Practical Element Research Articles

Practical fuzzy finite element analysis of structures

A practical approach for analyzing the response of structures with fuzzy parameters is developed. The methodology involves integrated finite element modelling, response surface analysis and fuzzy analysis. The uncertainties in the material, loading and structural properties are represented using convex normal fuzzy sets. Vertex solution methodology that is based on α-cut representation is used for the fuzzy analysis. Response surface methodology is used to approximate the fuzzy finite element response quantity at the normal point. Combinatorial optimization is then performed on the response surface approximate quantity to determine the binary combinations of the fuzzy variables that result in extreme responses at an α-level. The true values of the extreme responses at an α-level are obtained by applying the binary combinations of the fuzzy variables that result in extreme responses to the finite element model. The merit of the proposed methodology is computational efficiency without compromise on accuracy and this is demonstrated through some example problems.

On fully practical finite element approximations of degenerate Cahn-Hilliard systems

We consider a model for phase separation of a multi-component alloy with non-smooth free energy and a degenerate mobility matrix. In addition to showing well-posedness and stability bounds for our approximation, we prove convergence in one space dimension. Furthermore an iterative scheme for solving the resulting nonlinear discrete system is analysed. We discuss also how our approximation has to be modified in order to be applicable to a logarithmic free energy. Finally numerical experiments with three components in one and two space dimensions are presented.

Hybrid learning - a safe route into web-based open and distance learning for the computer science teacher

The hybrid learner is located on a continuum between the traditional student attending face to face classes in a University and the distance learner who may never visit the institution, except perhaps to graduate. Modern methods of web-based open and distance learning make hybrid learning attractive and accessible to students.Computer Science students in particular make very good hybrid students because the content of the Computer Science curriculum has a strong practical element that is conducive to independent learning methods, and because they have a familiarity with the tools used in hybrid learning.Suggestions are given on how a teacher may develop web-based open and distance learning (WEB-ODL) for hybrid learners.

An improved error bound for a finite element approximation of a model for phase separation of a multi-component alloy with a concentration dependent mobility matrix

Using a slightly different discretization scheme in time and adapting the approach in Nochetto et al. (1998) for analysing the time discretization error in the backward Euler method, we improve on the error bounds derived in (i) Barrett and Blowley (1998) and (ii) Barrett and Blowey (1999c) for a fully practical piecewise linear finite element approximation of a model for phase separation of a multi-component alloy with a concentration dependent mobility matrix and (i) a logarithmic free energy, and (ii) a non-smooth free energy (the deep quench limit); respectively. Moreover, the improved error bound in the deep quench limit is optimal. Numerical experiments with three components illustrating the above error bounds are also presented.

Taking the Classroom into the Real World

Abstract The increase in number of international tourist arrivals, the holding of the Olympic Games in Sydney in 2000, and a solid domestic tourism industry has had an effect on the meetings, incentive, convention, and exhibition (MICE) industry in Australia, worth A$7 billion in 1996/1997. To meet this increasing demand from the industry to train professionals for the tourism and hospitality industry, some institutions are offering specialized subjects to prepare students for employment in the MICE industry. One of the inherent problems in teaching such a subject is to introduce a practical and experiential element. This has been addressed successfully over the past two years by offering students an opportunity to take part as delegates attending a specifically designed conference while spending a night at one of the many 5-star international hotel properties with convention facilities on the Gold Coast. In 1999, 135 students stayed at an international 5-star hotel, with the hotel cooperating with the un...

Numerical methods for Stefan problems with prescribed convection and nonlinear flux

This paper deals with numerical methods for a class of nonlinear degenerate parabolic equations with nonlinear flux boundary conditions, which in particular includes the well-known continuous casting Stefan problem. A practical piecewise linear finite element scheme with numerical integration which is based on an implicit discretization of the diffusion and an explicit approximation of the enthalpy-dependent convection is proposed. The convergence of the scheme is proved without requiring the quasi-uniformity and the acuteness of the finite element meshes. The key ingredient of the analysis is an estimate on the fractional derivative in time of the discrete temperature which provides the necessary strong convergence property. The results of some numerical tests are provided in order to show the accuracy of the scheme.

An optimal error bound for a finite element approximation of a model for phase separation of a multi-component alloy with non-smooth free energy

Using the approach in (5) for analysing time discretization error and assuming more reg- ularity on the initial data, we improve on the error bound derived in (2) for a fully practical piecewise linear nite element approximation with a backward Euler time discretization of a model for phase separation of a multi-component alloy with non-smooth free energy. AMS Subject Classication. 65M60, 65M15, 35K55, 35K35.

