Date of Award

2012

Degree Type

Thesis

Degree Name

Master of Science (MS)

Department

Mechanical Engineering and Applied Mechanics

First Advisor

Martin H. Sadd

Abstract

The mechanical behavior of cellular topologies aligned with stress trajectories (ST) has been investigated. Two-dimensional stress trajectory topologies were generated for each of seven problems. The problems include: cantilever beam with shear end loading; two simply supported beams, one using the elasticity solution and an identical problem using the strength of materials solution; a disk under diametric compression; and a plate with a central stress free hole under equal biaxial, uniaxial and unequal biaxial loadings. The stress trajectory topologies were generated using MATLAB and the problems were simulated using Abaqus, a commercial finite element package. In each problem results from the stress trajectory topology were compared to other alternate topologies that came from random or uniform generation or from another problem.

The purpose of this study was to determine if stress trajectory cellular topologies would reduce the maximum and average stresses in comparison to control and uniform topologies. It is believed that a topology aligned with the stress trajectories will carry and distribute the stresses better than a random topology which often has localized areas of high stress. In the beam and disk problems, the topology effect was investigated by comparing the stress trajectory topology to a uniform topology. In the plate problems, the effect of element size in the ST topologies as well as the effect of the topology was investigated. The effect of the size of the element was investigated by comparing three different ST topologies of various densities. The effect of the topology was investigated by comparing the medium stress trajectory topology to two random topologies and the medium topologies of other plate problems.

For all cases it was found that stress trajectory topologies are better than other alternate topologies. The stress trajectory topology lowered the maximum and average stresses in the beam and disk problems. In the plate problems it was found that the size of the element has little effect as the maximum and average stresses were about the same. In looking at the different topologies for the plate problems it was found that the medium stress trajectory topology was the best of the five alternate topologies. The maximum and average stresses were lower than the random topologies and the stresses on the hole were much less than the other medium topologies.

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