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Article
Publication date: 4 June 2020

Tiago Oliveira, Wilber Vélez and Artur Portela

This paper is concerned with new formulations of local meshfree and finite element numerical methods, for the solution of two-dimensional problems in linear elasticity.

Abstract

Purpose

This paper is concerned with new formulations of local meshfree and finite element numerical methods, for the solution of two-dimensional problems in linear elasticity.

Design/methodology/approach

In the local domain, assigned to each node of a discretization, the work theorem establishes an energy relationship between a statically admissible stress field and an independent kinematically admissible strain field. This relationship, derived as a weighted residual weak form, is expressed as an integral local form. Based on the independence of the stress and strain fields, this local form of the work theorem is kinematically formulated with a simple rigid-body displacement to be applied by local meshfree and finite element numerical methods. The main feature of this paper is the use of a linearly integrated local form that implements a quite simple algorithm with no further integration required.

Findings

The reduced integration, performed by this linearly integrated formulation, plays a key role in the behavior of local numerical methods, since it implies a reduction of the nodal stiffness which, in turn, leads to an increase of the solution accuracy and, which is most important, presents no instabilities, unlike nodal integration methods without stabilization. As a consequence of using such a convenient linearly integrated local form, the derived meshfree and finite element numerical methods become fast and accurate, which is a feature of paramount importance, as far as computational efficiency of numerical methods is concerned. Three benchmark problems were analyzed with these techniques, in order to assess the accuracy and efficiency of the new integrated local formulations of meshfree and finite element numerical methods. The results obtained in this work are in perfect agreement with those of the available analytical solutions and, furthermore, outperform the computational efficiency of other methods. Thus, the accuracy and efficiency of the local numerical methods presented in this paper make this a very reliable and robust formulation.

Originality/value

Presentation of a new local mesh-free numerical method. The method, linearly integrated along the boundary of the local domain, implements an algorithm with no further integration required. The method is absolutely reliable, with remarkably-accurate results. The method is quite robust, with extremely-fast computations.

Details

Multidiscipline Modeling in Materials and Structures, vol. 16 no. 5
Type: Research Article
ISSN: 1573-6105

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Article
Publication date: 6 November 2017

Gholamreza Shobeyri and Mohammad Yourdkhani

The purpose of this paper is to develop an efficient and accurate mesh-less method to simulate free flows with continuous deformation in boundary positions.

Abstract

Purpose

The purpose of this paper is to develop an efficient and accurate mesh-less method to simulate free flows with continuous deformation in boundary positions.

Design/methodology/approach

A two-step pressure projection method in a Lagrangian form is used to solve the governing equations of mass and momentum conservation. In the first step, velocity field is calculated in which incompressibility is not enforced. In the second step, a pressure Poisson equation is applied to satisfy incompressibility conditions. The numerical proposed method is used for spatial discretization of the governing equations. Three benchmark-free surface problems, namely, dam break, solitary wave propagation and evolution of an elliptical bubble with available experimental results and analytical solutions, are used to test the accuracy of the proposed method. The results prove the accuracy of the method in simulating free surface problems.

Findings

The Voronoi diagram instead of kernel function summation can be used to estimate the particle or nodal volume concept in particle-based (mesh-less) methods for function approximation. This idea probably works well especially for highly irregular node distributions.

Originality/value

The continuous moving least squares shape functions are applied for function approximation, and the Voronoi diagram concept is also used to estimate region influence of computational nodal points or particle volumes. Combinations of these two concepts and finite differences formulation for first derivatives gives an accurate numerical model for Laplacian operator in the proposed method.

Details

Engineering Computations, vol. 34 no. 8
Type: Research Article
ISSN: 0264-4401

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Article
Publication date: 22 February 2013

Paul W. Cleary, Raymond C.Z. Cohen, Simon M. Harrison, Matthew D. Sinnott, Mahesh Prakash and Stuart Mead

The purpose of this paper is to show how simulation of the flow of particulates and fluids using discrete element modelling (DEM) and smoothed particle dynamics (SPH…

Abstract

Purpose

The purpose of this paper is to show how simulation of the flow of particulates and fluids using discrete element modelling (DEM) and smoothed particle dynamics (SPH) particle methods, offer opportunities for better understanding the dynamics of flow processes.

