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1 – 10 of 328S.‐Y. HAHN, I.‐H. PARK, H.‐K. JUNG and J. SIKORA
In the shadow of X‐ray tomography and nuclear magnetic resonance tomography a new tomographic technique based on low‐frequency electric currents has been successfully developed in…
Abstract
In the shadow of X‐ray tomography and nuclear magnetic resonance tomography a new tomographic technique based on low‐frequency electric currents has been successfully developed in the past decade. Impedance computed tomography (ICT), although it gives poor spatial resolution images, is unmatched in certain cases. Two different approaches to the sensitivity analysis are presented in this paper. The direct differentiation method has been applied, but the adjoint variable method has not been used in ICT reconstruction algorithms until now. Some problems associated with the adjoint variable method of sensitivity analysis are discussed. The new algorithm is compared with the direct differentiation approach.
Rtimi Youness and Frederic Messine
The presented study aims to minimize the energy consumed by a Hall effect thruster (HET) under a constraint which makes it possible to generate a specified magnetic field in a…
Abstract
Purpose
The presented study aims to minimize the energy consumed by a Hall effect thruster (HET) under a constraint which makes it possible to generate a specified magnetic field in a target region of the thruster.
Design/methodology/approach
Herein topology optimization (TO) is used to reduce the energy consumption of an HET while keeping its performance unchanged. The design variables are the current densities in the coils and the distribution of materials in the polar pieces of the thruster. Intermediate values of material distribution are penalized using the solid isotropic material with penalization method to favor binary solutions. By means of the adjoint method, this paper provides the derivatives of the objective and constraint functions with respect to material distribution and current density variables.
Findings
The TO-based design methodology is developed and validated on a design example involving 2,051 variables. The approach shows its interest and its effectiveness of on a large scale two-criteria problem.
Research limitations/implications
In this paper, TO is presented as a tool that has allowed to explore new and innovative designs. However, although the design presented is original, its fabrication is not feasible. Despite this, the designs found give a good idea of the starting points for shape and parametric optimization tools.
Practical implications
Through the HET design problem, TO shows the ability to explore more original design possibilities of a complex magnetostatic design problem and to discover designs that make a HET more efficient with respect to several criteria at the same time.
Originality/value
A new way to reduce the energy consumption of a HET is presented. To achieve this, an adjoint-based TO method is developed and then implemented in a simple way. This approach shows that, for efficiency purposes, TO is a key tool for extending the state of the art of HET designs.
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Stephane Durand, Ivan Cimrák and Peter Sergeant
The purpose of this paper is to study the optimization problem of low‐frequency magnetic shielding using the adjoint variable method (AVM). This method is compared with…
Abstract
Purpose
The purpose of this paper is to study the optimization problem of low‐frequency magnetic shielding using the adjoint variable method (AVM). This method is compared with conventional methods to calculate the gradient.
Design/methodology/approach
The equation for the vector potential (eddy currents model) in appropriate Sobolev spaces is studied to obtain well‐posedness. The optimization problem is formulated in terms of a cost functional which depends on the vector potential and its rotation. Convergence of a steepest descent algorithm to a stationary point of this functional is proved. Finally, some numerical results for an axisymmetric induction heater are presented.
Findings
Using Friedrichs' inequality, the existence and uniqueness of the vector potential, its gradient and the corresponding adjoint variable can be proved. From the numerical results, it is concluded that the AVM is advantageous if the number of parameters to optimize is larger than two.
Research limitations/implications
The AVM is only faster than conventional methods if the gradients can be calculated with sufficient accuracy.
Originality/value
Theoretical results for eddy currents model are often based on a non‐vanishing conductivity. The theoretical value of this paper is the presence of non‐conducting materials in the domain. From a practical viewpoint, it has been demonstrated that the AVM can yield a significant reduction of computational time for advanced optimization problems.
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A shape design sensitivity analysis (SDSA) oftwo‐dimensional transient heat diffusion problems is proposed based onthe BIE formulation. The adjoint variable method is used by…
Abstract
A shape design sensitivity analysis (SDSA) of two‐dimensional transient heat diffusion problems is proposed based on the BIE formulation. The adjoint variable method is used by using the Ionescu—Cazimir integral identity. The procedure is checked against the analytical solution in the case of a rod example, and by numerical comparisons with the finite differencing for a rectangular block under thermal shock and a plunger model. An optimal design problem is then formulated for the plunger and solved to obtain a realistic shape.
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Takayuki Maruyama, Kota Watanabe and Hajime Igarashi
The purpose of this paper is to present a new method to obtain robust solutions to electromagnetic optimization problems, solved with evolutional algorithms, which are insensitive…
Abstract
Purpose
The purpose of this paper is to present a new method to obtain robust solutions to electromagnetic optimization problems, solved with evolutional algorithms, which are insensitive to changes in design parameters such as spatial size, positioning and material constant.
Design/methodology/approach
Adjoint variable method is employed to evaluate the sensitivity of individuals in evolutional processes.
Findings
It is shown in the numerical examples, where the present method is applied to optimization of a superconducting energy storage system and C‐shape magnet, that robust solutions are actually obtained which are insensitive to deviations in spatial sizes.
Originality/value
Unlike usual optimization methods, the present method takes into account deviation in the design parameters due to production errors and long‐term changes. Moreover, the present method is limited to about twice the computational cost of non‐robust optimization methods.
