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Article
Publication date: 13 June 2016

Zahur Ullah, Will Coombs and C Augarde

A variety of meshless methods have been developed in the last 20 years with an intention to solve practical engineering problems, but are limited to small academic…

Abstract

Purpose

A variety of meshless methods have been developed in the last 20 years with an intention to solve practical engineering problems, but are limited to small academic problems due to associated high computational cost as compared to the standard finite element methods (FEM). The purpose of this paper is to develop an efficient and accurate algorithms based on meshless methods for the solution of problems involving both material and geometrical nonlinearities.

Design/methodology/approach

A parallel two-dimensional linear elastic computer code is presented for a maximum entropy basis functions based meshless method. The two-dimensional algorithm is subsequently extended to three-dimensional adaptive nonlinear and three-dimensional parallel nonlinear adaptively coupled finite element, meshless method cases. The Prandtl-Reuss constitutive model is used to model elasto-plasticity and total Lagrangian formulations are used to model finite deformation. Furthermore, Zienkiewicz and Zhu and Chung and Belytschko error estimation procedure are used in the FE and meshless regions of the problem domain, respectively. The message passing interface library and open-source software packages, METIS and MUltifrontal Massively Parallel Solver are used for the high performance computation.

Findings

Numerical examples are given to demonstrate the correct implementation and performance of the parallel algorithms. The agreement between the numerical and analytical results in the case of linear elastic example is excellent. For the nonlinear problems load-displacement curve are compared with the reference FEM and found in a very good agreement. As compared to the FEM, no volumetric locking was observed in the case of meshless method. Furthermore, it is shown that increasing the number of processors up to a given number improve the performance of parallel algorithms in term of simulation time, speedup and efficiency.

Originality/value

Problems involving both material and geometrical nonlinearities are of practical importance in many engineering applications, e.g. geomechanics, metal forming and biomechanics. A family of parallel algorithms has been developed in this paper for these problems using adaptively coupled finite element, meshless method (based on maximum entropy basis functions) for distributed memory computer architectures.

Article
Publication date: 1 January 2014

Hooman Razmjoo and Masoud Movahhedi

In this paper, a modified meshless method, as one of the numerical techniques that has recently emerged in the area of computational electromagnetics, is extended to…

Abstract

Purpose

In this paper, a modified meshless method, as one of the numerical techniques that has recently emerged in the area of computational electromagnetics, is extended to solving time-domain wave equation. The paper aims to discuss these issues.

Design/methodology/approach

In space domain, the fields at the collocation points are expanded into a series of new Shepard's functions which have been suggested recently and are treated with a meshless method procedure. For time discretization of the second-order time-derivative, two finite-difference schemes, i.e. backward difference and Newmark-β techniques, are proposed.

Findings

Both schemes are implicit and always stable and have unconditional stability with different orders of accuracy and numerical dispersion. The unconditional stability of the proposed methods is analytically proven and numerically verified. Moreover, two numerical examples for electromagnetic field computation are also presented to investigate characteristics of the proposed methods.

Originality/value

The paper presents two unconditionally stable schemes for meshless methods in time-domain electromagnetic problems.

Details

COMPEL: The International Journal for Computation and Mathematics in Electrical and Electronic Engineering, vol. 33 no. 1/2
Type: Research Article
ISSN: 0332-1649

Keywords

Article
Publication date: 19 April 2011

Isa Ahmadi and M.M. Aghdam

The purpose of this paper is to present a micromechanical model based on a new truly local meshless method for analysis of heat transfer in composite materials.

Abstract

Purpose

The purpose of this paper is to present a micromechanical model based on a new truly local meshless method for analysis of heat transfer in composite materials.

Design/methodology/approach

The presented meshless method is based on the integral form of energy equation in the sub‐particles in the material. In the presented meshless method due to elimination of domain integration the computational efforts are decreased substantially.

Findings

Numerical results are presented for temperature distribution, heat flux and thermal conductivity. Numerical results show that the presented meshless method is simple, effective, accurate and less costly method in micromechanical modeling of heat conduction in heterogeneous materials.

Research limitations/implications

A small area of the composite system called representative volume element is considered as the solution domain. The fully bonded fiber‐matrix interface is considered and contact thermal resistant is neglected from the fiber matrix interface and so the continuity of temperature and reciprocity of heat flux is satisfied in the fiber‐matrix interface.

Originality/value

For the first time a new truly local meshless method based on the integral form of energy equation for the sub‐particles in the materials is presented for analysis of heat transfer in composite materials.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 21 no. 3
Type: Research Article
ISSN: 0961-5539

Keywords

Article
Publication date: 26 November 2020

Armagan Karamanli

The study aims to present a new meshless method based on the Taylor series expansion. The compact supported radial basis functions (CSRBFs) are very attractive, can be…

156

Abstract

Purpose

The study aims to present a new meshless method based on the Taylor series expansion. The compact supported radial basis functions (CSRBFs) are very attractive, can be considered as a numerical tool for the engineering problems and used to obtain the trial solution and its derivatives without differentiating the basis functions for a meshless method. A meshless based on the CSRBF and Taylor series method has been developed for the solutions of engineering problems.

