. However, the behavior of structures made of composite materials can be improved using smart materials. Among several kinds of commercially available smart materials, the piezoelectric materials are widely used as sensors and actuators for the monitoring and control of structures. The direct piezoelectric effect states that a mechanical strain applied to the material is converted to an electric charge. On the other hand, the converse piezoelectric effect states that an electric potential applied to the material is converted to mechanical strain. These effects govern the electromechanical interaction in piezoelectric materials. The finite element method, a widely accepted and powerful tool for analyzing complex structures, is capable of dealing with the integration of smart components and classic structural parts. So, linear and geometrically nonlinear static and dynamic behavior of thin laminate composite structures embedded with piezoelectric layers are analyzed in this work using the Finite Element Method (FEM). Triangular elements, called GPL-T9, with three nodes and six degrees of freedom per node (three displacement and three rotation components) and one degree of freedom per piezoelectric layer (electrical potential) are used. For static analysis the nonlinear equilibrium equations are solved using the Generalized Displacement Control Method (GDCM) while the dynamic solution is performed using the classical Newmark Method with an Updated Lagrangean Formulation (ULF). The system of equations is solved using the Gradient Cojugate Method (GCM) and in nonlinear cases an iterative-incremental scheme is employed. Several numerical examples are presented and compared with results obtained by other authors with different kind of elements and different schemes. The agreement among these results demonstrates the validity and effectiveness of the developed models.