Robust topology optimization of hinge-free compliant mechanisms with material uncertainties based on a non-probabilistic field model

doi:10.1007/s11465-019-0529-y

Front. Mech. Eng.

2019, Vol. 14

Issue (2) : 201-212 https://doi.org/10.1007/s11465-019-0529-y

RESEARCH ARTICLE

Robust topology optimization of hinge-free compliant mechanisms with material uncertainties based on a non-probabilistic field model

Junjie ZHAN, Yangjun LUO(

)

State Key Laboratory of Structural Analysis for Industrial Equipment, School of Aeronautics and Astronautics, Dalian University of Technology, Dalian 116024, China

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Abstract

This paper presents a new robust topology optimization framework for hinge-free compliant mecha- nisms with spatially varying material uncertainties, which are described using a non-probabilistic bounded field model. Bounded field uncertainties are efficiently represented by a reduced set of uncertain-but-bounded coefficients on the basis of the series expansion method. Robust topology optimization of compliant mechanisms is then defined to minimize the variation in output displacement under constraints of the mean displacement and predefined material volume. The nest optimization problem is solved using a gradient-based optimization algorithm. Numerical examples are presented to illustrate the effectiveness of the proposed method for circumventing hinges in topology optimization of compliant mechanisms.

Keywords compliant mechanisms robust topology optimization hinges uncertainty bounded field

Corresponding Author(s): Yangjun LUO

Just Accepted Date: 19 December 2018 Online First Date: 25 January 2019 Issue Date: 22 April 2019

Cite this article:

Junjie ZHAN,Yangjun LUO. Robust topology optimization of hinge-free compliant mechanisms with material uncertainties based on a non-probabilistic field model[J]. Front. Mech. Eng., 2019, 14(2): 201-212.

URL:

https://academic.hep.com.cn/fme/EN/10.1007/s11465-019-0529-y
https://academic.hep.com.cn/fme/EN/Y2019/V14/I2/201

Fig.1 First eight modes

ψ j

(j = 1, 2, ..., 8)

in the series expansion of field uncertainties

Fig.2 Approximate Heaviside function with different values of

β

Fig.3 Flowchart for solving the nested optimization problem

Fig.4 Design domain and boundary conditions of a compliant inverter

Fig.5 Optimized topologies (left), worst-case realization (middle), and best-case realization (right) of uncertain field for the compliant inverter when

l c = 120

. (a)

u * = 16

Δ u out = 1.562

; (b)

u * = 15

Δ u out = 1.293

; (c)

u * = 14

Δ u out = 0.965

; (d)

u * = 13

Δ u out = 0.731

; (e)

u * = 12

Δ u out = 0.550

Fig.6 Iteration histories for the compliant inverter when

l c = 120

Fig.7 Nominal value and deviation range of output displacement versus

F in

for topological configurations in Figs. 5(a)?5(e) when

l c = 120

Fig.8 Optimized topologies (left), worst-case realization (middle), and best-case realization (right) of uncertain field for the compliant inverter when

l c = 60

. (a)

u * = 16

Δ u out = 1.495

; (b)

u * = 15

Δ u out = 1.165

; (c)

u * = 14

Δ u out = 0.900

; (d)

u * = 13

Δ u out = 0.698

; (e)

u * = 12

Δ u out = 0.535

Fig.9 Design domain and boundary conditions of a compliant gripper

Fig.10 Optimized topologies (left), worst-case realization (middle), and best-case realization (right) of uncertain field for the compliant gripper when

l c = 60

. (a)

u * = 26

Δ u out = 2.804

; (b)

u * = 24

Δ u out = 1.999

, (c)

u * = 22

Δ u out = 1.468

Fig.11 Optimized topologies (left), worst-case realization (middle), and best-case realization (right) of uncertain field for the compliant gripper when

l c = 30

. (a)

u * = 26

Δ u out = 2.882

; (b)

u * = 24

Δ u out = 2.131

; (c)

u * = 22

Δ u out = 1.617

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