Constructive solid analysis (CSA): A geometry based meshless procedure for integrated analysis and design

Design is an inherently iterative process consisting of alternate modeling and analysis phases, each requiring input from the other. The research in the two communities however has grown independently of one another in spite of the similitude between the two with only a few attempts at bridging this “great divide.”; In this work we propose an analysis methodology that is both “mathematically” and “procedurally” integrated with the modeling phase, thereby enabling efficient optimal design. The procedure, due to its analogous nature to CSG, is termed Constructive Solid Analysis (CSA). The analysis methodology developed in the paper is partitioned, hierarchical and is based on constructing the boundary value problem for a compound geometry through operations on the field quantities of the primitives, thus, facilitating design changes and achieving “procedural” integration. Non-Uniform Rational B-Splines (NURBS), currently popular in the geometric modeling literature, are used as mathematical representation for both the geometry modeling phase and in the analysis phase, thus achieving “mathematical” integration. Meshless Analysis using NURBS (MAN) is motivated as a stand-alone meshless methodology, especially for solving problems involving discontinuities. Properties inherent to NURBS enable modeling of discontinuities through enrichment procedures without re-discretization. The NURBs based meshless procedure is shown to be computationally superior to the Element Free Galerkin method. Shape optimization is used as a vehicle to demonstrate the potency of the CSA in addressing iterative design problems. The problems selected highlight the ability of the CSA to capture the underlying simplicity of the modeling procedure through procedural “integration”. This simplicity is often obfuscated by the complexities of a conventional approach. Shape optimization problems are generally incapable of creating new topologies. This information can be acquired through topology optimization. Topology optimization problems are solved in a meshless format with the density defined as a field entity over the design domain. An isoparametric representation is used. The integration of topology and shape optimization processes is a promising future endeavor. (Abstract shortened by UMI.)...