Design/methodology/approach

DEM and SPH methods are demonstrated in a broad range of computationally‐demanding applications including comminution, biomedical, geophysical extreme flow events (risk/disaster modelling), eating of food by humans and elite water‐based sports.

Findings

DEM is ideally suited to predicting industrial and geophysical applications where collisions between particles are the dominant physics. SPH is highly suited to multi‐physics fluid flow applications in industrial, biophysical and geophysical applications. The advantages and disadvantages of these particle methods are discussed.

Research limitations/implications

Research results are limited by the numerical resolution that can currently be afforded.

Practical implications

The paper demonstrates the use of particle‐based computational methods in a series of high value applications. Enterprises that share interests in these applications will benefit in their product and service development by adopting these methods.

Social implications

The ability to model disasters provides governments and companies with the opportunity and obligation to use these to render knowable disasters which were previously considered unknowable. The ability to predict the breakdown of food during eating opens up opportunities for the design of superior performing foods with lower salt, sugar and fat that can directly contribute to improved health outcomes and can influence government food regulatory policy.

Originality/value

The paper extends the scale and range of modelling of particle methods for demanding leading‐edge problems, of practical interest in engineering and applied sciences.

Details

Engineering Computations, vol. 30 no. 2
Type: Research Article
ISSN: 0264-4401

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Article
Publication date: 1 July 1967

Whereas the Minister of Labour (hereafter in this Order referred to as “the Minister”) has received from the Rope, Twine and Net Wages Council (Great Britain) the wages…

Abstract

Whereas the Minister of Labour (hereafter in this Order referred to as “the Minister”) has received from the Rope, Twine and Net Wages Council (Great Britain) the wages regulation proposals set out in Schedules 1 and 2 hereof;

Details

Managerial Law, vol. 2 no. 4
Type: Research Article
ISSN: 0309-0558

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Article
Publication date: 31 January 2020

Zehba A.S. Raizah

The purpose of this study is to apply the incompressible smoothed particle hydrodynamics method for simulating the natural convection flow inside a cavity including cross…

Abstract

Purpose

The purpose of this study is to apply the incompressible smoothed particle hydrodynamics method for simulating the natural convection flow inside a cavity including cross blades or circular cylinder cylinder.

Design/methodology/approach

The base fluid is water and copper-water nanofluid is treated as a working fluid. The left and rights walls are maintained at a cool temperature, the horizontal cavity walls are isolated and the inner shape was heated. The physical parameters are the length of the blades L_Blade, the number of cross blades, circular cylinder radius L_R, Rayleigh number Ra and the nanoparticles volume fraction.

Findings

The results reveal that the lengths of the cross blade, number of the blades and radius of the circular cylinder is working as an enhancement factor for heat transfer and fluid flows inside a cavity. Adding nanoparticles augments heat transfer and reduces the fluid flow intensity inside a cavity. The best case for buoyancy-driven flow was obtained when the inner shape is the circular cylinder at a higher Rayleigh number.

Originality/value

This work uses a distinctive numerical method to study the natural convection heat from cross blades inside a cavity filled with nanofluid. It provides a new analysis of this issue and presented good results.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 30 no. 10
Type: Research Article
ISSN: 0961-5539

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Article
Publication date: 2 March 2015

Ruding Lou, Jean-Philippe Pernot, Franca Giannini, Philippe Veron and Bianca Falcidieno

The purpose of this paper is to set up a new framework to enable direct modifications of volume meshes enriched with semantic information associated to multiple…

Abstract

Purpose

The purpose of this paper is to set up a new framework to enable direct modifications of volume meshes enriched with semantic information associated to multiple partitions. An instance of filleting operator is prototyped under this framework and presented in the paper.