Design/methodology/approach

This paper is devoted to present a truly meshless method which is called a radial basis Taylor series method (RBTSM) based on the CSRBFs and Taylor series expansion (TSE). The basis function and its derivatives are obtained without differentiating CSRBFs.

Findings

The RBTSM does not involve differentiation of the approximated function. This property allows us to use a wide range of CSRBF and weight functions including the constant one. By using a different number of terms in the TSE, the global convergence properties of the RBTSM can be improved. The global convergence properties are satisfied by the RBTSM. The computed results based on the RBTSM shows excellent agreement with results given in the open literature. The RBTSM can provide satisfactory results even with the problem domains which have curved boundaries and irregularly distributed nodes.

Originality/value

The CSRBFs have been widely used for the construction of the basic function in the meshless methods. However, the derivative of the basis function is obtained with the differentiation of the CSRBF. In the RBTSM, the derivatives of the basis function are obtained by using the TSE without differentiating the CSRBF.

Details

Engineering Computations, vol. 38 no. 5
Type: Research Article
ISSN: 0264-4401

Keywords

Article
Publication date: 3 July 2017

Arman Shojaei, Mirco Zaccariotto and Ugo Galvanetto

The paper aims to use a switching technique which allows to couple a nonlocal bond-based Peridynamic approach to the Meshless Local Exponential Basis Functions (MLEBF…

Abstract

Purpose

The paper aims to use a switching technique which allows to couple a nonlocal bond-based Peridynamic approach to the Meshless Local Exponential Basis Functions (MLEBF) method, based on classical continuum mechanics, to solve planar problems.

Design/methodology/approach

The coupling has been achieved in a completely meshless scheme. The domain is divided in three zones: one in which only Peridynamics is applied, one in which only the meshless method is applied and a transition zone where a gradual transition between the two approaches takes place.

Findings

The new coupling technique generates overall grids that are not affected by ghost forces. Moreover, the use of the meshless approach can be limited to a narrow boundary region of the domain, and in this way, it can be used to remove the “surface effect” from the Peridynamic solution applied to all internal points.

Originality/value

The current study paves the road for future studies on dynamic and static crack propagation problems.

Details

Engineering Computations, vol. 34 no. 5
Type: Research Article
ISSN: 0264-4401

Keywords

Article
Publication date: 24 May 2013

Hong Wang, Jyri Leskinen, Dong‐Seop Lee and Jacques Périaux

The purpose of this paper is to investigate an active flow control technique called Shock Control Bump (SCB) for drag reduction using evolutionary algorithms.

Abstract

Purpose

The purpose of this paper is to investigate an active flow control technique called Shock Control Bump (SCB) for drag reduction using evolutionary algorithms.

Design/methodology/approach

A hierarchical genetic algorithm (HGA) consisting of multi‐fidelity models in three hierarchical topological layers is explored to speed up the design optimization process. The top layer consists of a single sub‐population operating on a precise model. On the middle layer, two sub‐populations operate on a model of intermediate accuracy. The bottom layer, consisting of four sub‐populations (two for each middle layer populations), operates on a coarse model. It is well‐known that genetic algorithms (GAs) are different from deterministic optimization tools in mimicking biological evolution based on Darwinian principle. In HGAs process, each population is handled by GA and the best genetic information obtained in the second or third layer migrates to the first or second layer for refinement.

Findings

The method was validated on a real life optimization problem consisting of two‐dimensional SCB design optimization installed on a natural laminar flow airfoil (RAE5243). Numerical results show that HGA is more efficient and achieves more drag reduction compared to a single population based GA.

Originality/value

Although the idea of HGA approach is not new, the novelty of this paper is to combine it with mesh/meshless methods and multi‐fidelity flow analyzers. To take the full benefit of using hierarchical topology, the following conditions are implemented: the first layer uses a precise meshless Euler solver with fine cloud of points, the second layer uses a hybrid mesh/meshless Euler solver with intermediate mesh/clouds of points, the third layer uses a less fine mesh with Euler solver to explore efficiently the search space with large mutation span.

Details

Engineering Computations, vol. 30 no. 4
Type: Research Article
ISSN: 0264-4401

Keywords

Article
Publication date: 28 September 2022

Wei Wang, Junping Shi, Xiaoshan Cao and Yifeng Hu

The partition of unity of the standard meshless Galerkin method is used as basis in expressing the discontinuity of the contact surface displacement, particularly by…

Abstract

Purpose

The partition of unity of the standard meshless Galerkin method is used as basis in expressing the discontinuity of the contact surface displacement, particularly by adding discontinuous terms into the displacement mode, and constructing the discontinuous meshless displacement field function. In this study the contact surface equation is aimed to derive from the improved Coulomb friction contact model.

