Second‐order defeaturing error estimation for multiple boundary features

Abstract

SUMMARYA posteriori estimation of defeaturing error, that is, engineering analysis error caused by defeaturing, remains a key challenge in computer-aided design/computer-aided engineering integration; indeed, it is essential if analysis based on automatic simplification of the geometry of a complex design is to be reliable. Previous work has mainly focused on removing a single, negative, internal design feature (i.e. a void within the model's interior); effects of removal of multiple features are found by simple summation. In this paper, we give a second-order defeaturing error estimator that can handle multiple boundary features, either positive or negative (cutouts or additions on the model's boundary). This is the first such method to take into account interactions between different features. (Removing internal holes in 2D or through holes in 3D will change the model's topology and is not addressed here.) The proposed estimator is also the first to handle positive features without heuristics. Our approach uses second-order shape sensitivity, on the basis of reformulating defeaturing as a shape transformation process. The reference model used for sensitivity computation is carefully chosen, as is the associated shape variation velocity, to ensure efficient computation and simple sensitivity expressions. Mixed partial derivatives in a second-order Taylor expansion are used to account for interaction between features. The advantages of our approach are demonstrated using various numerical examples.

Second‐order defeaturing estimator of manufacturing‐induced porosity on structural elasticity

“…We define U(Ω ts ) as a suitable functional space on the perturbed domain, and U(Ω 𝜂 ) as a functional space on the parameterized domain Ω 𝜂 . The weak form on the perturbed domain in Figure 5 can be derived by following Appendix B in Equations ( 24)- (26), and the performance function on the perturbed domain Ω ts is written as Equation (27).…”

“…24 Li and Gao 25 estimated the error of suppressing arbitrarily sized geometric features by using adjoint theory where the feature can be negative (i.e., geometry cutout) or positive (i.e., geometry addition). In their later work, 26 a second-order defeaturing method was proposed for error estimations when multiple interactive boundary features are suppressed. A limitation of this method is that it only accounts for boundary features but not for topological changes.…”

“…23,[46][47][48][49][50] The authors of Reference 26 were the first to utilize higher-order shape sensitivity to estimate the errors in elastic behaviors when removing regular surface features. Following, 26 we further extend the higher-order design sensitivities in this work to quantify the interactions among internal pores in structural elasticity.…”

CAD Model Simplification Error Estimation for Electrostatics Problems

“…The above discussed results can only handle the error caused by simplifying a single feature. [21] shows how to construct a defeaturing error estimator for secondorder shape sensitivity that considers the interaction between different internal or boundary features. However, the estimation results are quite inaccurate, and the assumptions made concerning boundary features result in rather wide error estimate ranges.…”

The generation of triangular meshes for NURBS‐enhanced FEM

“…In many occasions, it is necessary to invest a non‐negligible amount of time removing these small features present in the computer‐aided design (CAD) model before attempting to produce a mesh suitable for finite element analysis . Although the feature removal can be assisted by some semi‐automatic tools , the problem is not just the huge amount of time that is invested in removing geometric features but also the uncertainty that the geometric simplification can generate in the finite element solution obtained in the simplified model. The problem becomes particularly dramatic when different simulations are required in the same geometry.…”