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Article
Publication date: 7 May 2020

Jéderson da Silva, Jucélio Tomás Pereira and Diego Amadeu F. Torres

The purpose of this paper is to propose a new scheme for obtaining acceptable solutions for problems of continuum topology optimization of structures, regarding the…

Abstract

Purpose

The purpose of this paper is to propose a new scheme for obtaining acceptable solutions for problems of continuum topology optimization of structures, regarding the distribution and limitation of discretization errors by considering h-adaptivity.

Design/methodology/approach

The new scheme encompasses, simultaneously, the solution of the optimization problem considering a solid isotropic microstructure with penalization (SIMP) and the application of the h-adaptive finite element method. An analysis of discretization errors is carried out using an a posteriori error estimator based on both the recovery and the abrupt variation of material properties. The estimate of new element sizes is computed by a new h-adaptive technique named “Isotropic Error Density Recovery”, which is based on the construction of the strain energy error density function together with the analytical solution of an optimization problem at the element level.

Findings

Two-dimensional numerical examples, regarding minimization of the structure compliance and constraint over the material volume, demonstrate the capacity of the methodology in controlling and equidistributing discretization errors, as well as obtaining a great definition of the void–material interface, thanks to the h-adaptivity, when compared with results obtained by other methods based on microstructure.

Originality/value

This paper presents a new technique to design a mesh made with isotropic triangular finite elements. Furthermore, this technique is applied to continuum topology optimization problems using a new iterative scheme to obtain solutions with controlled discretization errors, measured in terms of the energy norm, and a great resolution of the material boundary. Regarding the computational cost in terms of degrees of freedom, the present scheme provides approximations with considerable less error if compared to the optimization process on fixed meshes.

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Article
Publication date: 7 August 2009

Karen L. Ricciardi and Stephen H. Brill

The Hermite collocation method of discretization can be used to determine highly accurate solutions to the steady‐state one‐dimensional convection‐diffusion equation…

Abstract

Purpose

The Hermite collocation method of discretization can be used to determine highly accurate solutions to the steady‐state one‐dimensional convection‐diffusion equation (which can be used to model the transport of contaminants dissolved in groundwater). This accuracy is dependent upon sufficient refinement of the finite‐element mesh as well as applying upstream or downstream weighting to the convective term through the determination of collocation locations which meet specified constraints. Owing to an increase in computational intensity of the application of the method of collocation associated with increases in the mesh refinement, minimal mesh refinement is sought. Very often this optimization problem is the one where the feasible region is not connected and as such requires a specialized optimization search technique. This paper aims to focus on this method.

Design/methodology/approach

An original hybrid method that utilizes a specialized adaptive genetic algorithm followed by a hill‐climbing approach is used to search for the optimal mesh refinement for a number of models differentiated by their velocity fields. The adaptive genetic algorithm is used to determine a mesh refinement that is close to a locally optimal mesh refinement. Following the adaptive genetic algorithm, a hill‐climbing approach is used to determine a local optimal feasible mesh refinement.

Findings

In all cases the optimal mesh refinements determined with this hybrid method are equally optimal to, or a significant improvement over, mesh refinements determined through direct search methods.

Research limitations

Further extensions of this work could include the application of the mesh refinement technique presented in this paper to non‐steady‐state problems with time‐dependent coefficients with multi‐dimensional velocity fields.

Originality/value

The present work applies an original hybrid optimization technique to obtain highly accurate solutions using the method of Hermite collocation with minimal mesh refinement.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 19 no. 7
Type: Research Article
ISSN: 0961-5539

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Article
Publication date: 29 August 2019

Song Gao, Jory Seguin, Wagdi G. Habashi, Dario Isola and Guido Baruzzi

This work aims to describe the physical and numerical modeling of a CFD solver for hypersonic flows in thermo-chemical non-equilibrium. This paper is the second of a…

Abstract

Purpose

This work aims to describe the physical and numerical modeling of a CFD solver for hypersonic flows in thermo-chemical non-equilibrium. This paper is the second of a two-part series that concerns the application of the solver introduced in Part I to adaptive unstructured meshes.

Design/methodology/approach

The governing equations are discretized with an edge-based stabilized finite element method (FEM). Chemical non-equilibrium is simulated using a laminar finite-rate kinetics, while a two-temperature model is used to account for thermodynamic non-equilibrium. The equations for total quantities, species and vibrational-electronic energy conservation are loosely coupled to provide flexibility and ease of implementation. To accurately perform simulations on unstructured meshes, the non-equilibrium flow solver is coupled with an edge-based anisotropic mesh optimizer driven by the solution Hessian to carry out mesh refinement, coarsening, edge swapping and node movement.

