HiGeoM: A symbolic framework for a unified function space representation of geometry and attributes of solids
Abstract
This thesis proposes functional spaces and an algebra which operates on elements in those spaces for the representation of heterogeneous solids: their geometry and attributes. The domain of functions representable are the Hilbert space Hm of functions and the space of smooth, C∞, functions. This formal representation is codified in a computational environment called HiGeoM. A declarative programming language is provided which accepts a subset of mathematical semantics specified using the Mathematical Markup Language (MathML) as well as a fortran-like syntax. The language enables solid model definition using continuous affine transformation and boolean operators leading to a mixed-dimensional representation. It is possible to construct analytically defined shapes as well as spline representation of complex geometry. The capabilities of the implemented system further extends to allow arbitrary algebra to be defined and suitable for the symbolic definition of boundary value problems as well as the definition of arbitrary computational models. The capabilities of the system has been implemented to demonstrate the notion of enrichment-based modeling as well the hierarchical partition of unity field composition (HPFC). The capabilities have been utilized for demonstrating the construction of complex engineered solids and the definition of weight fields defined over the interior of the structure. The weight fields constitute a fundamental attribute which enables the definition of other attribute fields such as the behavior through the solution to boundary value problems.
Degree
Ph.D.
Advisors
Anderson, Purdue University.
Subject Area
Mechanical engineering
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