The shape and topological optimizations connection

By J. Cea, Stéphane Garreau, Philippe Guillaume, Mohamed Masmoudi. 2000

358 citations recorded by the source corpus.

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

View Paper: https://www.semanticscholar.org/paper/d2538575946881f934ddcb7cf1e61d5bbacc531c

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In Civil and Structural Engineering

In Computational Mechanics

In Mechanics of Materials

Citations in the corpus

THE TOPOLOGICAL DERIVATIVE FOR THE POISSON'S PROBLEM (2003, methodology): “In Céa et al.[2] a relation between the Topological Derivative and the classical Shape Derivative is discussed.”
A topological derivative method for topology optimization (2007, methodology): “The main difference between our algorithm and the one developed in Cea et al. (2000) is that ours uses the smooth geometry projection onto the fictitious analysis domain to vary the boundary ∂ω continuously.”
Topological derivative for multi‐scale linear elasticity models applied to the synthesis of microstructures (2010, methodology): “In contrast to the homogenization approach, we propose in this paper a microstructural synthesis/optimization algorithm relying on the mathematical concept of topological derivative [46, 12, 16] combined with a level-set domain representation.”
Topology optimization of shell structures using adaptive inner-front (AIF) level set method (2008, methodology): “noted that the topological derivative for the compliance minimization problem of a linear elastic structure can be expressed some constant times of strain energy density ( Cea et al. 2000; Mei and Wang 2004; Allaire et al. 2005).”
Stress-constrained topology optimization: a topological level-set approach (2013, methodology): “63 In essence, we carry out a fixed-point iteration [36], [42], 64 [23] involving three quantities (see Figure 5): (1) domain 65 τ Ω , (2) displacement fields u and v over τ Ω , and (3) 66 topological sensitivity field over τ Ω .”
Topological optimization of structures subject to Von Mises stress constraints (2010, background): “A relatively new approach for this kind of problem is based on the concept of topological derivative [15, 18, 33].”
Explicit level‐set‐based topology optimization using an exact Heaviside function and consistent sensitivity analysis (2012, positive): “A mechanism of nucleating holes can be incorporated in the optimization process by introducing the concept of a topological derivative [14, 15].”
Shape and topology optimization based on the phase field method and sensitivity analysis (2010, methodology): “Coupling to the topological derivative To resolve the above initial-dependency problem, the bubble method or topological derivative [62, 63, 64, 65] can be introduced to our method in the same way as the level set method [66, 67].”
A quasi-reversibility approach to solve the inverse obstacle problem (2010, background): “3), some others on shape sensitivity, in the spirit of [32, 18] or topological gradient like in [13, 20].”