Findings

The paper shows, through comparisons with experimental and other numerical results, how FEM + anisotropic mesh optimization are the natural choice to accurately simulate hypersonic non-equilibrium flows on unstructured meshes. Three-dimensional test cases demonstrate how, for high-speed flows, shocks resolution, and not necessarily boundary layers resolution, is the main driver of solution accuracy at walls. Equally distributing the error among all elements in a suitably defined Riemannian space yields highly anisotropic grids that feature well-resolved shock waves. The resulting high level of accuracy in the computation of the enthalpy jump translates into accurate wall heat flux predictions. At the opposite end, in all cases examined, high-quality but isotropic unstructured meshes gave very poor solutions with severely inadequate heat flux distributions not even featuring expected symmetries. The paper unequivocally demonstrates that unstructured anisotropically adapted meshes are the best, and may be the only, way for accurate and cost-effective hypersonic flow solutions.

Originality/value

Although many hypersonic flow solvers are developed for unstructured meshes, few numerical simulations on unstructured meshes are presented in the literature. This work demonstrates that the proposed approach can be used successfully for hypersonic flows on unstructured meshes.

Details

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

Keywords

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Article
Publication date: 30 October 2007

Ergüven Vatandas

This paper seeks to outline a forward swept wing (FSW) design problem to reduce the optimization time and cost and to compare it with previous backward swept wing (BSW…

Abstract

Purpose

This paper seeks to outline a forward swept wing (FSW) design problem to reduce the optimization time and cost and to compare it with previous backward swept wing (BSW) results to see the differences.

Design/methodology/approach

Dynamic mesh technique was used in the design of a transonic FSW by coupling it with heuristic algorithms. To obtain the initial FSW mesh from BSW domain, a modified dynamic mesh method was developed. It was also compared with experimental results.

Findings

It is observed that the drag coefficient can be reduced by 15 percent in 500 calculations while the lift coefficient is tried to be close to the design value determined at the beginning as a design constraint. Especially, the taper ratio change direction differs from previous BSW optimization.

Originality/value

It is the first time that the dynamic mesh technique is used for obtaining the mesh structures of the new FSW members through genetic optimization. A modified dynamic mesh was used to convert BSW domain to FSW, which means a huge movement for the cells. A physical model of initial FSW is also produced for wind tunnel and tested.

Details

Aircraft Engineering and Aerospace Technology, vol. 79 no. 6
Type: Research Article
ISSN: 0002-2667

Keywords

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Article
Publication date: 29 April 2014

Yoshifumi Okamoto, Yusuke Tominaga, Shinji Wakao and Shuji Sato

The purpose of this paper is to improve the multistep algorithm using evolutionary algorithm (EA) for the topology optimization of magnetostatic shielding, and the paper…

Abstract

Purpose

The purpose of this paper is to improve the multistep algorithm using evolutionary algorithm (EA) for the topology optimization of magnetostatic shielding, and the paper reveals the effectiveness of methodology by comparison with conventional optimization method. Furthermore, the design target is to obtain the novel shape of magnetostatic shielding.

Design/methodology/approach

The EAs based on random search allow engineers to define general-purpose objects with various constraint conditions; however, many iterations are required in the FEA for the evaluation of the objective function, and it is difficult to realize a practical solution without island and void distribution. Then, the authors proposed the multistep algorithm with design space restriction, and improved the multistep algorithm in order to get better solution than the previous one.

Findings

The variant model of optimized topology derived from improved multistep algorithm is defined to clarify the effectiveness of the optimized topology. The upper curvature of the inner shielding contributed to the reduction of magnetic flux density in the target domain.

Research limitations/implications

Because the converged topology has many pixel element unevenness, the special smoother to remove the unevenness will play an important role for the realization of practical magnetostatic shielding.

Practical implications

The optimized topology will give us useful detailed structure of magnetostatic shielding.

Originality/value

First, while the conventional algorithm could not find the reasonable shape, the improved multistep optimization can capture the reasonable shape. Second, An additional search is attached to the multistep optimization procedure. It is shown that the performance of improved multistep algorithm is better than that of conventional algorithm.

Details

COMPEL: The International Journal for Computation and Mathematics in Electrical and Electronic Engineering, vol. 33 no. 3
Type: Research Article
ISSN: 0332-1649

Keywords

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Article
Publication date: 1 December 2001

Jaroslav Mackerle

Gives a bibliographical review of the finite element meshing and remeshing from the theoretical as well as practical points of view. Topics such as adaptive techniques for…

Abstract

Gives a bibliographical review of the finite element meshing and remeshing from the theoretical as well as practical points of view. Topics such as adaptive techniques for meshing and remeshing, parallel processing in the finite element modelling, etc. are also included. The bibliography at the end of this paper contains 1,727 references to papers, conference proceedings and theses/dissertations dealing with presented subjects that were published between 1990 and 2001.

