A geometry projection method for the topology optimization of plate structures

2016 ◽  
Vol 54 (5) ◽  
pp. 1173-1190 ◽  
Author(s):  
Shanglong Zhang ◽  
Julián A. Norato ◽  
Arun L. Gain ◽  
Naesung Lyu
Keyword(s):  
Topology Optimization ◽  
Projection Method ◽  
Plate Structures ◽  
Geometry Projection

A Topology Optimization Method for the Design of Orthotropic Plate Structures

2020 ◽  
Author(s):  
Hollis Smith ◽  
Julian Norato
Keyword(s):  
Topology Optimization ◽  
Projection Method ◽  
Anisotropic Material ◽  
Optimization Method ◽  
Rectangular Plates ◽  
Material Anisotropy ◽  
Fixed Amount ◽  
Plate Structures ◽  
Geometry Projection ◽  
Topology Optimization Method

Abstract This work introduces a topology optimization method for the design of structures composed of rectangular plates each of which is made of a predetermined anisotropic material. This work builds upon the geometry projection method with two notable additions. First, a novel geometric parameterization of plates represented by offset surfaces is formulated that is simpler than the one used in previous works. Second, the formulation presented herein adds support to the geometry projection method for geometric components with general anisotropic material properties. A design-generation framework is formulated that produces optimal designs composed exclusively of rectangular plates that may be made of a predetermined, generally anisotropic material. The efficacy of the proposed method is demonstrated with a numerical example comparing optimal cantilever beam designs obtained using isotropic- and orthotropic-material plates. For this example, we maximize the stiffness of the structure for a fixed amount of material. The example reveals the importance of considering material anisotropy in the design of plate structures. Moreover, it is demonstrated that an optimally stiff design for plates made of an isotropic material can exhibit detrimental performance if the plates are naively replaced with an anisotropic material. Although the example given in this work is in the context of orthotropic plates, since the formulation presented in this work supports arbitrary anisotropic materials, it may be readily extended to support the design of each component’s material anisotropy as a part of the optimization routine.

Topology optimization of magnetic cores for WPT using the geometry projection method

2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Yoshitsugu Otomo ◽  
Hajime Igarashi
Keyword(s):  
Topology Optimization ◽  
Projection Method ◽  
Optimization Method ◽  
Magnetic Core ◽  
Material Distribution ◽  
Coupling Coefficients ◽  
Content Type ◽  
Magnetic Cores ◽  
Geometry Projection ◽  
Topology Optimization Method

Purpose The purpose of this study is to search for an optimal core shape that is robust against misalignment between the transmitting and receiving coils of the wireless power transfer (WPT) device. During the optimization process, the authors maximize the coupling coefficients while minimizing the leakage flux around the coils to ensure the safety of the WPT device. Design/methodology/approach In this study, a novel topology optimization method for WPT devices using the geometry projection method is proposed to optimize the magnetic core shape. This method facilitates the generation of bar-shaped magnetic cores because the material distribution is represented by a set of elementary bars. Findings It is shown that an optimized core shape, which is obtained through topology optimization, effectively increases the net magnetic flux interlinked with the receiving coil and outperforms the conventional core. Originality/value In the previous topology optimization method, the material distribution is represented by a linear combination of Gaussian functions. However, this method does not usually result in bar-shaped cores, which are widely used in WPT. In this study, the authors propose a novel topology optimization method for WPT devices using geometry projection that is used in structural optimization, such as beam and cantilever shapes.

TOPOLOGY OPTIMIZATION OF PLATE STRUCTURES WITH ANISOTROPIC MATERIALS

2021 ◽  
Author(s):  
HOLLIS A. SMITH, ◽  
JULIÁN A. NORATO
Keyword(s):  
Topology Optimization ◽  
Anisotropic Material ◽  
Poor Performance ◽  
Optimization Method ◽  
Rectangular Plates ◽  
Material Anisotropy ◽  
Fixed Amount ◽  
Plate Structures ◽  
Design Iteration ◽  
Geometry Projection

This work presents a topology optimization method for the design of structures composed exclusively of rectangular plates made of a predetermined, generally anisotropic material. The geometry projection method is employed to map the highlevel geometry and material properties to a fixed grid for the analysis, thus circumventing the need to re-mesh upon each design iteration. We also impose an overlap constraint in the optimization that reduces waste material when fabricating structures by cutting and joining rectangular plates. We demonstrate our method with a numerical example comparing optimal cantilever beam designs obtained using isotropic- and orthotropic-material plates. For this example, we maximize the stiffness of the structure for a fixed amount of material, and we impose a constraint to reduce overlaps between plates. The examples demonstrate the importance of considering material anisotropy in the design of plate structures. Moreover, it is demonstrated that an optimally stiff design for plates made of an isotropic material can exhibit poor performance if the plates are naively replaced with an anisotropic material.

A Systematic Topology Optimization Approach for Optimal Stiffener Design

1998 ◽  
Author(s):  
Jian Hui Luo ◽  
Hae Chang Gea
Keyword(s):  
Topology Optimization ◽  
Location Problem ◽  
Eigenvalue Problems ◽  
Three Dimensional ◽  
Orthotropic Materials ◽  
Optimization Approach ◽  
Design Domain ◽  
Plate Structures ◽  
Shell Plate

Abstract A systematic topology optimization approach is developed to design the optimal stiffener of three dimensional shell/plate structures in static and eigenvalue problems. Optimal stiffener design involves the determination of the best location and orientation. In this paper, the stiffener location problem is solved by a microstructure-based design domain method and the orientation probelm is modeled as an optimal orientation problem of equivalent orthotropic materials, which is solved by a newly developed energy based method. Examples are presented to demonstrate the application of the proposed approach.

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