Domain composition methods for associating geometric modeling with finite element modeling

Publisher Website
Google Scholar
Abstract
This paper &velops a new method for associating geometxic models, and the operations used to construct them, with the formulation of continuum field equations. Current methods of engineering analysis link a geometric model to the continuum equatioos of a corresponding analysis model via intermediate geometries, or meshes. These meshes “know” little about the global or local geometries. They represent decompositions of the global domain into solvable, non-intemecting subdomains (t%tite elements) that approximate the geometric model. Often the elements of these meshes all share a similar shape, and they tend to impose this shape on the solution of the field equations throughout the model with little regard for the local character of the geometry. Furthermore, it can be a complex and lengthy process to construct a mesh of similarly shaped, non-intersecting elements when the corresponding geometric model has been constructed of intersecting gtmmetric primitives in a variety of shapes. The presented method domain compositi~ utilizes the local geometry to parametrize the field equations, capturing the local character of the geometry in the solution to the field equations. Each geometric primitive defms a local coordinate system in which the field equations are formulated. Knowledge of the construction of the global geometric model is used to generate coupling and constraint equations which combme the local formulations into a global fotmuh-ttion. The analysis of the continuum field model can be carried out as the geometric model is constructed. It is possible to implement the domain composition method in such a way that the analysis is automatically generated from the geometric model and the boundary conditions on the continuum field. Ordy the geometric pritnhives need to be meshe~ and the type of element employed for meshing each primitive can be chosen to suit the particular shape of the prirnhive. Special formulations of the field equations, such as for crack tip analysis, can be incorporated into the model in the form of new geometric primitives. Even coaracly meshed models are geometrically accurate and are amenable to use in preliminary design.

This publication has 0 references indexed in Scilit: