Topology optimization for minimum stress design with the homogenization method

By Grégoire Allaire, François Jouve, H. Maillot. 2004

185 citations recorded by the source corpus.

Subfields: Civil and Structural Engineering, Mechanics of Materials

View Paper: https://www.semanticscholar.org/paper/f83b26802ce883129da72a550c2875a3328eb87b

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In Civil and Structural Engineering

In Mechanics of Materials

Citations in the corpus

Isogeometric Analysis for Topology Optimization with a Phase Field Model (2012, methodology): “In this framework a possible approach is the homogenization method [4], for which the macroscopic properties of the material are deduced from the microscopic properties of the porous material represented by the density function; the first numerical approximation for an homogenized material was prese”
Topological optimization of structures subject to Von Mises stress constraints (2010, background): “This is in contrast with the existing literature on the topic, where either dual methods are implemented [14, 16, 19, 31], with the well-known difficulties related to the irregularity of the Lagrange multiplier, or a simple power law penalization is considered [3, 4], generally leading to unfeasible”
Minimum stress optimal design with the level set method. (2008, methodology): “There are relatively fewer papers on this topic in the context of topology optimization, based either on the homogenization method, SIMP or phase-(cid:12)eld method, see [5], [17], [16], [23], [39].”
Topology Optimization (2009, methodology): “In general, well-performing designs were found in the range P ∈ [16,28].”
Dynamic Response Topology Optimization in the Time Domain Using Equivalent Static Loads (2012, background): “Various objective functions and constraints have been widely studied: minimization of compliance [13, 14]; eigenvalues and vibration [15, 16]; buckling load [17, 18]; stress constraints [19-21]; damage and impact [22]; multiobjective functions [23].”
Topological derivative-based topology optimization of structures subject to Drucker–Prager stress constraints (2012, methodology): “Such methods have been widely applied with success to problems such as compliance minimization [10] but, despite its fundamental importance in engineering design, only a relatively small number of publications appear to deal with the incorporation of local (point-wise) stress constraints [2, 3, 11, ”
Stress-based topology optimization for continua (2010, background): “Hence, we consider neither composite nor functionally graded materials (Lipton 2002; Stump et al. 2007; Allaire et al. 2004).”
Simultaneous design of components layout and supporting structures using coupled shape and topology optimization technique (2008, methodology): “Meanwhile, effective approaches like homogenization-based method (Bendsøe and Kikuchi 1988; Allaire et al. 2004), solid isotropic material with penalization model (Bendsøe 1989; Zhou and Rozvany 1991), evolutionary method (Xie and Steven 1997), etc. have been proposed so far.”
Sequential integer programming methods for stress constrained topology optimization (2007, methodology): “Also in Allaire et al. (2004) the problem is initially kept infinite dimensional, and a minimum stress problem is treated by the use of the homogenization method, see e.g.”
Topology optimization for minimum mass design considering local failure constraints and contact boundary conditions (2006, background): “A different approach to defining this effective stress is given in Allaire et al. (2004) in the context of homogenized microstructures.”
A level set approach for topology optimization with local stress constraints (2014, methodology): “On the other hand, the work in [5] also extended the homogenization method to treat problems involving stress but to objective functions corresponding to minimum stress design subject to volume constraint.”
Sensitivity analysis with the modified Heaviside function for the optimal layout design of multi-component systems (2012, unknown): “were established [2–7].”