Practical Element Research Articles

Finite element approximation of a phase field model for surface diffusion of voids in a stressed solid

We consider a fully practical finite element approximation of the degenerate Cahn–Hilliard equation with elasticity: Find the conserved order parameter, θ ( x , t ) ∈ [ − 1 , 1 ] \theta (x,t)\in [-1,1] , and the displacement field, u _ ( x , t ) ∈ R 2 \underline {u}(x,t) \in \mathbb {R}^2 , such that γ ∂ θ ∂ t a m p ; = ∇ . ( b ( θ ) ∇ [ − γ Δ θ + γ − 1 Ψ ′ ( θ ) + 1 2 c ′ ( θ ) C E _ _ ( u _ ) : E _ _ ( u _ ) ] ) , ∇ . ( c ( θ ) C E _ _ ( u _ ) ) a m p ; = 0 _ , \begin{align*} \gamma \,\textstyle {\frac {\partial \theta }{\partial t}} & = \nabla \,.\, (b(\theta ) \,\nabla \,[- \gamma \, \Delta \theta + \gamma ^{-1}\, \Psi ’(\theta ) + \textstyle \frac 12\,c’(\theta )\,\mathcal {C} \,\underline {\underline {\mathcal {E}}} (\underline {u}): \underline {\underline {\mathcal {E}}} (\underline {u})]\,) \,, \nonumber \nabla \,.\, (c(\theta ) \,\mathcal {C}\, \underline {\underline {\mathcal {E}}} (\underline {u}) ) & = \underline {0}\,, \end{align*} subject to an initial condition θ 0 ( ⋅ ) ∈ [ − 1 , 1 ] \theta ^0(\cdot ) \in [-1,1] on θ \theta and boundary conditions on both equations. Here γ ∈ R > 0 \gamma \in {\mathbb R}_{>0} is the interfacial parameter, Ψ \Psi is a non-smooth double well potential, E _ _ \underline {\underline {\mathcal {E}}} is the symmetric strain tensor, C \mathcal {C} is the possibly anisotropic elasticity tensor, c ( s ) := c 0 + 1 2 ( 1 − c 0 ) ( 1 + s ) c(s):=c_0+\textstyle \frac 12\,(1-c_0)\,(1+s) with c 0 ( γ ) ∈ R > 0 c_0(\gamma )\in {\mathbb R}_{>0} and b ( s ) := 1 − s 2 b(s):=1-s^2 is the degenerate diffusional mobility. In addition to showing stability bounds for our approximation, we prove convergence, and hence existence of a solution to this nonlinear degenerate parabolic system in two space dimensions. Finally, some numerical experiments are presented.

Structural Finite Element Model Updating Using Ambient Vibration Test Results

This paper presents a practical and user-friendly finite element (FE) model updating technique for real structures using ambient vibration test results. The first case study of a simulated simply supported beam demonstrates a comparative study of the influence of different possible residuals in objective function. Frequency residual only, mode shape related function only, modal flexibility residual only, and their combinations are studied independently. In view of tuning as well as damage localization, full objective function that considers all three residuals is the best for FE updating. This objective function is implemented in a second case study of a real concrete-filled steel tubular arch bridge. The bridge was tested by ambient vibration measurements. Followed by the three-dimensional FE modeling of the bridge, an eigenvalue sensitivity study is carried out to see the most sensitive parameters to the concerned modes. FE model mass matrix obtained from Guyan reduction technique is used to the mass normalization of the mode shapes extracted from ambient modal test to calculate the modal flexibility. The updated FE model of the bridge is able to produce a sufficient improvement on modal parameters of the concerned modes which is in close agreement with the experimental results still preserving the physical meaning of updated parameters.

