A sharp interface isogeometric strategy for moving boundary problems

<p>The proposed methodology is first utilized to model stationary and propagating cracks. The crack face is enriched with the Heaviside function which captures the displacement discontinuity. Meanwhile, the crack tips are enriched with asymptotic displacement functions to reproduce the tip singularity. The enriching degrees of freedom associated with the crack tips are chosen as stress intensity factors (SIFs) such that these quantities can be directly extracted from the solution without <em>a-posteriori</em> integral calculation.</p> <p>As a second application, the Stefan problem is modeled with a hybrid function/derivative enriched interface. Since the interface geometry is explicitly defined, normals and curvatures can be analytically obtained at any point on the interface, allowing for complex boundary conditions dependent on curvature or normal to be naturally imposed. Thus, the enriched approximation naturally captures the interfacial discontinuity in temperature gradient and enables the imposition of Gibbs-Thomson condition during solidification simulation.</p> <p>The shape optimization through configuration of finite-sized heterogeneities is lastly studied. The optimization relies on the recently derived configurational derivative that describes the sensitivity of an arbitrary objective with respect to arbitrary design modifications of a heterogeneity inserted into a domain. The THB-splines, which serve as the underlying approximation, produce sufficiently smooth solution near the boundaries of the heterogeneity for accurate calculation of the configurational derivatives. (Abstract shortened by ProQuest.)</p>

Name thesis:degree_name

Doctor of Philosophy (PhD)

Level thesis:degree_level

Dissertation

Discipline thesis:degree_discipline

Mechanical Engineering

Year

2016

Author dc:creator

• Song, Tao

Contributors dc:contributor

• Ganesh Subbarayan
• Ahmed H. Sameh
• Thomas S. Siegmund
• Kejie Zhao

• Applied sciences
• Algebraic point projection
• Enriched isogeometric analysis
• Immersed boundary problems
• Applied Mechanics
• Mechanical Engineering

Repository record dc:identifier

https://docs.lib.purdue.edu/open_access_dissertations/1002

OAI identifier oai:identifier

oai:docs.lib.purdue.edu:open_access_dissertations-2217