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Research Papers

Topology Optimization of a Three-Dimensional Flexible Multibody System Via Moving Morphable Components

[+] Author and Article Information
Jialiang Sun

State Key Laboratory of Mechanics and Control
of Mechanical Structures,
College of Aerospace Engineering,
Nanjing University of Aeronautics and
Astronautics,
Nanjing 210016, China
e-mail: sunjialiang@nuaa.edu.cn

Qiang Tian

MOE Key Laboratory of Dynamics and Control of
Flight Vehicle,
School of Aerospace Engineering,
Beijing Institute of Technology,
Beijing 100081, China
e-mail: tianqiang_hust@aliyun.com

Haiyan Hu

State Key Laboratory of Mechanics and Control
of Mechanical Structures,
College of Aerospace Engineering,
Nanjing University of Aeronautics and
Astronautics,
Nanjing 210016, China;
MOE Key Laboratory of Dynamics and Control
of Flight Vehicle,
School of Aerospace Engineering,
Beijing Institute of Technology,
Beijing 100081, China
e-mail: hhyae@nuaa.edu.cn

1Corresponding author.

Contributed by the Design Engineering Division of ASME for publication in the JOURNAL OF COMPUTATIONAL AND NONLINEAR DYNAMICS. Manuscript received July 26, 2017; final manuscript received September 23, 2017; published online November 9, 2017. Assoc. Editor: Zdravko Terze.

J. Comput. Nonlinear Dynam 13(2), 021010 (Nov 09, 2017) (11 pages) Paper No: CND-17-1328; doi: 10.1115/1.4038142 History: Received July 26, 2017; Revised September 23, 2017

In this work, an efficient topology optimization approach is proposed for a three-dimensional (3D) flexible multibody system (FMBS) undergoing both large overall motion and large deformation. The FMBS of concern is accurately modeled first via the solid element of the absolute nodal coordinate formulation (ANCF), which utilizes both nodal positions and nodal slopes as the generalized coordinates. Furthermore, the analytical formulae of the elastic force vector and the corresponding Jacobian are derived for efficient computation. To deal with the dynamics in the optimization process, the equivalent static load (ESL) method is employed to transform the topology optimization problem of dynamic response into a static one. Besides, the newly developed topology optimization method by moving morphable components (MMC) is used and reevaluated to optimize the 3D FMBS. In the MMC-based framework, a set of morphable structural components serves as the building blocks of optimization and hence greatly reduces the number of design variables. Therefore, the topology optimization approach has a potential to efficiently optimize an FMBS of large scale, especially in 3D cases. Two numerical examples are presented to validate the accuracy of the solid element of ANCF and the efficiency of the proposed optimization methodology, respectively.

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Figures

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Fig. 2

A schematic diagram of the 3D MMC-based topology optimization process

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Fig. 4

A basic 3D structural component

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Fig. 5

TDF of a 3D cuboid structural component

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Fig. 6

The flowchart of ESL-based topology optimization computation for an FMBS

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Fig. 8

Dynamic configurations of the flexible ellipsograph

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Fig. 9

Comparison results of midpoint A coordinates

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Fig. 10

The initial configuration of a 3D rigid–flexible slide–crank mechanism

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Fig. 11

Topology optimization results of the flexible rod for five typical time steps: (a) t = 0.2 s, (b) t = 0.4 s, (c) t = 0.6 s, (d) t = 0.8 s, and (e) t = 1 s

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Fig. 12

Topology optimization results of the flexible rod for initial case 1: (a) iteration no. 1, (b) iteration no. 5, (c) iteration no. 20, (d) iteration no. 50, (e) iteration no. 150, and (f) iteration no. 400

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Fig. 13

Topology optimization results of the flexible rod for initial case 2: (a) iteration no. 1, (b) iteration no. 5, (c) iteration no. 20, (d) iteration no. 50, (e) iteration no. 150, and (f) iteration no. 400

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Fig. 14

Topology optimization results of the flexible rod for initial case 3: (a) iteration no. 1, (b) iteration no. 5, (c) iteration no. 20, (d) iteration no. 50, (e) iteration no. 150, and (f) iteration no. 400

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Fig. 15

Convergence of the objective function for the three initial cases of the flexible piston rod

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Fig. 16

Convergence of the volume ratio for the three initial cases of the flexible piston rod

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Fig. 17

Optimized results of the 3D rigid–flexible slide–crank mechanism for the three initial cases: (a) initial case 1, (b) initial case 2, and (c) initial case 3

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Fig. 18

Absolute lateral deformations dA of midpoint A of unoptimized and optimized models: (a) unoptimized model, (b) optimized model for initial case 1, (c) optimized model for initial case 2, and (d) optimized model for initial case 3

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Fig. 19

Comparison example: a simply supported beam under a static load

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Fig. 20

Topology optimization results of the simply supported beam for the three initial cases: (a) initial case 1, (b) initial case 2, and (c) initial case 3

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Fig. 21

Convergence of the objective function of the simply supported beam for the three initial cases

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Fig. 7

A schematic diagram of a flexible ellipsograph

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Fig. 3

Definition of the rotation angles

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Fig. 1

A deformed solid element of ANCF with eight nodes

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