Spatial variability of chilling temperature in Turkey and its effect on human comfort

Air temperature, absolute humidity and wind speed are the most important meteorological parameters that affect human thermal comfort. Because of heat loss, the human body feels air temperatures different to actual temperatures. Wind speed is the most practical element for consideration in terms of human comfort. In winter, due to the strong wind speeds, the sensible temperature is generally colder than the air temperature. This uncomfortable condition can cause problems related to tourism, heating and cooling. In this study, the spatial and temporal distributions of cooling temperatures and Wind Chill Index (WCI) are analyzed for Turkey, and their effect on the human body is considered. In this paper, monthly cooling temperatures between October and March in the years 1929 to 1990 are calculated by using measured temperature and wind speed at 79 stations in Turkey. The influence of wind chill is especially observed in the regions of the Aegean, west and middle Black Sea and east and central Anatolia. The wind chill in these regions has an uncomfortable effect on the human body. Usually, the WCI value is higher in western, northern and central Anatolia than in other regions.

Institutional arrangement and unauthorised building works in Hong Kong

PurposeTo explain the serious social problem of unauthorised building works (UBWs) in Hong Kong and why this problem is difficult to overcome.Design/methodology/approachAn institutional economics approach is adopted. This paper concentrates on the governance zone of the institutional arrangement.FindingsThe current institutional arrangement in Hong Kong encourages owners to build UBWs, and makes the identification of UBWs very complicated. This paper concludes that the existing framework of governance fails to take into account the conflict of interests in collective goods. The no‐retrospective‐approval stipulation also renders a no‐alternative solution.Research limitations/implicationsIt is a case study of Hong Kong, but it has research implications on institutional economics under the current arrangement of co‐ownership.Practical implicationsAn important element in structural surveys is to ensure the structural safety of a building. An understanding on the governance of UBWs has serious implications for the structural survey approach.Originality/valueThis paper is the first paper on exploring UBWs from an institutional economics framework.

A practical large-strain solid finite element for sheet forming

An alternative approach for developing practical large-strain finite elements has been introduced and used to create a three-dimensional solid element that exhibits no locking or hourglassing, but which is more easily and reliably derived and implemented than typical reduced-integration schemes with hourglassing control. Typical large-strain elements for forming applications rely on reduced integration to remove locking modes that occur with the coarse meshes that are necessary for practical use. This procedure introduces spurious zero-energy deformation modes that lead to hourglassing, which in turn is controlled by complex implementations that involve lengthy derivations, knowledge of the material model, and/or undetermined parameters. Thus, for a new material or new computer program, implementation of such elements is a daunting task. Wang–Wagoner-3-dimensions (WW3D), a mixed, hexahedral, three-dimensional solid element, was derived from the standard linear brick element by ignoring the strain components corresponding to locking modes while maintaining full integration (8 Gauss points). Thus, WW3D is easily implemented for any material law, with little chance of programming error, starting from programming for a readily available linear brick element. Surprisingly, this approach and resulting element perform similarly or better than standard solid elements in a series of numerical tests appearing in the literature. The element was also tested successfully for an applied sheet-forming analysis problem. Many variations on the scheme are also possible for deriving special-purpose elements. Copyright © 2005 John Wiley & Sons, Ltd.

Finite element approximation of a Stefan problem with degenerate Joule heating

We consider a fully practical finite element approximation of the following degenerate system subject to an initial condition on the temperature, u, and boundary conditions on both u and the electric potential, ϕ. In the above p(u) is the enthalpy incorporating the latent heat of melting, α(u) > 0 is the temperature dependent heat conductivity, and σ(u) > 0 is the electrical conductivity. The latter is zero in the frozen zone, u ≤ 0, which gives rise to the degeneracy in this Stefan system. In addition to showing stability bounds, we prove (subsequence) convergence of our finite element approximation in two and three space dimensions. The latter is non-trivial due to the degeneracy in σ(u) and the quadratic nature of the Joule heating term forcing the Stefan problem. Finally, some numerical experiments are presented in two space dimensions.

Bond and interfacial properties of reinforcement in self-compacting concrete

This paper reports a study carried out to assess the impact of the use of self-compacting concrete (SCC) on bond and interfacial properties around steel reinforcement in practical concrete element. The pull-out tests were carried out to determine bond strength between reinforcing steel bar and concrete, and the depth-sensing nano-indentation technique was used to evaluate the elastic modulus and micro-strength of the interfacial transition zone (ITZ) around steel reinforcement. The bond and interfacial properties around deformed steel bars in different SCC mixes with strength grades of 35 MPa and 60 MPa (C35, C60) were examined together with those in conventional vibrated reference concrete with the same strength grades.

