Defeaturing: <i>A posteriori</i> error analysis via feature sensitivity

SUMMARYThe problem of optimal reduction of a linear dynamic subsystem is revisited. The subsystem may represent, for example, a complex but minor part of a large elastic structure. The goal is to drastically reduce the number of degrees of freedom of a subsystem attached through an interface to a main system in such a way as to affect the dynamic behavior of the main system in the least possible way. In a recent publication, the Optimal Modal Reduction (OMR) algorithm was developed to this end. This algorithm seeks a reduction of the subsystem that will have minimal effect, in the L 2 norm, on the Dirichlet-to-Neumann (DtN) map on the interface. Here this algorithm is extended and improved in a number of ways. First, a family of alternative formulations are derived for the DtN map, which lead to alternative OMR algorithms; one of them, called OMR j=2 , is shown to yield better results than the original formulation. Second, the OMR algorithm, which was originally developed for undamped subsystems, is extended to subsystems undergoing Rayleigh damping. In addition, an enhanced derivation of the original OMR algorithm is presented, and the good pointwise performance of OMR is explained by relating to minimization with respect to the H 1 norm. The extensions mentioned above are discussed theoretically as well as demonstrated via numerical examples. Experiments and discussion include comparison of the OMR algorithm to simple coarsening of the subsystem discretization. In all cases, central finite difference discretization in space and explicit time-stepping are employed to solve the scalar wave equation.

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“…from the model and thus relaxing the complexity of its discretization. See [15] for an a posteriori estimation of defeaturing errors.…”

Section: Mü(t)+ku(t) = F(t)mentioning

confidence: 99%

Optimal modal reduction of dynamic subsystems: Extensions and improvements

Tayeb

Givoli

2010

Numerical Meth Engineering

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“…If T i is chosen, we may write the mapping in an explicit form so that each point x * on ∂ Ω 0 is found using

x^{MathClass-bin*} MathClass-rel\in \partial Ω_{0} MathClass-punc: x^{MathClass-bin*} MathClass-rel= bold-italicx MathClass-bin+ s_{i} V_{i} MathClass-punc, bold-italicx MathClass-rel\in \partial Ω_{i} MathClass-punc, 0 ⩽ s_{i} ⩽ 1 MathClass-punc,

and so model Ω i is the reference domain for shape sensitivity computation. The velocity V i can be easily set, for example, by following the approach in , mapping ∂ω i to the centre point O of feature ω i .…”

Section: Domain Transformationmentioning

confidence: 99%

“…Most previous defeaturing analysis methods focus on negative, internal features , that is, internal holes, while the approach here focuses on boundary features, which can be either negative or positive or both; Figure compares the kinds of features studied previously and the type of features studied here. Consider negative features that allowed earlier approaches to use the fact that the original model is contained within its simplification.…”

Section: Introductionmentioning

confidence: 99%

“…Our work is the first to build a second‐order defeaturing error for multiple features and is also the first to handle positive features without heuristics. However, heuristic estimators have been proposed for positive features, and other estimators for negative boundary features . Ferrandes et al .…”

Section: Introductionmentioning

confidence: 99%

“…Figure 2. An example showing the effect of feature interactions on defeaturing error.Recent work has mainly focused on defeaturing error caused by removing a single feature, for example, considering the Poisson equation [8][9][10][11], linear elasticity [10,12,13], plate bending [14] and specific nonlinear problems [9,10,15]. Such work builds some first-order approximation to the defeaturing error.…”

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confidence: 99%

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Second‐order defeaturing error estimation for multiple boundary features

Zhang

Martin

2014

Numerical Meth Engineering

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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.

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

Deng

Soderhjelm

Apelian

et al. 2022

Numerical Meth Engineering

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Manufactured metallic components often contain nonuniformly distributed pores of complex morphologies. Since such porosity defects have a significant influence on material behaviors and affect the usage in high‐performance applications, it is significant to understand the impact of porosity characteristics on the behaviors of components. In this work, a gradient‐enhanced porosity defeaturing estimator, which allows for the modeling of pore geometry and spatial distribution, is proposed within a general elastostatic framework. In this approach, the first‐order shape sensitivity is implemented to account for the change in the elastic quantity of interests to variations of pore sizes and shapes, which is then supplemented by a second‐order shape sensitivity whose mixed partial derivative quantifies the interactions between pores in proximity. The efficacy of the proposed method comes from its posterior manner that it only relies on field solutions of reference models where pores are suppressed. In this context, meshing difficulty and solution convergence issues are avoided, which would otherwise arise in a direct finite element analysis on porous structures. The impact of porosity on structural elastic performance is approximated using a second‐order Taylor expansion where the topological difference between the porous and reference domains is estimated by topological sensitivity; the field variables on pore boundaries are approximated as explicit functions of design variables using exterior formulations. Numerical results show that the elastic performances of components are influenced by the existence of pores. The pore‐to‐pore interactions are significant when pores are close by.

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Defeaturing: A posteriori error analysis via feature sensitivity

Cited by 14 publications

References 23 publications

Optimal modal reduction of dynamic subsystems: Extensions and improvements

Optimal modal reduction of dynamic subsystems: Extensions and improvements

Second‐order defeaturing error estimation for multiple boundary features

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

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