Date of Award

August 2020

Document Type


Degree Name

Master of Science (MS)


Mechanical Engineering

Committee Member

Georges Fadel

Committee Member

Lonny Thompson

Committee Member

Vincent Ervin


Advances in manufacturing capabilities, such as additive manufacturing, have expanded the design freedom given to engineers enabling more efficient designs through the use of complex geometries. However, determining the optimal geometric structure for a given set of performance criteria can be quite challenging when given such design freedom. One technique to do so is with the use of topology optimization methods, in which optimal material distribution within a given design space is determined. Many established topology optimization methods are developed such that a set of boundary conditions are prescribed to the design domain and remain fixed throughout the optimization process of determining the material distribution. This eliminates the ability to implement design dependent loading conditions, such as pressure loading, which requires tracking (following) the pressure surface as the geometry evolves during the optimization process. In this thesis, a level-set topology optimization method is implemented based on voxel elements on design domains in R^3 subjected to internal pressure loading, such as in the case of a non-spherical or cylindrical pressure vessel.

Following a thorough literature review, a level-set function was chosen to define a crisp material/void boundary for identifying loading conditions caused by the applied pressure. This pressure loading is calculated as an applied traction across all material elements, excluding exterior surface nodes. This results in an equal and opposite cancelation throughout the material domain and leaving forces only at desired nodes along the material/void boundary. This implementation only requires material elements to be meshed, allowing for remeshing throughout the process to increase accuracy while saving computational cost by excluding void regions. Additionally, to improve convergence, the Lagrangian formulation of a penalty is replaced by a method analogous to PID-control systems as the algorithm hones in on convergence.

To test the effectiveness of the method and the practicality of designing an irregular pressure vessel, the gas storage tanks of the MK16 rebreather for the US NAVY were redesigned within the current system’s geometric constraints in an effort to increase gas storage capacity. To do this, an outside domain geometry of the irregular shaped pressure vessel was defined, and not subject to change, while the optimization code was executed on the interior structure to minimize compliance subjected to an overall volume fraction constraint. This was done at various target volume fractions, and then stresses and compliance values were analyzed and compared to the existing pressure vessel of the MK16. The findings of this research concluded that designing an irregular shaped pressure vessel is a viable means of increasing storage capacity although future work would need to be executed to manufacture and experimentally validate these findings.



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