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This paper aims to present an improved finite element method used for achieving faster convergence in simulations of incompressible fluid flows. For stable computations of incompressible fluid flows, it is important to ensure that the flow field satisfies the equation of continuity in each element of a generally distorted mesh. The study aims to develop a numerical approach that satisfies this requirement based on the highly simplified marker-and-cell (HSMAC) method and increases computational speed by introducing a new algorithm into the simultaneous relaxation of velocity and pressure.

First, the paper shows that the classical HSMAC method is equivalent to a Jacobi-type method in terms of the simultaneous relaxation of velocity and pressure. Then, a Gauss–Seidel or successive over-relaxation (SOR)-type method is introduced in the Newton–Raphson iterations to take into account all the derivative terms in the first-order Taylor series expansion of a nodal-averaged error explicitly. Here, the nine-node quadrilateral (Q2–Q1) elements are used.

The new finite element approach based on the improved HSMAC algorithm is tested on fluid flow problems including the lid-driven square cavity flow and the flow past a circular cylinder. The results show significant improvement of the convergence property with the accuracy of the numerical solutions kept unchanged even on a highly distorted mesh.

To the best of the author’s knowledge, the idea of using the Gauss–Seidel or SOR method in the simultaneous relaxation procedure of the HSMAC method has not been proposed elsewhere.

This paper proposed a bi-level mathematical model for location, routing and allocation of medical centers to distribution depots during the COVID-19 pandemic outbreak. The developed model has two players including interdictor (COVID-19) and fortifier (government). Accordingly, the aim of the first player (COVID-19) is to maximize system costs and causing further damage to the system. The goal of the second player (government) is to minimize the costs of location, routing and allocation due to budget limitations.

The approach of evolutionary games with environmental feedbacks was used to develop the proposed model. Moreover, the game continues until the desired demand is satisfied. The Lagrangian relaxation method was applied to solve the proposed model.

Empirical results illustrate that with increasing demand, the values of the objective functions of the interdictor and fortifier models have increased. Also, with the raising fixed cost of the established depot, the values of the objective functions of the interdictor and fortifier models have raised. In this regard, the number of established depots in the second scenario (COVID-19 wave) is more than the first scenario (normal COVID-19 conditions).

The results of the current research can be useful for hospitals, governments, Disaster Relief Organization, Red Crescent, the Ministry of Health, etc. One of the limitations of the research is the lack of access to accurate information about transportation costs. Moreover, in this study, only the information of drivers and experts about transportation costs has been considered. In order to implement the presented solution approach for the real case study, high RAM and CPU hardware facilities and software facilities are required, which are the limitations of the proposed paper.

The main contributions of the current research are considering evolutionary games with environmental feedbacks during the COVID-19 pandemic outbreak and location, routing and allocation of the medical centers to the distribution depots during the COVID-19 outbreak. A real case study is illustrated, where the Lagrangian relaxation method is employed to solve the problem.

The distinction between nominal and effective tariffs (or protection) is well established in the theoretical literature, albeit in the context of the traditional analysis of inter‐industry trade flows. This analysis is based upon assumptions such as product and production homogeneity, non‐increasing returns, armslength trade, and small open economy country conditions. Relaxation of some or all of these assumptions has direct implications for effective protection analysis under any type of trade flows. As is now widely recognised, however, relaxation of these assumptions is also likely to be associated with intra‐industry specialisation and exchange. It is to this wider issue of effective protection analysis in the context of “within‐industry” specialisation (vertical and/or horizontal) and of two‐way trade, that this paper is addressed.

Glass material is largely used for load-bearing components in buildings. For this reason, standardized calculation methods can be used in support of safe structural design in common loading and boundary conditions. Differing from earlier literature efforts, the present study elaborates on the load-bearing capacity, failure time and fire endurance of ordinary glass elements under fire exposure and sustained mechanical loads, with evidence of major trends in terms of loading condition and cross-sectional layout. Traditional verification approaches for glass in cold conditions (i.e. stress peak check) and fire endurance of load-bearing members (i.e. deflection and deflection rate limits) are assessed based on parametric numerical simulations.

The mechanical performance of structural glass elements in fire still represents an open challenge for design and vulnerability assessment. Often, special fire-resisting glass solutions are used for limited practical applications only, and ordinary soda-lime silica glass prevails in design applications for load-bearing members. Moreover, conventional recommendations and testing protocols in use for load-bearing members composed of traditional constructional materials are not already addressed for glass members. This paper elaborates on the fire endurance and failure detection methods for structural glass beams that are subjected to standard ISO time–temperature for fire exposure and in-plane bending mechanical loads. Fire endurance assessment methods are discussed with the support of Finite Element (FE) numerical analyses.

