A topological derivative method for topology optimization

By Julian A. Norato, Martin P. Bendsøe, Robert B. Haber, Daniel A. Tortorelli. 2007

152 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/e1e3109236513928a099d9769682e12a8913a5d0

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

Bi-directional Evolutionary Structural Optimization on Advanced Structures and Materials: A Comprehensive Review (2016, methodology): “In fact, soft-kill optimization algorithms such as the level set method using continuous design variables may also produce a similar result [97].”
Efficient generation of large-scale pareto-optimal topologies (2013, methodology): “iteration (proposed in [37], and also adopted in [45]).”
Multiresolution topology optimization using isogeometric analysis (2017, unknown): “Since the pioneering paper to topology optimization was published by Bendsøe and Kikuchi,(1) many subsequent approaches have been developed to solve this problem such as Solid Isotropic Material with Penalization (SIMP) approach,(2,3) Evolutionary Structural Optimization,(4,5) level set method,(6) a”
Stress-constrained topology optimization: a topological level-set approach (2013, methodology): “Finally, the authors in Norato et al. (2007), use the topological sensitivity field with fictitious domain method to enhance the convergence of topology optimization.”
A critical review of established methods of structural topology optimization (2009, methodology): “4a) by Norato et al. (2007).”
Isogeometric Analysis for Topology Optimization with a Phase Field Model (2012, methodology): “On this basis the parameter κ introduces the possibility to solve the topology optimization problem (26) by means of the continuation method [12, 20, 23, 71].”
Topology optimization approaches (2013, background): “2004)), or the topological derivatives may be directly used in element-based update schemes (Cea et al. 2000; Norato et al. 2007; Novotny et al. 2007; Amstutz 2011).”
Topological derivative-based topology optimization of structures subject to Drucker–Prager stress constraints (2012, background): “More recently, a new class of methodologies for structural topology optimization has emerged based on the use of the topological derivative of the relevant objective functionals [30, 12, 25, 5, 24, 26].”
A level set method for shape and topology optimization of large‐displacement compliant mechanisms (2008, methodology): “The topological derivative method [30, 32, 33] can be incorporated into the standard level set method to allow the nucleation of new small holes, but there is still a lack of an effective approach to make it physically meaningful to switch between topological derivative and shape derivative [31].”
A survey of structural and multidisciplinary continuum topology optimization: post 2000 (2014, methodology): “pressible Navier-Stokes flow at low Reynolds numbers for channels while Oleson et al. (2006) utilized a similar formulation along with the commercial tool FEMLAB. Evgrafov (2006) also demonstrated topology optimization of NavierStokes flow in addition to using filters to improve results and provide ”