Design/methodology/approach

In this paper, a generic mesh modification operator has been designed and a new instance of this operator for filleting finite element (FE) sharp edges of tetrahedral multi-partitioned meshes is also pro-posed. The filleting operator works in two main steps. The outer skin of the tetrahedral mesh is first deformed to round user-specified sharp edges while satisfying constraints relative to the shape of the so-called Virtual Group Boundaries. Then, in the filleting area, the positions of the inner nodes are relaxed to improve the aspect ratio of the mesh elements.

Findings

The classical mainstream methodology for product behaviour optimization involves the repetition of four steps: CAD modelling, meshing of CAD models, enrichment of models with FE simulation semantics and FEA. This paper highlights how this methodology could be simplified by two steps: simulation model modification and FEA. The authors set up a new framework to enable direct modifications of volume meshes enriched with semantic information associated to multiple partitions and the corresponding fillet operator is devised.

Research limitations/implications

The proposed framework shows only a paradigm of direct modifications of semantic enriched meshes. It could be further more improved by adding or changing the modules inside. The fillet operator does not take into account the exact radius imposed by user. With this proposed fillet operator the mesh element density may not be enough high to obtain wished smoothness.

Originality/value

This paper fulfils an identified industry need to speed up the product behaviour analysis process by directly modifying the simulation semantic enriched meshes.

Details

Engineering Computations, vol. 32 no. 1
Type: Research Article
ISSN: 0264-4401

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Article
Publication date: 19 August 2019

Abdelraheem M. Aly

This paper aims to adopt incompressible smoothed particle hydrodynamics (ISPH) method to simulate MHD double-diffusive natural convection in a cavity containing an…

Abstract

Purpose

This paper aims to adopt incompressible smoothed particle hydrodynamics (ISPH) method to simulate MHD double-diffusive natural convection in a cavity containing an oscillating pipe and filled with nanofluid.

Design/methodology/approach

The Lagrangian description of the governing partial differential equations are solved numerically using improved ISPH method. The inner oscillating pipe is divided into two different pipes as an open and a closed pipe. The sidewalls of the cavity are cooled with a lower concentration C_c and the horizontal walls are adiabatic. The inner pipe is heated with higher concentration C_h. The analysis has been conducted for the two different cases of inner oscillating pipes under the effects of wide range of governing parameters.

Findings

It is found that a suitable oscillating pipe makes a well convective transport inside a cavity. Presence of the oscillating pipe has effects on the heat and mass transfer and fluid intensity inside a cavity. Hartman parameter suppresses the velocity and weakens the maximum values of the stream function. An increase on Hartman, Lewis and solid volume fraction parameters leads to an increase on average Nusselt number on an oscillating pipe and left cavity wall. Average Sherwood number on an oscillating pipe and left cavity wall decreases as Hartman parameter increases.

Originality/value

The main objective of this work is to study the MHD double-diffusive natural convection of a nanofluid in a square cavity containing an oscillating pipe using improved ISPH method.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 30 no. 2
Type: Research Article
ISSN: 0961-5539

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Article
Publication date: 24 September 2010

M. Grujicic, G. Arakere and T. He

This paper aims to conduct a combined Eulerian/Lagrangian fluid/solid transient non‐linear dynamics computational analysis of the interaction between a single planar blast…

Abstract

Purpose

This paper aims to conduct a combined Eulerian/Lagrangian fluid/solid transient non‐linear dynamics computational analysis of the interaction between a single planar blast wave and a human head in order to assess the extent of intra‐cranial shock wave generation and its potential for causing traumatic brain injury.

Design/methodology/approach

Two levels of blast peak overpressure were selected, one corresponding to the unprotected lung‐injury threshold while the other associated with a 50 percent probability for lung injury caused death. Collision of the head with a stationary/rigid barrier (at an initial collision velocity of 5 m/s) was also analyzed computationally, since blunt‐object impact conditions may lead to mild traumatic brain injury (mTBI), i.e. concussion.

