A geometry projection method for shape optimization

By Julian A. Norato, Robert B. Haber, Daniel A. Tortorelli, Martin P. Bendsøe. 2004

146 citations recorded by the source corpus.

Subfields: Civil and Structural Engineering, Computational Mechanics, Industrial and Manufacturing Engineering

View Paper: https://www.semanticscholar.org/paper/5e9e2e6a1e54b5b0dc8924e436864bc1154c1def

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In Civil and Structural Engineering

In Computational Mechanics

In Industrial and Manufacturing Engineering

Citations in the corpus

A level set method for structural shape and topology optimization using radial basis functions (2009, methodology): “Among these level set methods, an alternative level-set topology optimization method [27,28] was proposed by using the multiquadric and inverse multiquadric splines functions based on [25,32].”
A topological derivative method for topology optimization (2007, methodology): “Note that the filter window diameter 2� is proportional to the local grid spacing, so the geometry projection is consistent and the numerical solution converges to the continuum solution in the limit of mesh refinement (cf. Norato et al. 2004 ).”
A gradient-based shape optimization scheme using an interface-enriched generalized FEM (2015, methodology): “These Eulerian methods incorporate mesh-free [20,21], fictitious domain [15,17,19,22,23], material perturbation [24], level-set [16,18,25,26], and the generalized/extended finite element methods (G/XFEM) [16,27–31].”
Topology optimization approaches (2013, methodology): “For example, to obtain a smooth level set function, alternative approaches for discretizing the level set function are often used, such as radial basis function, high-order polynomial functions with local support, and spectral methods (Norato et al. 2004; de Ruiter and van Keulen 2004; Wang and Wang”
A level set method for shape and topology optimization of large‐displacement compliant mechanisms (2008, methodology): “Parameterization scheme with compactly supported RBFs In this study, based on the contributions of [36, 39, 41], the compactly supported radial basis functions (CSRBFs) [55] are used in approximating the implicit level set surface by taking advantage of their favorable multivariate interpolation pro”
Piecewise constant level set method for structural topology optimization (2009, methodology): “Previously, the level set method based implicit form of energy principle was first proposed in [5] and also implemented in implicit geometry model in [6, 7].”
Integrated layout design of multi-component systems using XFEM and analytical sensitivity analysis (2012, unknown): “[18].”
Shape optimization of 2D structures using simulated annealing (2007, background): “geometric model may become unfeasible [20,21], stresses may exceed the admissible stress level [20,21,24,29–31,35,38– 41,51,62,71,78,79,84], fatigue life may be shorter than the lowest allowable number of cycles [74], natural frequency may be lower than a certain limit [24], displacements may be too”
Full analytical sensitivities in NURBS based isogeometric shape optimization (2010, methodology): “Note, the optimal designs for the finite and infinite plates are distinct [24, 25].”
Stress concentration minimization of 2D filets using X-FEM and level set description (2007, background): “(27), a circular connectio n to a straight domain is not the best solution and it is better t o replace it by a super-circular connection as defined by: x1 +x η 2 = r (20)”
A level set‐based parameterization method for structural shape and topology optimization (2008, methodology): “[26] presented a geometry projection method for shape optimization, and Haber [27] proposed a method of combining a reduced sequential quadratic programming with multilevel schemes.”