Research Papers

Multiobjective Hybrid Optimization–Antioptimization for Force Design of Tensegrity Structures

[+] Author and Article Information
Makoto Ohsaki1

Department of Architecture,  Hiroshima University, 1-4-1, Kagamiyama, Higashi-Hiroshima 739-8527, Japanohsaki@hiroshima-u.ac.jp

Jingyao Zhang

Department of Architecture and Urban Design,  Ritsumeikan University, Kusatsu 525-8577, Japanzhang@fc.ritsumei.ac.jp

Isaac Elishakoff

Department of Ocean and Mechanical Engineering, Florida Atlantic University, Boca Raton, FL 33431-0991elishako@fau.edu


Corresponding author.

J. Appl. Mech 79(2), 021015 (Feb 24, 2012) (8 pages) doi:10.1115/1.4005580 History: Received February 13, 2011; Revised August 28, 2011; Posted February 01, 2012; Published February 13, 2012; Online February 24, 2012

Properties of Pareto optimal solutions considering bounded uncertainty are first investigated using an illustrative example of a simple truss. It is shown that the nominal values of the Pareto optimal solutions considering uncertainty are slightly different from those without considering uncertainty. Next a hybrid approach of multiobjective optimization and antioptimization is presented for force design of tensegrity structures. We maximize the lowest eigenvalue of the tangent stiffness matrix and minimize the deviation of forces from the specified target distribution. These objective functions are defined as the worst values due to the possible errors in the fabrication and construction processes. The Pareto optimal solutions are found by solving the two-level optimization–antioptimization problems using a nonlinear programming approach for the upper optimization problem and enumeration of the vertices of the uncertain region for the lower antioptimization problem.

Copyright © 2012 by American Society of Mechanical Engineers
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Figure 2

Relation between H and W for the design A1  = 1.0 and A2  = 1.857

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Figure 3

Relations between W and V of Pareto optimal solutions; dotted line: solutions without uncertainty, solid line: solutions with uncertainty, dashed line: nominal values of the solutions with uncertainty

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Figure 4

A simple tensegrity structure

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Figure 5

Feasible region of the coefficients of self-equilibrium force vectors of the small tensegrity structure

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Figure 6

Pareto optimal solutions for C = 0.5 and the region of uncertainty; + : Pareto optimal solution with uncertainty, × : Pareto optimal solution without uncertainty

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Figure 7

Tensegrity grid constructed by assembling the unit cell shown in Fig. 8 in x and y directions

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Figure 8

Unit cell for the tensegrity grid

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Figure 9

Pareto optimal solutions in objective function space

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Figure 10

Relation between minimum eigenvalue and square-root of force deviation of Pareto optimal solutions



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