An object-oriented hierarchical paradigm for integrated parametric design and automated two-dimensional quadrilateral mesh generation
David Ellis Barker · 1993
This research presents a paradigm that integrates the steps in an engineering design and analysis cycle for two-dimensional finite element problems. An object-oriented, hierarchical structure is used to allow any change in the geometry definitions, material properties, or boundary conditions to progress automatically through all other dependent steps. Geometric objects can be defined through functional relationships with other geometric characteristics enabling parametric design. These functional relationships are dynamic and allow geometry to be defined recursively. The design geometry defines the boundaries of the analysis domains. Using a rule-based system approach, a two-step algorithm automatically divides planar domains into four-sided sections. The first step performs pattern matching to identify simple regions. Complex regions are broken into simple regions through a line splitting technique. The second step maps four-sided sections into each simple region. Another algorithm then merges and/or splits the sides of the four-sided sections so that grid conformity is enforced. This is accomplished by requiring sections with a common side to reference the same underlying geometric objects. A mapping technique is used on the four-sided sections to generate the grid for analysis. An optimum element density algorithm is used to determine node placement on the mapped sections, creating a grid composed entirely of quadrilateral elements. The viability of the integrated design and analysis paradigm is presented for several sample geometries. An evaluation of the paradigm and some areas of future research also are presented.