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A. Dutta and C.V. Ramakrishnan
Design sensitivities of plates and shells under transient dynamic loads with constraints on displacements and stresses are likely to be highly erroneous if proper care is not…
Abstract
Design sensitivities of plates and shells under transient dynamic loads with constraints on displacements and stresses are likely to be highly erroneous if proper care is not taken in selecting appropriate finite element mesh and time step size to be used in the analysis. An accurate value of design derivative is assured if an optimal mesh coupled with a reasonably fine time step size is used. The optimal mesh can be obtained iteratively and a number of examples are solved to demonstrate the importance of controlling discretization errors in space and time.
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Gonçalo das Neves Carneiro and Carlos Conceição António
In the reliability assessment of composite laminate structures with multiple components, the uncertainty space defined around design solutions easily becomes over-dimensioned, and…
Abstract
Purpose
In the reliability assessment of composite laminate structures with multiple components, the uncertainty space defined around design solutions easily becomes over-dimensioned, and not all of the random variables are relevant. The purpose of this study is to implement the importance analysis theory of Sobol’ to reduce the dimension of the uncertainty space, improving the efficiency toward global convergence of evolutionary-based reliability assessment.
Design/methodology/approach
Sobol’ indices are formulated analytically for implicit structural response functions, following the theory of propagation of moments and without violating the fundamental principles presented by Sobol’. An evolutionary algorithm capable of global convergence in reliability assessment is instrumented with the Sobol’ indices. A threshold parameter is introduced to identify the important variables. A set of optimal designs of a multi-laminate composite structure is evaluated.
Findings
Importance analysis shows that uncertainty is concentrated in the laminate where the critical stress state is found. Still, it may also be reasonable in other points of the structure. An accurate and controlled reduction of the uncertainty space significantly improves the convergence rate, while maintaining the quality of the reliability assessment.
Practical implications
The theoretical developments assume independent random variables.
Originality/value
Applying Sobol’ indices as an analytical dimension reduction technique is a novelty. The proposed formulation only requires one adjoint system of equilibrium equations to be solved once. Although a local estimate of a global measure, this analytical formulation still holds because, in structural design, uncertainty is concentrated around the mean-values.
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Satafa Sanogo and Frédéric Messine
In this work, the authors deal with topology optimization in electromagnetism using solid isotropic material with penalization (SIMP) method associated with a gradient-based…
Abstract
Purpose
In this work, the authors deal with topology optimization in electromagnetism using solid isotropic material with penalization (SIMP) method associated with a gradient-based algorithm. The purpose of this study is to propose and investigate the impact of new generalized material interpolation scheme (MIS) used in SIMP approaches.
Design/methodology/approach
The variable domains of this kind of electromagnetism design problem are decomposed into small squares which represent a material point (iron here) or void. A least square function where the magnetic field in a target zone has to be as close as possible to a fixed one is minimized. Then the binary optimization problem is relaxed to a continuous one. By using the adjoint variable method, the gradient is provided. By penalizing the objective function using MIS, gradient-based algorithms can then be directly applied to provide efficient solutions close to the binary ones.
Findings
In this work, new general MISs are proposed. It is shown on numerous numerical instances that the so-obtained design solutions are more precise to define the zones with or without materials.
Research limitations/implications
Only the linearity of the materials is addressed because the associated adjoint method needs this assumption. However, the new penalization approaches are not dependent directly on this assumption.
Originality/value
The new MISs are efficiently applied to design of a hall effect thruster (HET) magnetic circuits. Furthermore, these schemes are generic and can then be applied to other topology optimization applications in electromagnetism as well as and in mechanism.
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Aníbal J.J. Valido and João Barradas Cardoso
The purpose of this paper is to present a design sensitivity analysis continuum formulation for the cross-section properties of thin-walled laminated composite beams. These…
Abstract
Purpose
The purpose of this paper is to present a design sensitivity analysis continuum formulation for the cross-section properties of thin-walled laminated composite beams. These properties are expressed as integrals based on the cross-section geometry, on the warping functions for torsion, on shear bending and shear warping, and on the individual stiffness of the laminates constituting the cross-section.
Design/methodology/approach
In order to determine its properties, the cross-section geometry is modeled by quadratic isoparametric finite elements. For design sensitivity calculations, the cross-section is modeled throughout design elements to which the element sensitivity equations correspond. Geometrically, the design elements may coincide with the laminates that constitute the cross-section.
Findings
The developed formulation is based on the concept of adjoint system, which suffers a specific adjoint warping for each of the properties depending on warping. The lamina orientation and the laminate thickness are selected as design variables.
Originality/value
The developed formulation can be applied in a unified way to open, closed or hybrid cross-sections.
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Yingying Yao, Chang Seop Koh, Jae Seop Ryu, Dexin Xie and Tae Gun Um
A novel 3D shape optimization algorithm is presented for electromagnetic devices carrying eddy current. The algorithm integrates the 3D finite element performance analysis and the…
Abstract
A novel 3D shape optimization algorithm is presented for electromagnetic devices carrying eddy current. The algorithm integrates the 3D finite element performance analysis and the steepest descent method with design sensitivity and mesh relocation method. For the design sensitivity formula, the adjoint variable vector is defined in complex form based on the 3D finite element method for eddy current problems. A new 3D mesh relocation method is also proposed using the deformation theory of the elastic body under stress to renew the mesh as the shape changes. The design sensitivity for the surface nodal points is also systematically converted into that for the design variables for the parameterized optimization application. The proposed algorithm is applied to the optimum design of the tank shield model of transformer and the effectiveness is proved.
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