Micro V-Groove Grinding Technique of Large Germanium Immersion Grating Element for Mid-Infrared Spectrograph

The 8.2m SUBARU large space telescope in Hawaii requires a mid-infrared high dispersion spectrograph with a resolution of 200000 at 10µm which employs a Germanium Immersion Grating (GIG) element. For this, the GIG element with a large number of sharp and smooth micro V-grooves must be fabricated. Previous studies were focused on the fabrication of a prototype GIG element. The grinding system developed however was not applicable for the fabrication of practical larger GIG element due to insufficient machining space and fast wear of the small grinding wheel used. The ultimate goal of this project was therefore to develop a new grinding system capable of fabricating larger GIG elements for practical use. This paper discusses the results achieved in the first phase of the research, which focused on the principle of the grinding process and grinding system, as well as describes results of micro-truing and micro-grinding experiments using a #4000 metal bonded diamond grinding wheel. Wear variation of the grinding wheel and its effects on the corner radius of micro V-grooves are also discussed. The minimum wheel tip radius of 8.2µm was achieved using this #4000 grinding wheel by micro-truing, and V-groove corner radiuses ranging from 15µm to 25.8µm were also achieved using the same grinding wheel.

Finite Element Approximation of a Phase Field Model for Void Electromigration

We consider a fully practical finite element approximation of the nonlinear degenerate parabolic system \begin{align} \gamma\,\textstyle{\frac{\partial u}{\partial t}} - \nabla . ( \,b(u) \,\nabla [ w +\alpha\,\phi]\, ) = 0\,, \quad w = - \gamma\, \Delta u + \gamma^{-1}\,\Psi'(u)\,, %\nonumber \\ \quad \nabla . (\, c(u) \,\nabla \phi ) = 0\, \nonumber \end{align} subject to an initial condition $u^0(\cdot) \in [-1,1]$ on u and flux boundary conditions on all three equations. Here $\gamma \in {\mathbb R}_{>0}$, $\alpha \in {\mathbb R}_{\geq 0}$, $\Psi$ is a nonsmooth double well potential, and $c(u) :=1+u$, $b(u):=1-u^2$ are degenerate coefficients. %diffusional mobility. The degeneracy in b restricts $u(\cdot,\cdot) \in [-1,1]$. The above, in the limit $\gamma \rightarrow 0$, models the evolution of voids by surface diffusion in an electrically conducting solid. In addition to showing stability bounds for our approximation, we prove convergence, and hence existence of a solution to this nonlinear degenerate parabolic system in two space dimensions. Furthermore, an iterative scheme for solving the resulting nonlinear discrete system is introduced and analyzed. Finally, some numerical experiments are presented.

SWiSP: The social work students in schools project

Current changes to social work education require an increased emphasis on the practical element of the programme and a significant increase in the number of placement learning days undertaken by students: a minimum of 200 days overall. The Social Work Students in Schools Project (SWiSP) addressed this need whilst also raising the profile of the social work profession and local programme providers within the community. The project enhanced links and increased awareness of the role of social workers within primary and secondary schools at a time when the integration of social work, health care and education is increasingly promoted. This paper describes the context and rationale for the project, the views of stakeholders in the first phase and considers the learning potential for existing and changing social work education.

Modeling of hard part machining: effect of insert edge preparation in CBN cutting tools

High speed machining of hardened steels for manufacturing dies and molds offers various advantages, but the productivity often limited by mainly tool life. This study investigates the influence of edge preparation in cubic boron nitrite (CBN) cutting tools on process parameters and tool performance by utilizing practical finite element (FE) simulations and high speed orthogonal cutting tests. The predicted process parameters through FE simulations in high speed orthogonal cutting are expected to help optimize tool life and surface finish in hard machining of AISI H-13 hot work tool steel. A set of orthogonal cutting experiments using honed and chamfered CBN tools was performed and primary cutting force and thrust force were measured by using a force dynamometer along with a PC-based data acquisition system. The same set of cutting conditions was used in numerical FE simulations to predict forces, stresses and temperatures developed at the honed and chamfered CBN tools. Simulation results provided a distribution of stresses and temperatures at the cutting zone, chip–tool and workpiece–tool interfaces. Numerical simulations include testing different edge preparation geometry for CBN tools at different cutting speeds and feeds. The results show that a zone of workpiece material is formed under the chamfer acting as an effective rake angle during cutting. The presence of a chamfer affects the cutting forces and temperatures while no significant change in chip formation observed.

