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Research Papers

Topology Optimization of Dynamic Systems Under Uncertain Loads: An H-Norm-Based Approach

[+] Author and Article Information
Paolo Venini

Department of Civil Engineering
and Architecture,
University of Pavia,
Pavia 27100, Italy
e-mail: paolo.venini@unipv.it

Contributed by the Design Engineering Division of ASME for publication in the JOURNAL OF COMPUTATIONAL AND NONLINEAR DYNAMICS. Manuscript received June 8, 2018; final manuscript received November 20, 2018; published online January 7, 2019. Assoc. Editor: Yan Wang.

J. Comput. Nonlinear Dynam 14(2), 021007 (Jan 07, 2019) (9 pages) Paper No: CND-18-1265; doi: 10.1115/1.4042140 History: Received June 08, 2018; Revised November 20, 2018

An innovative approach to topology optimization of dynamic system is introduced that is based on the system transfer-function H-norm. As for the structure, the proposed strategy allows to determine the optimal material distribution that ensures the minimization of a suitable goal function, such as (an original definition of) the dynamic compliance. Load uncertainty is accounted for by means of a nonprobabilistic convex-set approach (Ben-Haim and Elishakoff, 1990, Convex Models of Uncertainty in Applied Mechanics, Elsevier Science, Amsterdam). At each iteration, the worst load is determined as the one that maximizes the current dynamic compliance so that the proposed strategy fits the so-called worst case scenario (WCS) approach. The overall approach consists of the repeated solution of the two steps (minimization of the dynamic compliance with respect to structural parameters and maximization of the dynamic compliance with respect to the acting load) until convergence is achieved. Results from representative numerical studies are eventually presented along with extensions to the proposed approach that are currently under development.

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Figures

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Fig. 1

Block diagram representation of the input/output Eq. (3)

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Fig. 2

(L) Standard SIMP Young's modulus interpolation—(R) nonlinear mass density interpolation

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Fig. 3

Two DOFs oscillator and dynamic compliance definition

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Fig. 4

Convex set Bq defining load uncertainty

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Fig. 5

The two-step WCS optimization problem

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Fig. 6

Square cantilever problem: (L) nominal static problem—(R) uncertain dynamic problem

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Fig. 7

Nominal square cantilever—H-optimal topology

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Fig. 8

Nominal square cantilever—(L) convergence curve—(R) initial versus H-optimal frequency response functions

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Fig. 9

Uncertain square cantilever—H-optimal topology

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Fig. 10

Uncertain square cantilever—(L) convergence curve—(R) initial versus H-optimal frequency response functions

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Fig. 11

Messerschmitt-Bölkow-Blohm beam problem: (L) nominal static problem—(R) uncertain dynamic problem

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Fig. 12

Nominal MBB beam—H-optimal topology

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Fig. 13

Nominal MBB beam—(L) convergence curve—(r) initial versus H-optimal frequency response function

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Fig. 14

Nominal MBB beam—static optimal topology

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Fig. 15

Nominal MBB beam—static-optimal versus H-optimal frequency response function

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Fig. 16

Messerschmitt-Bölkow-Blohm beam under uncertain load—H-optimal topology

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Fig. 17

Messerschmitt-Bölkow-Blohm beam under uncertain load—(L) convergence curve—(R) initial versus H-optimalfrequency response function

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