The Topological Asymptotic for PDE Systems: The Elasticity Case

By Stéphane Garreau, Philippe Guillaume, Mohamed Masmoudi. SIAM Journal of Control and Optimization, 2000

497 citations recorded by the source corpus.

Subfields: Civil and Structural Engineering, Computational Theory and Mathematics, Mechanics of Materials

View Paper: https://www.semanticscholar.org/paper/69ef8ca50a38357dbc341a1d321cf980561dcb48

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Civil and Structural Engineering

In Computational Theory and Mathematics

In Mechanics of Materials

Citations in the corpus

Shape and topology optimization of the robust compliance via the level set method (2008, methodology): “Other topology optimization methods are the bubble method or topological gradient approach [2, 12, 13, 24], which amounts to create holes in a given shape, and the thin ligament method [17], not yet implemented, which creates thin ligaments between two parts of the boundary.”
A new algorithm for topology optimization using a level-set method (2006, methodology): “In structural optimization, one usually uses a ﬁxed point method of the type where g k denotes the topological gradient computed in the domain Ω k and c k 0 is a threshold playing the role of a step size (see [16, 15]).”
Connections between topological sensitivity analysis and material interpolation schemes in topology optimization (2011, background): “This concept has been introduced in Eschenauer et al. (1994), mathematically justified in Garreau et al. (2001) and Sokooowski and u”
THE TOPOLOGICAL DERIVATIVE FOR THE POISSON'S PROBLEM (2003, methodology): “As will be seen, this creates a complication that the Domain Truncation Method (see Garreau et al.[4]) will avoid.”
SHAPE OPTIMIZATION IN FLUID MECHANICS (2004, background): “Following Cea (1980) and Delfour et al. (2001) one may consider a velocity of deformation V (x) and define a time-dependent shape (t) = {x + V (x)t : x ∈ } and compute d Jdt , known as the material derivative of J. Recently, the concept of topological derivative was introduced by Sokolowski (Sokolow”
Minimum stress optimal design with the level set method. (2008, unknown): “The notion of topological gradient (in the context of optimal design) has been introduced by Schumacher, Masmoudi, Sokolowski and their co-workers [18], [15], [19], [36], [37] and has been further developped by many authors [11], [25], [32].”
A level-set method for vibration and multiple loads structural optimization (2005, methodology): “Another method of topology optimization is the so-called bubble method, or topological derivative, proposed by [19], [21], and [34].”
A topological derivative method for topology optimization (2007, background): “ψ depends on the solution to the linear elasticity problem, the topological derivative can be expressed as ( Garreau et al. 2001 ):”
A new method in inverse scattering based on the topological derivative (2004, methodology): “In [12] a method for computing the topological derivative (31) was developed using a domain truncation technique and a generalization of the adjoint method.”
Topological sensitivity analysis (2003, methodology): “[10]) D T (x̂) := lim →0 ψ (Ω )− ψ (Ω) f ( ) , (1) where f ( ) is a negative function that decreases monotonically so that f ( ) → 0 with → 0 (0 ≤ < 1), depending on the problem under analysis.”
Shape optimization and its extension to topological design based on isogeometric analysis (2010, background): “Topological derivative with respect to compliance is written as following equation (Garreau et al., 2001).”
Topological optimization of structures subject to Von Mises stress constraints (2010, background): “The topological derivative of the area is obvious, and that of the compliance is known (see [6, 21]).”
Topology optimization using a Topology Description function (2004, methodology): “provided. Ideas to do so may be found by looking at the bubble insertion techniques used in the bubble method (Eschenauer et al. 1994), or using a topological derivative (Sokolowski and ˙ Zochowski 1999; Garreau et al. 2001 ).”
Shape and topology optimization based on the phase field method and sensitivity analysis (2010, methodology): “In the 2D case, the topological derivative of the compliance is derived as follows [65]:”
Self–adjoint Extensions for the Neumann Laplacian and Applications (2006, methodology): “in [8], is not a reliable tool in the topology and shape optimization.”