Title page for ETD etd-07122006-141758


Type of Document Dissertation
Author Stuebner, Michael
Author's Email Address stuebner@math.lsu.edu
URN etd-07122006-141758
Title An Inverse Homogenization Design Method for Stress Control in Composites
Degree Doctor of Philosophy (Ph.D.)
Department Mathematics
Advisory Committee
Advisor Name Title
Robert Lipton Committee Chair
Frank Neubrander Committee Member
Raymond Fabec Committee Member
Richard Litherland Committee Member
Robert Perlis Committee Member
Guoqiang Li Dean's Representative
Keywords
  • optimal structural design
  • stress constraints
  • homogenization theory
  • numerical methods
Date of Defense 2006-04-24
Availability unrestricted
Abstract
This thesis addresses the problem of optimal design of microstructure in composite materials.

The work involves new developments in homogenization theory and numerical analysis.

A computational design method for

grading the microstructure in composite materials for the control of local stress in

the vicinity of stress concentrations is developed. The method is based upon new rigorous multiscale

stress criteria connecting the macroscopic or homogenized stress to local stress

fluctuations at the scale of the microstructure.

These methods are applied to three different types of design problems. The first treats the problem

of optimal distribution of fibers with circular cross section inside a long shaft subject to torsion loading.

The second treats the same problem but now the shaft cross section is filled with locally

layered material. The third one treats the problem of composite design for a flange fixed at one end

and loaded at the other end.

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