Design/methodology/approach

In this paper based on the basic idea of meshless method, an improved moving least squares approximation function (expansion method based on out of unit division) is applied to the analysis of two-dimensional contact problems.

Findings

On the basis of this equation after discrete processing, it is combined with the discrete form of the virtual work equation with added contact conditions, and eventually transformed into a standard linear complementary problem. Moreover, it is solved by using the Lemke algorithm, and a corresponding example is provided in this research.

Originality/value

The proposed method can effectively control the mutual embedding of the contact surface, and the stress distribution that is the same as the actual situation can be obtained on the contact surface.

Details

Engineering Computations, vol. 39 no. 9
Type: Research Article
ISSN: 0264-4401

Keywords

Article
Publication date: 1 February 2022

Diogo Gonçalves, Joel Lopes, Raul Campilho and Jorge Belinha

The purpose of the present work is to develop the combination of the radial point interpolation method (RPIM) with a bi-directional evolutionary structural optimization…

Abstract

Purpose

The purpose of the present work is to develop the combination of the radial point interpolation method (RPIM) with a bi-directional evolutionary structural optimization (BESO) algorithm and extend it to the analysis of benchmark examples and automotive industry applications.

Design/methodology/approach

A BESO algorithm capable of detecting variations in the stress level of the structure, and thus respond to those changes by reinforcing the solid material, is developed. A meshless method, the RPIM, is used to iteratively obtain the stress field. The obtained optimal topologies are then recreated and numerically analyzed to validate its proficiency.

Findings

The proposed algorithm is capable to achieve accurate benchmark material distributions. Implementation of the BESO algorithm combined with the RPIM allows developing innovative lightweight automotive structures with increased performance.

Research limitations/implications

Computational cost of the topology optimization analysis is constrained by the nodal density discretizing the problem domain. Topology optimization solutions are usually complex, whereby they must be fabricated by additive manufacturing techniques and experimentally validated.

Practical implications

In automotive industry, fuel consumption, carbon emissions and vehicle performance is influenced by structure weight. Therefore, implementation of accurate topology optimization algorithms to design lightweight (cost-efficient) components will be an asset in industry.

Originality/value

Meshless methods applications in topology optimization are not as widespread as the finite element method (FEM). Therefore, this work enhances the state-of-the-art of meshless methods and demonstrates the suitability of the RPIM to solve topology optimization problems. Innovative lightweight automotive structures are developed using the proposed methodology.

Details

Engineering Computations, vol. 39 no. 6
Type: Research Article
ISSN: 0264-4401

Keywords

Article
Publication date: 1 February 2001

Suvranu De and Klaus‐Jürgen Bathe

Computational efficiency and reliability are clearly the most important requirements for the success of a meshless numerical technique. While the basic ideas of meshless

Abstract

Computational efficiency and reliability are clearly the most important requirements for the success of a meshless numerical technique. While the basic ideas of meshless techniques are simple and well understood, an effective meshless method is very difficult to develop. The efficiency depends on the proper choice of the interpolation scheme, numerical integration procedures and techniques of imposing the boundary conditions. These issues in the context of the method of finite spheres are discussed.

Details

Engineering Computations, vol. 18 no. 1/2
Type: Research Article
ISSN: 0264-4401

Keywords

Article
Publication date: 22 May 2008

Kevin Erhart, Eduardo Divo and Alain Kassab

This paper aims to develop and describe an improved process for determining the rate of heat generation in living tissue.

Abstract

Purpose

This paper aims to develop and describe an improved process for determining the rate of heat generation in living tissue.

Design/methodology/approach

Previous work by the authors on solving the bioheat equation has been updated to include a new localized meshless method which will create a more robust and computationally efficient technique. Inclusion of this technique will allow for the solution of more complex and realistic geometries, which are typical of living tissue. Additionally, the unknown heat generation rates are found through genetic algorithm optimization.

Findings

The localized technique showed superior accuracy and significant savings in memory and processor time. The computational efficiency of the newly proposed meshless solver allows the optimization process to be carried to a higher level, leading to more accurate solutions for the inverse technique. Several example cases are presented to demonstrate these conclusions.

Research limitations/implications

This work includes only 2D development of the approach, while any realistic modeling for patient‐specific cases would be inherently 3D. The extension to 3D, as well as studies to improve the technique by decreasing the sensitivity to measurement noise and to incorporate non‐invasive measurement positioning, are under way.

Practical implications

As medical imaging continuously improves, such techniques may prove useful in patient diagonosis, as heat generation can be correlated to the presence of tumors, infections, or other conditions.

Originality/value

This paper describes a new application of meshless methods. Such methods are becoming attractive due to their decreased pre‐processing requirements, especially for problems involving complex geometries (such as patient specific tissues), as well as optimization problems, where geometries may be constantly changing.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 18 no. 3/4
Type: Research Article
ISSN: 0961-5539

Keywords

1 – 10 of 305