A design-through-analysis approach using the Finite Cell Method (ECCOMAS Congress 2016)

TL;DR

This paper introduces a design-through-analysis methodology that leverages Constructive Solid Geometry (CSG) models and the Finite Cell Method (FCM) to enable efficient finite element analysis of complex, water-tight geometries without extensive meshing or conversion.

Contribution

It presents a novel integration of CSG modeling with FCM, including a fast point-in-membership test derived from CSG operations for improved analysis of complex geometries.

Findings

Efficient point-in-membership test derived from CSG models.

Successful application to complex mechanical engineering models.

Discussion of advantages and limitations in practical scenarios.

Abstract

Modern 3D Computer-Aided-Design (CAD) systems use mainly two types of geometric models. Classically, objects are defined by a Boundary Representation (B-Rep), where only the objects' surfaces with their corresponding edges and nodes are stored. One disadvantage concerning a numerical simulation is that B-Rep models are not necessarily watertight. These 'dirty geometries' cause major difficulties in computational analysis because even basic geometric operations such as point-in-membership tests fail, not to mention meshing as required by classical boundary conforming finite element methods. Alternatively, objects may be represented by Constructive Solid Geometry (CSG), which is strongly related to Procedural Modeling (PM). In this context, the model is created using Boolean operations on primitives. The modeling process is then either stored as a sequence (PM), or as a construction tree (CSG). In contrast to B-Rep models, CSG models are intrinsically water-tight. To run a finite element simulation on a water-tight CSG model, two alternatives are possible: (i) it can either be converted to a B-Rep-model to obtain a finite element mesh or (ii) its implicit description can be used directly by applying an embedded domain approach, like the Finite Cell Method (FCM). In this contribution, we present a design-through analysis methodology using CSG and FCM. A crucial point in FCM is a fast and reliable point-in-membership test which can be directly derived from the CSG model. We present the outline of the modeling approach, the realization of the point-in-membership test as a sequence of CSG-operations, and discuss advantages and limitations on complex models of relevance in mechanical engineering.