Woven fabric composites?developments in engineering bounds, homogenization and applications

Various approaches for approximating upper and lower bounds for the elastic stiffness tensor for general woven fabric composites are first described. Well accepted minimum energy principles are briefly presented to establish the foundation for practical finite element procedures for determining these bounds. Secondly, comparisons of four common homogenization procedures are shown: the strain energy balance method, the plate approximation method, a direct approach via area averaging, and asymptotic expansion homogenization. As a limiting case, all of the methods obtain the well-known Rule of Mixtures for a unidirectional uniaxial specimen. In attempting to consolidate much of the existing knowledge of structural constitutive models for woven fabric composites, this research seeks to summarize and compare various homogenization methods via finite element analyses. Finally, some illustrative applications are presented. Copyright © 1999 John Wiley & Sons, Ltd.

FINITE ELEMENT APPROXIMATION OF A MODEL FOR PHASE SEPARATION OF A MULTI-COMPONENT ALLOY WITH NONSMOOTH FREE ENERGY AND A CONCENTRATION DEPENDENT MOBILITY MATRIX

We consider a model for phase separation of a multi-component alloy with nonsmooth free energy and a concentration dependent mobility matrix. In particular we prove that there exists a unique solution for sufficiently smooth initial data. Further, we prove an error bound for a fully practical piecewise linear finite element approximation in one and two space dimensions. Finally numerical experiments with three components in one space dimension are presented.

The application of Piagetian and Neo-Piagetian ideas to further and higher education

Piaget's theory of learning and stage theory applies to adults, as well as to children and adolescents. Some implications of this are worked out. According to Sutherland (1982) and others not all adults can be assumed to be formal operational thinkers. More than half are concrete operational (or at an even lower stage) at the age of 16. However some mature adults may develop late to the formal operational stage. Whether this is the case or not has yet to be determined empirically. The ideas of some other educational psychologists who have developed Piaget's ideas for adults are outlined and evaluated. These stem from a number of theoretical perspectives: (i) neo-Piagetian: Kohlberg, Peel and Labouvie-Vief; (ii) theorists synthesizing Piaget's ideas with those of others: Kolb, Biggs and Pascual-Leone; and (iii) others striking out in alternative directions: Perry and Gilligan. If accepted, these findings have important implications for teaching in both further and higher education. Neither can continue to assume that all students can operate at a formal operational stage. In further education and training courses teachers may need to assume that students need a practical element to their learning. In higher education teachers need to cater for some students who are concrete operational or transitional between concrete and formal operations.

Finite element approximation of the Cahn-Hilliard equation with concentration dependent mobility

We consider the Cahn-Hilliard equation with a logarithmic free energy and non-degenerate concentration dependent mobility. In particular we prove that there exists a unique solution for sufficiently smooth initial data. Further, we prove an error bound for a fully practical piecewise linear finite element approximation in one and two space dimensions. Finally some numerical experiments are presented.

Finite Element Approximation of the Cahn--Hilliard Equation with Degenerate Mobility

We consider a fully practical finite element approximation of the Cahn--Hilliard equation with degenerate mobility $$ \textstyle \frac{\partial u}{\partial t}= \del .(\,b(u)\, \del (-\gamma\lap u+\Psi'(u))) , $$ where $b(\cdot)\geq 0$ is a diffusional mobility and $\Psi(\cdot)$ is a homogeneous free energy. In addition to showing well posedness and stability bounds for our approximation, we prove convergence in one space dimension. Furthermore, an iterative scheme for solving the resulting nonlinear discrete system is analyzed. We also discuss how our approximation has to be modified in order to be applicable to a logarithmic homogeneous free energy. Finally, some numerical experiments are presented.

An improved error bound for a finite element approximation of a model for phase separation of a multi-component alloy

Using the approach of Rulla (1996 SIAM J. Numer. Anal. 33, 68-87) for analysing the time discretization error and assuming more regularity on the initial data, we improve on the error bound derived by Barrett and Blowey (1996 IMA J. Numer. Anal. 16, 257-287) for a fully practical piecewise linear finite element approximation with a backward Euler time discretization of a model for phase separation of a multi-component alloy.

