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Frontiers of Mechanical Engineering

Front. Mech. Eng.    2019, Vol. 14 Issue (2) : 129-140     https://doi.org/10.1007/s11465-019-0532-3
RESEARCH ARTICLE |
Connected morphable components-based multiscale topology optimization
Jiadong DENG1, Claus B. W. PEDERSEN2, Wei CHEN1()
1. Department of Mechanical Engineering, Northwestern University, Evanston, IL 60208, USA
2. Dassault Systèmes Deutschland GmbH, 200095 Hamburg, Germany
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Abstract

The advances of manufacturing techniques, such as additive manufacturing, have provided unprecedented opportunities for producing multiscale structures with intricate latticed/cellular material microstructures to meet the increasing demands for parts with customized functionalities. However, there are still difficulties for the state-of-the-art multiscale topology optimization (TO) methods to achieve manufacturable multiscale designs with cellular materials, partially due to the disconnectivity issue when tiling material microstructures. This paper attempts to address the disconnectivity issue by extending component-based TO methodology to multiscale structural design. An effective linkage scheme to guarantee smooth transitions between neighboring material microstructures (unit cells) is devised and investigated. Associated with the advantages of components-based TO, the number of design variables is greatly reduced in multiscale TO design. Homogenization is employed to calculate the effective material properties of the porous materials and to correlate the macro/structural scale with the micro/material scale. Sensitivities of the objective function with respect to the geometrical parameters of each component in each material microstructure have been derived using the adjoint method. Numerical examples demonstrate that multiscale structures with well-connected material microstructures or graded/layered material microstructures are realized.

Keywords multiscale topology optimization      morphable component      material microstructure      homogenization     
Corresponding Authors: Wei CHEN   
Just Accepted Date: 29 November 2018   Online First Date: 14 January 2019    Issue Date: 22 April 2019
 Cite this article:   
Jiadong DENG,Claus B. W. PEDERSEN,Wei CHEN. Connected morphable components-based multiscale topology optimization[J]. Front. Mech. Eng., 2019, 14(2): 129-140.
 URL:  
http://journal.hep.com.cn/fme/EN/10.1007/s11465-019-0532-3
http://journal.hep.com.cn/fme/EN/Y2019/V14/I2/129
Fig.1  A CMC in global coordinate
Fig.2  Design scheme for multiscale structure using CMC-based TO
Fig.3  A linkage scheme to ensure well-connected microstructures
Fig.4  Topology of the unit cell after optimization
Fig.5  A macrostructure divided into different microstructure material partitions
Fig.6  Flowchart for CMC-based multiscale TO
Fig.7  A simply supported beam example with 3 load cases
Fig.8  Optimized microstructure topologies on the right and macro-scale structural topology on the left without linkage scheme
Fig.9  Optimized microstructure topologies on the right and structural topology on the left with linkage scheme
Fig.10  Objective iteration curves for designs with/without linkage scheme
Fig.11  Optimized microstructure topologies on the right and structural topology on the left. (a) Without linkage scheme; (b) with linkage scheme
Fig.12  Objective iteration curves for designs with/without linkage scheme
Fig.13  Optimized microstructure topologies on the right and structural topology on the left. (a) Without linkage scheme. (b) with linkage scheme
Fig.14  Femur macrostructure with different partitions (left) and finite element mesh (right)
Fig.15  Final designs
Fig.16  Objective and volume constraint iteration curves for different designs
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