University of Illinois Urbana-Champaign

Topology design with optimized self-adaptive materials

Jog, Chandrashekhar S.; Haber, Robert B.; Bendsoe, Martin P.

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https://hdl.handle.net/2142/112396

Description

Title
Topology design with optimized self-adaptive materials
Author(s)
  • Jog, Chandrashekhar S.
  • Haber, Robert B.
  • Bendsoe, Martin P.
Issue Date
1993-03
Keyword(s)
  • Topology Optimization
  • Self-adaptive Materials
Abstract
Significant performance improvements can be obtained if the topology of an elastic structure is allowed to vary in shape optimization problems. We study the optimal shape design of a two-dimensional elastic continuum for minimum compliance subject to a constraint on the total volume of material. The macroscopic version of this problem is not well-posed if no restrictions are placed on the structure topology; relaxation of the optimization problem via quasiconvexification or homogenization methods is required. The effect of relaxation is to introduce a perforated microstructure that must be optimized simultaneously with the macroscopic distribution of material. A combined analytical-computational approach is proposed to solve the relaxed optimization problem. Both stress and displacement analysis methods are presented. Since rank-2 layered composites are known to achieve optimal energy bounds, we restrict the design space to this class of microstructures whose effective properties can easily be determined in explicit form. We develop a series of reduced problems by sequentially interchanging extermization operators and analytically optimizing the microstructural design fields. This results in optimization problems involving the distribution of an adaptive material that continuously optimizes its microstructure in response to the current-state of stress or strain. A further reduced problem, involving only the response field, can be obtained in the stress-based approach, but the requisite interchange of extremization operators is not valid in the case of the displacement-based model. Finite element optimization procedures based on the reduced displacement formulation are developed and numerical solutions are presented. Care must be taken in selecting the discrete function spaces for the design density and displacement response, since the reduced problem is a two-field, mixed variational problem. An improper choice for the solution space leads to instabilities in the optimal design similar to those encountered in mixed formulations of the Stokes problem.
Publisher
Department of Theoretical and Applied Mechanics. College of Engineering. University of Illinois at Urbana-Champaign
Series/Report Name or Number
  • TAM R 708
  • 1993-6006
ISSN
0073-5264
Type of Resource
text
Language
eng
Permalink
http://hdl.handle.net/2142/112396
Sponsor(s)/Grant Number(s)
National Science Foundation 93/03; Danish Research Academy 93/03; Cray Research Inc 93/03
Copyright and License Information
Copyright 1993 Board of Trustees of the University of Illinois

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Technical Reports - Theoretical and Applied Mechanics (TAM) PRIMARY
TAM technical reports include manuscripts intended for publication, theses judged to have general interest, notes prepared for short courses, symposia compiled from outstanding undergraduate projects, and reports prepared for research-sponsoring agencies.