Doctor of Philosophy (Ph.D.)
Degree Granting Department
Civil and Environmental Engineering
Daniel C. Simkins, Ph.D.
Andrés E. Tejada-Martínez, Ph.D.
Les Piegl, Ph.D.
Lennox Hoyte, M.D.
Autar Kaw, Ph.D.
Meshfree Methods, Implicit Geometry, Analysis-Suitable Geometry
Patient-specific biomechanical analysis is an important tool used to understand the complex processes that occur in the body due to physical stimulation. Patient-specific models are generated by processing medical images; once an object from the image is identified via segmentation, a point cloud representation of the object is extracted. Generating an analysis suitable representation from the point cloud has traditionally required generating a finite element mesh, which often requires a well defined surface to accomplish. Point clouds lack a well defined geometry, meaning that the surface definition is incomplete at best. Point clouds that have been generated from images have a fuzzy boundary, meaning that no direct sampling of the boundary is guaranteed to exist and any method for completing the geometry definition requires assumptions on the part of the modeler. The process of generating a finite element mesh of the point cloud is difficult and tedious often requiring manual editing to alleviate poorly constructed elements.
An alternative to generating a finite element mesh is to use meshfree analysis to solve the boundary value problem. The geometric representation of meshfree analysis is a point cloud, thus making it a natural choice for patient-specific analysis. When using meshfree analysis, it is common to skip the geometric reconstruction and use the point cloud directly as an analysis suitable geometry. The lack of a well defined surface can be problematic for a variety of reasons, namely the visualization of results and solving contact driven problems.
The goal of this dissertation is to exploit some characteristics of the meshfree analysis to generate a well defined geometry for point clouds. Meshfree methods are commonly used for the solution of boundary value problems; their lack of a well defined geometry representation is a hindrance that is often remedied by accompanying the meshfree particle distribution with a secondary geometry representation, such as a mesh. The present work outlines a framework that can be used to define and study meshfree geometry representations. A particular meshfree geometry representation called the Meshfree Correction Implicit Geometry is introduced and studied under the guidelines of the framework.
Scholar Commons Citation
Alford, Joseph Bradley, "A Framework for Studying Meshfree Geometry and a Method for Explicit Boundary Determination" (2016). Graduate Theses and Dissertations.