Constructive modeling strategies and implementation frameworks for optimal hierarchical synthesis

Xuefeng Zhang, Purdue University

Abstract

A critical computational challenge to many design problems is the need for iterative changes to the geometry of the design domain followed by re-meshing and re-analysis. At the present time, a naturally hierarchical procedure, namely Constructive Solid Geometry is well established for the creation of geometry. The constructive procedure describes a complex object through Boolean operations on the primitives, but the analysis is carried out only on the final geometry. Thus, a change in the geometry of even one primitive necessitates the re-meshing of the final geometry and the re-analysis of the final discretized model. In this thesis, a hierarchical procedure integrating design and analysis termed Constructive Solid Modeling (CSM) is developed. The key idea in the methodology is that the hierarchy in the description of the geometry is mirrored by an identical hierarchy in the analysis fields and a hierarchy in material description, each guided by their appropriate governing equations. Non-Uniform Rational B-Spline (NURBS) is used to mathematically describe the shape of the primitive, and to discretize the analysis fields and the material fields defined on the primitives. This leads to a mathematical integration of the geometry, analysis, and material description. An object-oriented symbolic framework for integrated meshless analysis and optimal design termed jNURBS is developed to implement the proposed methodology. The method is applied to model and analyze heterogeneous material microstructures including complex 2D and 3D random microstructures. The method is then applied to shape optimization. It is shown that CSM can naturally handle the multi-phases in the microstructure and the iterative shape changes during shape optimization. With the NURBS based meshless discretization, meshing and re-meshing are avoided. Furthermore, the discretization of the primitives is far simpler than meshing the complex geometry; the constructive procedure can localize the shape changes to reduce the re-discretization and the re-analysis cost. Re-discretization and re-factorization of matrices, which constitute the major cost of re-analysis, are only carried out on the primitives affected by the design change. Thus, the CSM procedure is computationally advantageous compared to the finite element analysis for problems involving iterative shape changes.

Degree

Ph.D.

Advisors

Subbarayan, Purdue University.

Subject Area

Mechanics|Mechanical engineering

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