Based on extended parametric FE analyses, multiple loading, geometrical and thermo-mechanical configurations are taken into account for the analysis of simple glass elements under in-plane bending setup and fire exposure. The comparative results show that – in most of cases – thermal effects due to fire exposure have major effects on the actual load-bearing capacity of these members. Moreover, the conventional stress peak verification approach needs specific elaborations, compared to traditional calculations carried out in cold conditions.

The presented numerical results confirm that the fire endurance analysis of ordinary structural glass elements is a rather complex issue, due to combination of multiple aspects and influencing parameters. Besides, FE simulations can provide useful support for a local and global analysis of major degradation and damage phenomena, and thus support the definition of simple and realistic verification procedures for fire exposed glass members.

This paper aims to investigate the suitability of additive manufacturing to produce O-ring seals.

The O-rings were made by the PolyJet-Matrix technology using four different digital materials and then tested for relaxation properties under static and dynamic (sliding) conditions. The approximation of the relaxation curves involved modelling with a Prony series.

The PolyJet-Matrix technology offers new opportunities to model elastomeric elements, with examples being the O-rings produced and tested for their relaxation properties. Describing the behaviour of the particular materials fabricated with this technology by using relaxation functions will extend the knowledge base on digital materials.

The four types of photopolymers used in the experiment differed in viscoelastic properties. The analysis of the stress relaxation of the O-ring models was performed at four different step displacements of the loading element.

The test results may be useful for the design of O-ring seals made of new elastomeric materials. The relaxation properties of the O-rings made of such materials can be applied to analyse the dynamics of seals, for instance, face seals.

The originality of the work lies in the use of digital materials to design and produce elastomeric elements with different relaxation properties, which was confirmed by the test results. This paper presents results of a relaxation analysis for a ring model and the material that the ring is made of. It also discusses how 3D printing and digital materials can be applied in practice.

The optimisation of grid structure and relaxation parameter is considered in this paper in connection with two‐dimensional finite difference solution of Poisson's equation for determining the field profile in a reverse biased planar type p?n junction. By dividing the planar junction into regions with rectangular and circular symmetry, regional optimisations have been carried out using small area test sites. Having obtained the optimal grid size and relaxation parameter for each region, the complete solution was obtained easily with very fast convergence. The method involved in this kind of regional optimisation is presented in detail with discussions on its comparative usefulness with other known techniques.

Optimisation of the discretising steps in the space and time domains has been studied for the evaluation of corresponding optimum value of over‐relaxation parameter in the numerical solution of transient heat flow equation using successive‐over‐relaxation method in the finite difference code. No closed form solutions are available for the optimisation of a complete set of involved parameters in such problems. The present work deals quantitatively with the need for a more generalised closed form relation involving discretising steps in the space and the time domains for an optimal over‐relaxation parameter. The maximum finite difference error and the number of iterations required to achieve a reasonable error tolerance in the functional value are the two criteria used to obtain an optimised set of parameters. The effect of deviation from the optimised values of any of the involved parameters has been shown over a model problem of one‐dimensional diamond‐IIa medium of 100 micrometer length and for a time duration of 1.24 micro‐seconds.

This is a textbook on a subject that has been developed almost entirely within the last decade. It deals with a method of solving problems by successive approximations that have wide applications in engineering and physics.

The purpose of this paper is to consider the simultaneous flow of Casson Williamson non Newtonian fluids in a vertical porous medium under the influence of variable thermos-physical parameters.

The model equations are a set of partial differential equations (PDEs). These PDEs were transformed into a non-dimensionless form using suitable non-dimensional quantities. The transformed equations were solved numerically using an iterative method called spectral relaxation techniques. The spectral relaxation technique is an iterative method that uses the Gauss-Seidel approach in discretizing and linearizing the set of equations.

It was found out in the study that a considerable number of variable viscosity parameter leads to decrease in the velocity and temperature profiles. Increase in the variable thermal conductivity parameter degenerates the velocity as well as temperature profiles. Hence, the variable thermo-physical parameters greatly influence the non-Newtonian fluids flow.

This study considered the simultaneous flow of Casson-Williamson non-Newtonian fluids by considering the fluid thermal properties to vary within the fluid layers. To the best of the author’s knowledge, such study has not been considered in literature.

Examines the twelfth published year of the ITCRR. Runs the whole gamut of textile innovation, research and testing, some of which investigates hitherto untouched aspects. Subjects discussed include cotton fabric processing, asbestos substitutes, textile adjuncts to cardiovascular surgery, wet textile processes, hand evaluation, nanotechnology, thermoplastic composites, robotic ironing, protective clothing (agricultural and industrial), ecological aspects of fibre properties – to name but a few! There would appear to be no limit to the future potential for textile applications.