Findings

A comparison between the two blast and the single blunt‐object impact cases with the corresponding head‐to‐head‐collision results showed that, while the von Mises stress‐based head‐to‐head collision mTBI thresholds are not exceeded under blast‐loading conditions investigated, the high blast‐induced peak‐pressure levels within the intra‐cranial cavity may lead to mTBI.

Practical implications

While concussion is not generally considered as life altering/threatening, the associated temporary loss of situational awareness or consciousness may have devastating consequences in the case of common military tactical and battle‐field scenarios. This suggests that the head‐protection gear (primarily, the helmet) which are currently designed to withstand blunt‐object and ballistic impacts, should be redesigned in order to obtain the necessary level of head protection with respect to blast impact.

Originality/value

The paper provides a comprehensive computational investigation of impact on a human skull/brain assembly.

Details

Multidiscipline Modeling in Materials and Structures, vol. 6 no. 3
Type: Research Article
ISSN: 1573-6105

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Article
Publication date: 8 February 2021

Ouadie Koubaiti, Said EL Fakkoussi, Jaouad El-Mekkaoui, Hassan Moustachir, Ahmed Elkhalfi and Catalin I. Pruncu

This paper aims to propose a new boundary condition and a web-spline basis of finite element space approximation to remedy the problems of constraints due to homogeneous…

Abstract

Purpose

This paper aims to propose a new boundary condition and a web-spline basis of finite element space approximation to remedy the problems of constraints due to homogeneous and non-homogeneous; Dirichlet boundary conditions. This paper considered the two-dimensional linear elasticity equation of Navier–Lamé with the condition CAB. The latter allows to have a total insertion of the essential boundary condition in the linear system obtained; without using a numerical method as Lagrange multiplier. This study have developed mixed finite element; method using the B-splines Web-spline space. These provide an exact implementation of the homogeneous; Dirichlet boundary conditions, which removes the constraints caused by the standard; conditions. This paper showed the existence and the uniqueness of the weak solution, as well as the convergence of the numerical solution for the quadratic case are proved. The weighted extended B-spline; approach have become a much more workmanlike solution.

Design/methodology/approach

In this paper, this study used the implementation of weighted finite element methods to solve the Navier–Lamé system with a new boundary condition CA, B (Koubaiti et al., 2020), that generalises the well-known basis, especially the Dirichlet and the Neumann conditions. The novel proposed boundary condition permits to use a single Matlab code, which summarises all kind of boundary conditions encountered in the system. By using this model is possible to save time and programming recourses while reap several programs in a single directory.

Findings

The results have shown that the Web-spline-based quadratic-linear finite elements satisfy the inf–sup condition, which is necessary for existence and uniqueness of the solution. It was demonstrated by the existence of the discrete solution. A full convergence was established using the numerical solution for the quadratic case. Due to limited regularity of the Navier–Lamé problem, it will not change by increasing the degree of the Web-spline. The computed relative errors and their rates indicate that they are of order 1/H. Thus, it was provided their theoretical validity for the numerical solution stability. The advantage of this problem that uses the CA, B boundary condition is associated to reduce Matlab programming complexity.

Originality/value

The mixed finite element method is a robust technique to solve difficult challenges from engineering and physical sciences using the partial differential equations. Some of the important applications include structural mechanics, fluid flow, thermodynamics and electromagnetic fields (Zienkiewicz and Taylor, 2000) that are mainly based on the approximation of Lagrange. However, this type of approximation has experienced a great restriction in the level of domain modelling, especially in the case of complicated boundaries such as that in the form of curvilinear graphs. Recently, the research community tried to develop a new way of approximation based on the so-called B-spline that seems to have superior results in solving the engineering problems.

Details

Engineering Computations, vol. ahead-of-print no. ahead-of-print
Type: Research Article
ISSN: 0264-4401

Keywords

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