Details

Engineering Computations, vol. 18 no. 8
Type: Research Article
ISSN: 0264-4401

Keywords

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Article
Publication date: 8 August 2019

Ahmed Abou El-Azm Aly and Wagdi G. Habashi

Computational fluid dynamics (CFD) simulation of the flow field around marine propellers is challenging because of geometric complexity and rotational effects. To capture…

Abstract

Purpose

Computational fluid dynamics (CFD) simulation of the flow field around marine propellers is challenging because of geometric complexity and rotational effects. To capture the flow structure, grid quality and distribution around the blades is primordial. This paper aims to demonstrate that solution-based automatic mesh optimization is the most logical and practical way to achieve optimal CFD solutions.

Design/methodology/approach

In the current paper, open water propeller performance coefficients such as thrust and torque coefficients are numerically investigated. An anisotropic mesh adaptation technique is applied, believed for the first time, to marine propellers and to two computational domains.

Findings

The current study’s performance coefficients are compared with other previously published CFD results and improvements in terms of accuracy and computational cost are vividly demonstrated for different advance coefficients, as well as a much sharper capture of the complex flow features.

Originality/value

It will be clearly demonstrated that these two improvements can be achieved, surprisingly, at a much lower meshing and computational cost.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 29 no. 9
Type: Research Article
ISSN: 0961-5539

Keywords

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Article
Publication date: 24 May 2013

Michiel H. Straathof, Giampietro Carpentieri and Michel J.L. van Tooren

An aerodynamic shape optimization algorithm is presented, which includes all aspects of the design process: parameterization, flow computation and optimization. The…

Abstract

Purpose

An aerodynamic shape optimization algorithm is presented, which includes all aspects of the design process: parameterization, flow computation and optimization. The purpose of this paper is to show that the Class‐Shape‐Refinement‐Transformation method in combination with an Euler/adjoint solver provides an efficient and intuitive way of optimizing aircraft shapes.

Design/methodology/approach

The Class‐Shape‐Transformation method was used to parameterize the aircraft shape and the flow was computed using an in‐house Euler code. An adjoint solver implemented into the Euler code was used to compute the required gradients and a trust‐region reflective algorithm was employed to perform the actual optimization.

Findings

The results of two aerodynamic shape optimization test cases are presented. Both cases used a blended‐wing‐body reference geometry as their initial input. It was shown that using a two‐step approach, a considerable improvement of the lift‐to‐drag ratio in the order of 20‐30 per cent could be achieved. The work presented in this paper proves that the CSRT method is a very intuitive and effective way of parameterizating aircraft shapes. It was also shown that using an adjoint algorithm provides the computational efficiency necessary to perform true three‐dimensional shape optimization.

Originality/value

The novelty of the algorithm lies in the use of the Class‐Shape‐Refinement‐Transformation method for parameterization and its coupling to the Euler and adjoint codes.

Details

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

Keywords

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Article
Publication date: 14 November 2008

S. Coco, A. Laudani, F. Riganti Fulginei and A. Salvini

The aim of this work is to show how evolutionary computation can improve the quality of 3D‐FE mesh that is a crucial task for field evaluations using 3‐D FEM analysis.

Abstract

Purpose

The aim of this work is to show how evolutionary computation can improve the quality of 3D‐FE mesh that is a crucial task for field evaluations using 3‐D FEM analysis.

Design/methodology/approach

The evolutionary approach used for optimizing 3D mesh generation is based on the bacterial chemotaxis algorithm (BCA). The objective function corresponds to the virtual bacterium best habitat, and the motion rules followed by each virtual bacterium are inspired to the natural behaviour of bacteria in real habitat.

Findings

The obtained results show that the present approach returns good accuracy performances with low‐computational costs.

Practical implications

The procedure is robust and converges for all the practical cases examined for validation.

Originality/value

The adoption of a correct optimization algorithm is fundamental to obtain good performances in terms of robustness of the results and the low‐computational costs. In this sense, the BCA is a valid instrument for improving the quality of 3D‐FE mesh.

Details

COMPEL - The international journal for computation and mathematics in electrical and electronic engineering, vol. 27 no. 6
Type: Research Article
ISSN: 0332-1649

Keywords

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Article
Publication date: 1 January 2004

Xu Guo and Yuan Xian Gu

In this paper, a new density‐stiffness interpolation scheme for topology optimization of continuum structures is proposed. Based on this new scheme, not only the so‐called…

Abstract

In this paper, a new density‐stiffness interpolation scheme for topology optimization of continuum structures is proposed. Based on this new scheme, not only the so‐called checkerboard pattern can be eliminated from the final optimal topology, but also the boundary‐smooth effect associated with the traditional sensitivity averaging approach can also be overcome. A proof of the existence of the solution of the optimization problem is also given, therefore mesh independent optimization results can be obtained. Numerical examples illustrate the effectiveness and the advantage of the proposed interpolation scheme.

Details

Engineering Computations, vol. 21 no. 1
Type: Research Article
ISSN: 0264-4401

Keywords

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