The Internet—Changing the Way Horticulturists Communicate

Four key elements in the discipline of horticulture provide a strong incentive to use the Internet for communicating programatic information. First, a strong visual component characterizes horticultural knowledge and study. Second, the technical and practical element contained in the undergraduate curriculum, which, similar to plant identification, requires that students are presented highly visual information. Third, use of the Internet increases the efficiency and effectiveness of communicating program information and research results. Finally, the issue of content format for some applications precludes the use of any other media. Taken together, the Internet is significantly changing the environment in which horticulturists communicate.

Curriculum costs

AbstractA. W. Foshay has written a series of essays on what he calls the ‘curriculum matrix’. In them, he considers the interactions of unlikely elements such as aesthetics and history, and transcendence and mathematics. Thus far he has not explicitly attended to practice, one of the three dimensions of the model. Therefore, this article represents a first attempt at testing the model from the point of view of practice. In the process of exploring the practical element of cost, it becomes evident that the richness and depth of too easily disregarded terms, such as cost, must be reconsidered in order to enable sound curriculum decisions to be made in classrooms, school districts and national committees.

Finite element approximation of a model for phase separation of a multi-component alloy with a concentration-dependent mobility matrix

We consider a model for phase separation of a multi-component alloy with a concentration-dependent mobility matrix and logarithmic free energy. In particular we prove that there exists a unique solution for sufficiently smooth initial data. Further, we prove an error bound for a fully practical piecewise linear finite element approximation in one and two space dimensions. Finally numerical experiments with three components in one space dimension are presented.

Analysis of mutual interaction on sonar array and vibration velocity measurement using NAH

Recently, sonar has tended to use lower frequencies and large output power to enhance its search distance. However, for such sonar, it is known that unpredictable deterioration of output and the destruction of specific elements may occur because of interference between elements. This research was conducted to analyze the interference between elements in an array in which the elements were driven by a regulated voltage—the influence of the mutual radiation impedance on the vibration velocity of the elements—using an equivalent circuit. The vibration velocity of each element was calculated using mechanical parameters for a practical array element. After that, the vibration velocity regulations of elements of (1,3) and (2,2) mode array caused by interactions were verified experimentally using a NAH imaging system which makes it possible to visualize fine regulations. These results are according to simulations.

Climatic controls of the cool human thermal sensation in a summertime onshore wind

Afternoon observations in summer comparing shoreline with inland atmospheric conditions were made during onshore winds at Victoria, British Columbia, Canada. The onshore wind came from a cool water surface. Mean monthly water temperatures near to shore were between 11 and 11.5 degrees C. The onshore wind brought lower air, ground surface radiant and sky radiant temperatures; lower humidity and greater wind speed. All of these combine to produce a cooler human environment at the shoreline than inland. The relative importance of climatic elements in producing the cooler environment was assessed using sensitivity analyses with eight different human thermal exchange models/indices. Air temperature and wind speed had the greatest effect, followed by ground surface radiant temperature, sky radiant temperature and humidity. Wind speed is the most practical element to consider when trying to maximize human comfort along the shoreline.

Finite element approximation of a model for phase separation of a multi-component alloy with non-smooth free energy

A model for the phase separation of a multi-component alloy with non-smooth free energy is considered. An error bound is proved for a fully practical piecewise linear finite element approximation using a backward Euler time discretization. An iterative scheme for solving the resulting nonlinear algebraic system is analysed. Finally numerical experiments with three components in one and two space dimensions are presented. In the one dimensional case we compare some steady states obtained numerically with the corresponding stationary solutions of the continuous problem, which we construct explicitly.

Precise computations of resonant frequencies and quality factors for dielectric resonators in MICs with tuning elements

In this paper, the highly accurate results of resonant frequencies, field distributions, and quality factors of the TE/sub 01/spl delta// mode for the cylindrical shielded dielectric resonator (DR) in microwave integrated circuits (MIC's) with a practical tuning element, such as the metallic tuning screw and the dielectric tuning device, are presented. By using the newly developed FD-SIC method, numerical results can be calculated accurately and efficiently. The DR structures with tuning elements can be more easily modeled by the present approach than the other methods using approximate solutions or the mode-matching (MM) methods. Numerical results in the literature are compared to the present FD-SIC results for the DR without tuning elements and detailed discussions on these results are given. In addition, design curves are also presented for the DR with the metallic tuning screw and with the dielectric tuning device. These design curves are helpful for designing DR systems with tuning elements in MIC applications.