0
RESEARCH PAPERS

Synthesis of Bistable Periodic Structures Using Topology Optimization and a Genetic Algorithm

[+] Author and Article Information
J. Prasad

Department of Mechanical Engineering, Michigan State University, East Lansing, MI 48824-1226prasadji@egr.msu.edu

A. R. Diaz1

Department of Mechanical Engineering, Michigan State University, East Lansing, MI 48824-1226diaz@egr.msu.edu

1

Corresponding author.

J. Mech. Des 128(6), 1298-1306 (Dec 28, 2005) (9 pages) doi:10.1115/1.2338576 History: Received August 01, 2005; Revised December 28, 2005

A formulation for the automatic synthesis of two-dimensional bistable, compliant periodic structures is presented, based on standard methods for topology optimization. The design space is parametrized using nonlinear beam elements and a ground structure approach. A performance criterion is suggested, based on characteristics of the load-deformation curve of the compliant structure. A genetic algorithm is used to find candidate solutions. A numerical implementation of this methodology is discussed and illustrated using simple examples.

Copyright © 2006 by American Society of Mechanical Engineers
Your Session has timed out. Please sign back in to continue.

References

Figures

Grahic Jump Location
Figure 1

Strain energy versus strain in a typical bistable structure

Grahic Jump Location
Figure 2

Simplified double curved beam bistable mechanism

Grahic Jump Location
Figure 3

A bistable structure (first stable configuration) based on four double curved beam substructures

Grahic Jump Location
Figure 4

A substructure of Fig. 3 that is a bistable mechanism

Grahic Jump Location
Figure 5

A bistable structure (second stable configuration) based on four double curved beam substructures

Grahic Jump Location
Figure 6

A 3×3 periodic arrangement of bistable structures (a) first equilibrium configuration and (b) second equilibrium configuration

Grahic Jump Location
Figure 7

A member (bar) of the ground structure

Grahic Jump Location
Figure 8

Typical force-displacement diagram for a bistable structure

Grahic Jump Location
Figure 9

The external load factor as a function of time

Grahic Jump Location
Figure 10

Example 1: The package space (a) and corresponding ground structure (b) with dimensions (in mm) and boundary conditions

Grahic Jump Location
Figure 11

The force-displacement diagram for the reference structure (Fig. 3)

Grahic Jump Location
Figure 12

Example 1: Bistable structure obtained by the GA (a) first stable configuration and (b) second stable configuration

Grahic Jump Location
Figure 13

The force-displacement diagram for the structure in Fig. 1

Grahic Jump Location
Figure 14

Example 1: Another bistable structure (a) first stable configuration and (b) second stable configuration

Grahic Jump Location
Figure 15

The force-displacement diagram for the structure in Fig. 1 with polyurethane elastomer hinges

Grahic Jump Location
Figure 16

History of the best GA merit function value f

Grahic Jump Location
Figure 17

Example 2: the package space (a) and corresponding ground structure (b) with dimensions (in mm) and boundary conditions

Grahic Jump Location
Figure 18

Example 2: bistable structure obtained by the GA (a) first stable configuration and (b) second stable configuration

Grahic Jump Location
Figure 19

Example 2: plot of the internal force at the input port A versus the displacement at the output port B

Grahic Jump Location
Figure 20

Detail of the solution of Example 2: (a) first stable configuration and (b) second stable configuration

Grahic Jump Location
Figure 21

Example 3: the package space (a) and corresponding ground structure (b) with dimensions (in mm) and boundary conditions

Grahic Jump Location
Figure 22

Example 3: bistable structure obtained by the GA (a) first stable configuration and (b) second stable configuration

Grahic Jump Location
Figure 23

Example 3: plot of the total internal force at the input ports versus the average displacement at the output ports

Tables

Errata

Discussions

Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In