Complex variable step method for sensitivity analysis of effective properties in multi-field micromechanics

Dziatkiewicz, Grzegorz

doi:10.1007/s00707-015-1419-y

Cited by 12 publications

(8 citation statements)

References 46 publications

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“…17. Gradients are routinely computed numerically using forward finite difference (FFD) [86], backward finite difference (BFD) [86], central finite differences (CFD) [87]- [89], and complex-step methods [89]. The FFD and BFD methods require one additional simulation for each design parameter, whereas the more accurate CFD requires two extra simulations for each design parameter.…”

Section: ) Objective Gradient Calculation Methodsmentioning

confidence: 99%

Geometry and Topology Optimization of Switched Reluctance Machines: A Review

Abdalmagid

Sayed²,

Bakr

et al. 2022

IEEE Access

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Switched reluctance machines (SRMs) have recently attracted more interest in many applications due to the volatile prices of rare-earth permanent magnets (PMs) used in permanent magnet synchronous machines (PMSMs). They also have rugged construction and can operate at high speeds and high temperatures. However, acoustic noise and high torque ripples, in addition to the relatively low torque density, present significant challenges. Geometry and topology optimization are applied to overcome these challenges and enable SRMs to compete with PMSMs. Key geometric design parameters are optimized to minimize various objective functions within geometry optimization. On the other hand, the material distribution in a particular design space within the machine domain may be optimized using topology optimization. We discuss how these techniques are applied to optimize the geometries and topologies of SRMs to enhance machine performance. As optimizing the machine geometry and material distribution at the design phase is of substantial significance, this work offers a comprehensive literature review on the current state of the art and the possible trends in the optimization techniques of SRMs. The paper also reviews different configurations of SRMs and stochastic and deterministic optimization techniques utilized in optimizing different configurations of the machine.

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Section: ) Objective Gradient Calculation Methodsmentioning

confidence: 99%

Geometry and Topology Optimization of Switched Reluctance Machines: A Review

Abdalmagid

Sayed²,

Bakr

et al. 2022

IEEE Access

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“…The linear constitutive equations of the magnetoelectroelastic continuum can be expressed as [1,3,8]:…”

Section: Magnetoelectroelastic Linear Constitutive Modelmentioning

confidence: 99%

“…where q v is the volume charge density; for the static case the electromagnetic field is irrotational, therefore the static potentials can be introduced on the base of the Maxwell equations [1,3,8]:…”

Section: Magnetoelectroelastic Linear Constitutive Modelmentioning

confidence: 99%

Dual number algebra method for Green’s function derivatives in 3D magneto-electro-elasticity

Dziatkiewicz

2018

AIP Conference Proceedings

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Parallel fast multipole boundary element method applied to computational homogenization AIP Conference Proceedings 1922, 140003 (2018 Abstract. The Green functions are the basic elements of the boundary element method. To obtain the boundary integral formulation the Green function and its derivative should be known for the considered differential operator. Today the interesting group of materials are electronic composites. The special case of the electronic composite is the magnetoelectroelastic continuum. The mentioned continuum is a model of the piezoelectric-piezomagnetic composites. The anisotropy of their physical properties makes the problem of Green's function determination very difficult. For that reason Green's functions for the magnetoelectroelastic continuum are not known in the closed form and numerical methods should be applied to determine such Green's functions. These means that the problem of the accurate and simply determination of Green's function derivatives is even harder. Therefore in the present work the dual number algebra method is applied to calculate numerically the derivatives of 3D Green's functions for the magnetoelectroelastic materials. The introduced method is independent on the step size and it can be treated as a special case of the automatic differentiation method. Therefore, the dual number algebra method can be applied as a tool for checking the accuracy of the well-known finite difference schemes.

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“…Finite Element Method (FEM) is used in the following paper for building the numerical representation for its great advantages like versatility [4,5], adaptivity, stability and flexibility (possibility to model inhomogeneity, complex geometries and complex boundary conditions) [6].…”

Section: Fig 1 General Algorithm Of Hybrid Simulationmentioning

confidence: 99%