Constructive solid analysis: a hierarchical, geometry-based meshless analysis procedure for integrated design and analysis

In this paper, we propose an analysis methodology that is procedurally analogous to Constructive Solid Geometry (CSG) integrating design and analysis, and thereby enabling efficient optimal design. The procedure, due to its analogous nature to CSG, is termed Constructive Solid Analysis (CSA). The analysis methodology is partitioned, hierarchical and is based on constructing the boundary value problem for a compound geometry through operations on the field quantities defined on the primitives. Although the CSA procedure will allow any basis for approximating the fields, Non-Uniform Rational B-Splines (NURBS), currently popular in the geometric modeling literature, are used to represent the geometry of the primitives as well as the analysis fields. The use of the same basis to represent geometry and analysis fields enables ‘representational’ integration, and further, the developed methodology may be classified as a partition of unity meshless analysis scheme. A more general null-space solution scheme and a somewhat restrictive range-space solution scheme are outlined to solve the discretized equations resulting from the use of NURBS. Several representative problems from the field of linear elasticity are solved to demonstrate the validity of the procedure and to evaluate its computational cost relative to the finite element method. The optimal orientation of an elliptical hole to applied tractions is determined to demonstrate the power of the proposed methodology for shape optimal design. q 2003 Elsevier Ltd. All rights reserved.