Isogeometric Analysis for Topology Optimization with a Phase Field Model

By Luca Dede', Michael J. Borden, Thomas J. R. Hughes. 2012

305 citations recorded by the source corpus.

Subfields: Civil and Structural Engineering, Computational Mechanics, Computational Theory and Mathematics

View Paper: https://www.semanticscholar.org/paper/fa4b8fc43ae32248f1f17137376ea6121de5fa96

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In Civil and Structural Engineering

In Computational Mechanics

In Computational Theory and Mathematics

Citations in the corpus

The phase field method for geometric moving interfaces and their numerical approximations (2019, unknown): “Subsequent studies include applications to phase field models for topology optimization [136], phase field models of brittle fracture [62], high order equations on surfaces [47], Darcy flows [137], chemotaxis [330] and electrochemical reactions [462].”
Multiscale isogeometric topology optimization for lattice materials (2017, methodology): “[48] presented IGA for TO with a phase field model in both 2D and 3D problems, and demonstrated that IGA was particularly suitable for phase field problems as it allowed to handle exact CAD geometry.”
Topology optimization in B-spline space (2013, methodology): “In [23], a phasefield approach is adopted for topology optimization and isogeometric analysis is used for geometric exactness of the design domain and for solution of phase field problems.”
A new isogeometric topology optimization using moving morphable components based on R-functions and collocation schemes (2018, background): “[49] where an ITO with a phase field model for both 2D and 3D problems is presented.”
An Isogeometric design-through-analysis methodology based on adaptive hierarchical refinement of NURBS, immersed boundary methods, and T-spline CAD surfaces (2012, background): “This has been demonstrated for a variety of application areas such as structural vibrations [5, 7], incompressibility [8–10], shells [11–13], fluid-structure interaction [14, 15], turbulence [16–18], phase fields [19, 20], contact [21, 22], fracture [23] and optimization [24, 25].”
A NURBS-based immersed methodology for fluid–structure interaction (2015, methodology): “If we compare NURBS with Lagrange functions, which are typically used in the finite element method, NURBS have several advantages due to their higher continuity between elements and some of them are the following: First, spatial derivatives of second or higher order may be computed easily, which per”
Multimaterial topology optimization by volume constrained Allen–Cahn system and regularized projected steepest descent method (2014, methodology): “Because the step size αk acts as a virtual time-step size in our computational algorithm, similar to [43], using the adaptive time-stepping method [66] can reduce the number of iterations to find desired solutions.”
A multi-resolution method for 3D multi-material topology optimization (2015, unknown): “The concept of isogeometric analysis by Hughes et al. [43] has been used to minimize overall cost by reducing the dependence to the initial FE grid and the post-processing efforts of converting to NURBS based CAD models for problems with complex geometry [44–46].”
Isogeometric Analysis and error estimates for high order partial differential equations in Fluid Dynamics (2014, methodology): “In [27, 32] the fourth–order Cahn–Hillard equations have been solved, while in [9, 19, 28] high order phase field models have been used for fracture modeling, topology optimization, and crystal growth, respectively.”
Geometrically constrained isogeometric parameterized level-set based topology optimization via trimmed elements (2016, methodology): “[35] used a phase-field model for the formulation and solution of the TO and used IGA for geometric exactness of the design domain and for solution of phase field problems.”