Type of Document Dissertation Author Stuebner, Michael Author's Email Address email@example.com 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 AbstractThis 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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