Date of Award
Spring 1984
Document Type
Thesis
Degree Name
Master of Science (MS)
Department
Mechanical & Aerospace Engineering
Program/Concentration
Engineering Mechanics
Committee Director
Gene Hou
Committee Member
Earl A. Thorton
Committee Member
Chuh Mei
Call Number for Print
Special Collections; LD4331.E57C4465
Abstract
The problem of finding optimal cross-sectional shapes of elastic hollow bars in torsion is formulated and solved numerically. A variational formulation for the state equation is presented, and the material derivative of continuum mechanics is used for the shape design sensitivity analysis. Performance criteria include the bending stiffness, the torsional rigidity, and the weight of the bar. The existence of a keyway, an example of geometric irregularity, can be considered as well. The material can be either isotropic or anisotropic. The finite element method is used for the numerical solution of the variational state equation and is integrated into an iterative optimization algorithm. The effect of internal nodal movements, which is associated with the regriding process in order to avoid ill-meshing, on the shape design sensitivity is carefully examined. Results show that ignorance of internal nodal movements may induce very severe errors in the shape design sensitivity analysis. Taking the internal nodal movement into account, an alternative approach which constructs the velocity field over the element domain is introduced. Although it takes more computational time, the new approach improves the accuracy of the shape design sensitivity dramatically. Various numerical examples have been presented to show the applicability of the iterative shape optimization algorithm.
Rights
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DOI
10.25777/ep87-a355
Recommended Citation
Chen, Jahau L..
"Shape Optimization for Elastic Hollow Bars in Torsion"
(1984). Master of Science (MS), Thesis, Mechanical & Aerospace Engineering, Old Dominion University, DOI: 10.25777/ep87-a355
https://digitalcommons.odu.edu/mae_etds/422