A knowledge-based approach to the deflocculation problem: integrating on-line, off-line, and heuristic information

A knowledge-based approach for the supervision of the deflocculation problem in activated sludge processes was considered and successfully applied to a full-scale plant. To do that, a methodology that integrates on-line, off-line and heuristic information has been proposed. This methodology consists of three steps: (i) development of a decision tree (which involves knowledge acquisition and representation); (ii) implementation into a rule-based system; and (iii) validation. The set of symptoms most useful in diagnosing the deflocculation problem has been identified, the different branches to diagnose pin-point floc and dispersed growth have been built (using generic and specific knowledge), and all this knowledge has been codified into an object-oriented shell. The results obtained in the application of this knowledge-based approach to the Granollers WWTP (which treats about 130,000 inhabitants-equivalents) showed that the system was able to identify correctly the problem with reasonable accuracy. Our positive experience building this system suggests that this approach is a practical and valuable element to include in an intelligent supervisory system combining numerical and reasoning techniques.

Finite Element Approximation of Surfactant Spreading on a Thin Film

We consider a fully practical finite element approximation of the following system of nonlinear degenerate parabolic equations: \begin{alignat}{2} \textstyle{\frac{\partial u}{\partial t}} + \textstyle \frac{1}{2} \,\nabla . (u^2 \,\nabla [\sigma(v)]) - \textstyle \frac{1}{3}\, \nabla .(u^3 \,\nabla w) &= 0, &&%\quad\mbox{in} \;\;\Omega_T, \qquad %\hspace{2cm} \nonumber \\ w = - c \, \Delta u + a \, u^{-3} - \delta \, u^{-\nu}, \nonumber \\ \textstyle{\frac{\partial v}{\partial t}} + \nabla . (u\,v\,\nabla [\sigma(v)]) - \rho \,\Delta v - \textstyle \frac{1}{2}\, \nabla .(u^2\,v \,\nabla w) &= 0. &&%\quad\mbox{in} \;\;\Omega_T. \nonumber %\\ \end{alignat} The above models a surfactant-driven thin film flow in the presence of both attractive, a >0, and repulsive, $\delta >0$ with $\nu >3$, van der Waals forces, where u is the height of the film, v is the concentration of the insoluble surfactant monolayer, and $\sigma(v):=1-v$ is the typical surface tension. Here $\rho \geq 0$ and c>0 are the inverses of the surface Peclet number and the modified capillary number. In addition to showing stability bounds for our approximation, we prove convergence in one space dimension when $\rho >0$ and either $a=\delta=0$ or $\delta > 0$. Furthermore, iterative schemes for solving the resulting nonlinear discrete system are discussed. Finally, some numerical experiments are presented.

Service evaluation of the Teenage Clinic

The Teenage Clinic is a multidisciplinary service designed to cater to all the needs of pregnant and postnatal teenagers. Using the grounded theory approach, the present study evaluated the clinic from the service users' perspective. Six pregnant or postnatal teenagers aged between 15–20 years were interviewed to determine what they liked or disliked about the clinic and how the clinic could be improved and better advertised. Interviews lasted between 15 and 45 minutes from which the following seven themes emerged: (1) preparation and reduction of anxiety, (2) reduction of stigmatisation, normalisation and maintenance of self-esteem, (3) peer support, (4) acceptance of partners and other family members, (5) involvement in the process, (6) need for a practical element to sessions and, (7) inadequate promotion of the clinic. Attitudes towards the clinic were very positive, but there was a clear need for a greater practical element and wider promotion of the service.

