Dot sensitivity analysis of ferromagnetic materials for topology optimization in an axi-symmetric magnetostatic system

2019 ◽  
Vol 38 (3) ◽  
pp. 990-998 ◽  
Author(s):  
SeungGeon Hong ◽  
Kang Hyouk Lee ◽  
Il Han Park
Keyword(s):  
Sensitivity Analysis ◽  
Topology Optimization ◽  
Ferromagnetic Materials ◽  
Symmetric System ◽  
Local Optimum ◽  
Shape Sensitivity ◽  
Design Problems ◽  
Content Type ◽  
Sensitivity Method ◽  
Ferromagnetic Ring

Purpose The purpose of this paper is to propose dot sensitivity analysis of ferromagnetic materials for topology optimization in an axi-symmetric magnetostatic system. Design/methodology/approach The dot sensitivity formula for the axi-symmetric system is derived as a closed form using the continuum shape sensitivity formula. The dot sensitivity method is combined with the level set method to perform topology optimization. Findings Derived dot sensitivity analysis can generate a ferromagnetic ring torus in a vacant region. Thus, an initial design is not needed for the design material. Two design problems are tested to demonstrate the usefulness of dot sensitivity. Originality/value By simultaneously using the shape sensitivity and dot sensitivity, in axi-symmetric magnetic system, the design space is expanded and it includes the interface and the inside of the vacant region. This property can reduce the possibility of local optimum convergence.

A Velocity Predictor–Corrector Scheme in Level Set-Based Topology Optimization to Improve Computational Efficiency

2014 ◽  
Vol 136 (9) ◽  
Author(s):  
Benliang Zhu ◽  
Xianmin Zhang ◽  
Sergej Fatikow
Keyword(s):  
Sensitivity Analysis ◽  
Topology Optimization ◽  
Velocity Field ◽  
Level Set Method ◽  
Level Set ◽  
Velocity Fields ◽  
Shape Sensitivity ◽  
Shape Sensitivity Analysis ◽  
Predictor Corrector ◽  
Mean Compliance

This paper presents an optimization method for solving level set-based topology optimization problems. A predictor–corrector scheme for constructing the velocity field is developed. In this method, after the velocity fields in the first two iterations are calculated using the shape sensitivity analysis, the subsequent velocity fields are constructed based on those obtained from the first two iterations. To ensure stability, the velocity field is renewed based on the shape sensitivity analysis after a certain number of iterations. The validity of the proposed method is tested on the mean compliance minimization problem and the compliant mechanisms synthesis problem. This method is quantitatively compared with other methods, such as the standard level set method, the solid isotropic microstructure with penalization (SIMP) method, and the discrete level set method.

Topology optimization of rotor poles in a permanent-magnet machine using level set method and continuum design sensitivity analysis

2014 ◽  
Vol 33 (3) ◽  
pp. 711-728 ◽  
Author(s):  
Piotr Putek ◽  
Piotr Paplicki ◽  
Ryszard Pałka
Keyword(s):  
Sensitivity Analysis ◽  
Topology Optimization ◽  
Permanent Magnet ◽  
Level Set Method ◽  
Level Set ◽  
Numerical Approach ◽  
Design Sensitivity ◽  
Optimization Process ◽  
Content Type ◽  
Rotor Poles

Purpose – In this paper, a numerical approach to the topology optimization is proposed to design the permanent magnet excited machines with improved high-speed features. For this purpose the modified multi-level set method (MLSM) was proposed and applied to capture the shape of rotor poles on the fixed mesh using FE analysis. The paper aims to discuss these issues. Design/methodology/approach – This framework is based on theories of topological and shape derivative for the magnetostatic system. During the iterative optimization process, the shape of rotor poles and its evolution is represented by the level sets of a continuous level set function f. The shape optimization of the iron and the magnet rotor poles is provided by the combining continuum design sensitivity analysis with level set method. Findings – To obtain an innovative design of the rotor poles composed of different materials, the modified MLSM is proposed. An essential advantage of the proposed method is its ability to handle a topology change on a fixed mesh by the nucleating a small hole in design domain that leads to more efficient computational scheme then standard level set method. Research limitations/implications – The proposed numerical approach to the topology design of the 3D model of a PM machine is based on the simplified 2D model under assumption that the eddy currents in both the magnet and iron parts are neglected. Originality/value – The novel aspect of the proposed method is the incorporation of the Total Variation regularization in the MLSM, which distribution is additionally modified by the gradient derivative information, in order to stabilize the optimization process and penalize oscillations without smoothing edges.

Advanced solution methods in topology optimization and shape sensitivity analysis

1996 ◽  
Vol 13 (5) ◽  
pp. 57-90 ◽  
Author(s):  
Manolis Papadrakakis ◽  
Yiannis Tsompanakis ◽  
Ernest Hinton ◽  
Johann Sienz
Keyword(s):  
Sensitivity Analysis ◽  
Topology Optimization ◽  
Shape Sensitivity ◽  
Shape Sensitivity Analysis ◽  
Solution Methods

Efficient Sensitivity Analysis for Multibody Dynamics Systems Using an Iterative Steps Method With Application in Topology Optimization

2011 ◽  
Author(s):  
Guang Dong ◽  
Zheng-Dong Ma ◽  
Gregory Hulbert ◽  
Noboru Kikuchi ◽  
Sudhakar Arepally ◽  
...  
Keyword(s):  
Sensitivity Analysis ◽  
Topology Optimization ◽  
Multibody Dynamics ◽  
Optimization Problem ◽  
Finite Difference Methods ◽  
Analysis Method ◽  
Topology Optimization Problem ◽  
Design Variables ◽  
Sensitivity Analysis Method ◽  
Rotational Motions

Efficient and reliable sensitivity analyses are critical for topology optimization, especially for multibody dynamics systems, because of the large number of design variables and the complexities and expense in solving the state equations. This research addresses a general and efficient sensitivity analysis method for topology optimization with design objectives associated with time dependent dynamics responses of multibody dynamics systems that include nonlinear geometric effects associated with large translational and rotational motions. An iterative sensitivity analysis relation is proposed, based on typical finite difference methods for the differential algebraic equations (DAEs). These iterative equations can be simplified for specific cases to obtain more efficient sensitivity analysis methods. Since finite difference methods are general and widely used, the iterative sensitivity analysis is also applicable to various numerical solution approaches. The proposed sensitivity analysis method is demonstrated using a truss structure topology optimization problem with consideration of the dynamic response including large translational and rotational motions. The topology optimization problem of the general truss structure is formulated using the SIMP (Simply Isotropic Material with Penalization) assumption for the design variables associated with each truss member. It is shown that the proposed iterative steps sensitivity analysis method is both reliable and efficient.

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