Optimization of Structural Topology in the High-Porosity Regime

Abstract

This project explores homogenization-based design as a systematic approach to the optimization of high- porosity materials and structures. We have shown that when the goal is maximal stiffness, extremal effective behavior does not require multiscale architecture. In fact, optimal structures can be found within a simple class of closed-cell, high-porosity composites we call "single-scale laminates." Moreover there is a simple formula for the Hooke's law of a single-scale laminate. It reduces the task of structural optimization for minimum weight and maximal stiffness to a convex optimization specifically, a problem of semidefinite programming. The optimal structures are not in general unique - indeed, there is a high degree of degeneracy. It is natural to use simplicity and/or continuity as selection mechanisms. We have developed efficient schemes for doing so.

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Document Details

Document Type
Technical Report
Publication Date
Jul 20, 2004
Accession Number
ADA425439

Entities

People

  • Robert V. Kohn

Organizations

  • New York University

Tags

Communities of Interest

  • Air Platforms

DTIC Thesaurus Topics

  • Applied Mathematics
  • Composite Materials
  • Computer Programming
  • Laminates
  • Law
  • Linear Programming
  • Materials
  • Mathematical Programming
  • Mathematics
  • Mechanical Properties
  • Mechanics
  • Microstructure
  • New York
  • Optimization
  • Porosity
  • Semidefinite Programming
  • Stiffness

Readers

  • Computational Fluid Dynamics (CFD)
  • Operations Research
  • Structural Health Monitoring of Composite Structures.