Ancient Egyptian Rhetoric in the Old and Middle Kingdoms

The rhetorical ideas inherited from the Greeks have established the notion that skilled use of language is always indicated by eloquent expression, and that silence is either an aberration or a lack of skill. As we penetrate the silence that has surrounded one of the great civilizations of the earth, however, and look at Egyptian rhetoric, we find alternative views on what makes a skilled speaker. While the Egyptians esteemed eloquent speaking, a skill that in fact had a very high value in their society, Egyptian rules of rhetoric also clearly specify that knowing when not to speak is essential, and very respected, rhetorical knowledge. The Egyptian approach to rhetoric is thus a balance between eloquence and wise silence. Egyptian rules of speech also strongly emphasize adherence to social behaviors that support a conservative status quo. For the Egyptians, much more than for the Greeks, skilled speech should support, not question, society. The few studies of Egyptian rhetoric which have previously been done discuss some of the moral components of that rhetoric and the importance of silence. The current study looks at Egyptian attitudes toward language as both a magical and a practical element of life, and in addition this study places the rules of Egyptian rhetoric solidly within the Egyptian social system.

3D FEA Modeling of Hard Turning

A practical explicit 3D finite element analysis model has been developed and implemented to analyze turning hardened AISI 52100 steels using a PCBN cutting tool. The finite element analysis incorporated the thermo-elastic-plastic properties of the work material in machining. An improved friction model has been proposed to characterize tool-chip interaction with the friction coefficient and shear flow stresses determined by force calibration and material tests, respectively. A geometric model has been established to simulate a 3D turning. FEA Model predictions have reasonable accuracy for chip geometry, forces, residual stresses, and cutting temperatures. FEA model sensitivity analysis indicates that the prediction is consistent using a suitable magnitude of material failure strain for chip separation, the simulation gives reasonable results using the experimentally determined material properties, the proposed friction model is valid and the sticking region on the tool-chip interface is a dominant factor of model predictions.

볼트결합부를 포함한 구조물의 정적 및 동적 해석을 위한 유한요소 모델링

Many studies on the finite element modeling for bolted joints have proceeded, but the structures with bolted joints are complicated in shape and it is difficult to find out the characteristics according to joint condition. Usually, experimental methods have been used for bolted joint analysis. A reliable and practical finite element modeling technique for structure with bolted joints is very important for engineers in industry. In this study, three kinds of model are presented; a detailed model, a practical model and a simple model. The detailed model is modeled by using 3-D solid element and gap element, and the practical model is modeled by using shell element (a portion of bolt head) and beam element (a portion of bolt body), the simple model is modeled by simplifying practical model without using gap elements. Among these models, the simple model has the least degree of freedom and show the effect of memory reduction of 59%, when compared with the detailed model.

A phenomenological study of the body and its representations in painting

This research originates in my practice as a painter and teacher of life drawing; and seeks to question whether the figurative nude in painting is unfinished business. Being a practising artist and not an academic, has influenced both my methodology and the relationship between practice and theory. Reading, visual practice, writing, and the analysis of other artists' work, all stimulate and inform each other; with the result that practice and theory have equal weight, neither being an illustration of the other. These dual concerns are not unified in one investigation but have developed as interdependent parallel strands. The practical element is a search to find strategies for painting the figurative nude, which can stimulate a sense of a corporeal body for the viewer. This theoretical investigation is an examination of the nature and structure of realism, its hermeneutical association with the viewer and its position in relation to the Kantian sublime.

Finite Element Approximation of a Degenerate Allen--Cahn/Cahn--Hilliard System

We consider a fully practical finite element approximation of an Allen--Cahn/Cahn--Hilliard system with a degenerate mobility and a logarithmic free energy. This system arises in the modeling of phase separation and ordering in binary alloys. In addition to showing well-posedness and stability bounds for our approximation, we prove convergence in one space dimension. Finally, some numerical experiments are presented.

Finite element approximation of an Allen-Cahn/Cahn-Hilliard system

We consider an Allen–Cahn/Cahn–Hilliard system with a non‐degenerate mobility and (i) a logarithmic free energy and (ii) a non‐smooth free energy (the deep quench limit). This system arises in the modelling of phase separation and ordering in binary alloys. In particular we prove in each case 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 of (i) and (ii) in one and two space dimensions (and three space dimensions for constant mobility). The error bound being optimal in the deep quench limit. In addition an iterative scheme for solving the resulting nonlinear discrete system is analysed. Finally some numerical experiments are presented.