A scaled boundary finite element based explicit topology optimization approach for three‐dimensional structures

2020 ◽  
Vol 121 (21) ◽  
pp. 4878-4900
Author(s):  
Weisheng Zhang ◽  
Zhe Xiao ◽  
Chang Liu ◽  
Yue Mei ◽  
Sung‐kie Youn ◽  
...  
Keyword(s):  
Finite Element ◽  
Topology Optimization ◽  
Three Dimensional ◽  
Optimization Approach ◽  
Scaled Boundary Finite Element

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.

Three-Dimensional Electrical Impedance Tomography: A Topology Optimization Approach

2008 ◽  
Vol 55 (2) ◽  
pp. 531-540 ◽  
Author(s):  
LuÍs Augusto Motta Mello ◽  
CÍcero Ribeiro de Lima ◽  
Marcelo Britto Passos Amato ◽  
Raul Gonzalez Lima ◽  
EmÍlio Carlos Nelli Silva
Keyword(s):  
Topology Optimization ◽  
Electrical Impedance Tomography ◽  
Electrical Impedance ◽  
Three Dimensional ◽  
Optimization Approach ◽  
Impedance Tomography

Topology Optimization of Three-Dimensional Woven Materials Using a Ground Structure Design Variable Representation

2019 ◽  
Vol 141 (6) ◽  
Author(s):  
Seung-Hyun Ha ◽  
Hak Yong Lee ◽  
Kevin J. Hemker ◽  
James K. Guest
Keyword(s):  
Topology Optimization ◽  
Design Variable ◽  
Three Dimensional ◽  
Structure Design ◽  
Optimization Approach ◽  
Ground Structure ◽  
Flow Equations ◽  
Combined Algorithm ◽  
Variable Representation ◽  
3D Weaving

Three-dimensional (3D) weaving has recently arisen as viable means for manufacturing metallic, architected microlattices. Herein, we describe a topology optimization approach for designing the architecture of such 3D woven lattices. A ground structure design variable representation is combined with linear manufacturing constraints and a projection mapping to realize lattices that satisfy the rather restrictive topological constraints associated with 3D weaving. The approach is demonstrated in the context of inverse homogenization to design lattices with maximized fluid permeability. Stokes flow equations with no-slip conditions governing unit cell flow fields are interpolated using the Darcy–Stokes finite element model, leveraging existing work in the topology optimization of fluids. The combined algorithm is demonstrated to design manufacturable lattices with maximized permeability whose properties have been experimentally measured in other published work.

scholarly journals Topology optimization for three-dimensional electromagnetic waves using an edge element-based finite-element method

2016 ◽  
Vol 472 (2189) ◽  
pp. 20150835 ◽  
Author(s):  
Yongbo Deng ◽  
Jan G. Korvink
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Topology Optimization ◽  
Electromagnetic Waves ◽  
Three Dimensional ◽  
Free Condition ◽  
Edge Element ◽  
Divergence Free ◽  
The Magnetic Field ◽  
Element Method

This paper develops a topology optimization procedure for three-dimensional electromagnetic waves with an edge element-based finite-element method. In contrast to the two-dimensional case, three-dimensional electromagnetic waves must include an additional divergence-free condition for the field variables. The edge element-based finite-element method is used to both discretize the wave equations and enforce the divergence-free condition. For wave propagation described in terms of the magnetic field in the widely used class of non-magnetic materials, the divergence-free condition is imposed on the magnetic field. This naturally leads to a nodal topology optimization method. When wave propagation is described using the electric field, the divergence-free condition must be imposed on the electric displacement. In this case, the material in the design domain is assumed to be piecewise homogeneous to impose the divergence-free condition on the electric field. This results in an element-wise topology optimization algorithm. The topology optimization problems are regularized using a Helmholtz filter and a threshold projection method and are analysed using a continuous adjoint method. In order to ensure the applicability of the filter in the element-wise topology optimization version, a regularization method is presented to project the nodal into an element-wise physical density variable.

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