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.

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DOI

10.25777/ep87-a355

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