Topology optimization of non-linear elastic structures and compliant mechanisms

By T. Bruns, Daniel A. Tortorelli. 2001

1,443 citations recorded by the source corpus.

Subfields: Civil and Structural Engineering, Control and Systems Engineering, Mechanics of Materials

View Paper: https://www.semanticscholar.org/paper/5fd24d048ecab2e7c243fa5d17c89d45e5d55e95

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In Civil and Structural Engineering

In Control and Systems Engineering

In Mechanics of Materials

Citations in the corpus

Robust topology optimization of structures with imperfect geometry based on geometric nonlinear analysis (2015, methodology): “The design variables ρe are first smoothed by a density filter [25, 26] to obtain the intermediate densities ρ̃e:”
Numerical methods for the topology optimization of structures that exhibit snap‐through (2002, methodology): “Here, we restrict the design space by introducing a continuous density design eld and then ltering this eld to obtain the material density eld (refer to Bruns and Tortorelli [1] for the methodology and convergence studies and to Bourdin [13] for the proof of the well-posedness of the method).”
Efficient use of iterative solvers in nested topology optimization (2010, methodology): “In order to obtain regularized designs and to avoid checkerboard patterns, a density filter was applied (Bourdin 2001; Bruns and Tortorelli 2001).”
A reevaluation of the SIMP method with filtering and an alternative formulation for solid–void topology optimization (2005, methodology): “9b. Topology optimization with the SINH method is equally applicable to compliant mechanism design which requires nonlinear finite element analyses (Bruns and Tortorelli 2001; Pedersen et al. 2001).”
A geometric projection method for designing three‐dimensional open lattices with inverse homogenization (2017, background): “Since a point p will only have ρq = 1 when its sampling window Bp is fully within a bar, ie, when φq < −r, then Equations 2 and 3 imply we must have 2r ⩽ wq (9)”
Efficient generation of large-scale pareto-optimal topologies (2013, background): “Extending PareTO to such nonlinear problems is a promising avenue since the topological sensitivity concept has been generalized to nonlinear problems as well [49].”
Topology optimization approaches (2013, background): “Consequently, consistent derivatives have to be derived using the chain rule (Bruns and Tortorelli 2001; Bourdin 2001; Lazarov and Sigmund 2011; Kawamoto et al. 2011; Andreassen et al. 2011).”
Multi-material topology optimization of laminated composite beam cross sections (2012, methodology): “The filtered density for materialmat elemente is hence ρ̃em = ∑ ẽ∈Se w(xẽ)vẽρẽm ∑ ẽ∈Se w(xẽ)vẽ The weighting functionw(xe) is given by the functionw(xẽ) = fr − ‖xẽ − xe‖2 as suggested by Bruns and Tortorelli [8] and Bourdin [7].”
Multi-objective topology optimization of multi-component continuum structures via a Kriging-interpolated level set approach (2014, methodology): “2009), adaptive design variable fields (Guest and Genut 2010), density filters (Bourdin 2001; Burns and Tortorelli 2001; Sigmund 2007), wavelets (Poulsen 2002), NURBS basis functions (Azegami et al.”
Failure Mitigation in Optimal Topology Design Using a Coupled Nonlinear Continuum Damage Model (2014, methodology): “Therefore, we employ the density filtering technique introduced by Bruns and Tortorelli [26] to address both issues.”