Shape optimization directly from CAD: An isogeometric boundary element approach using T-splines

Lian, Haojie; Kerfriden, Pierre; Bordas, Stéphane

doi:10.1016/j.cma.2016.11.012

Cited by 127 publications

(49 citation statements)

References 82 publications

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“…Another interesting research topic is using boundary element method (BEM) for structural response analysis. On this aspect, the conventional BEM and the recently developed isogeometric BEM method [36] can all be employed to reduce the DOFs for structural analysis. It is also worth noting that the present approach is only implemented in a single core computing environment.…”

Section: Discussionmentioning

confidence: 99%

Explicit three dimensional topology optimization via Moving Morphable Void (MMV) approach

Zhang

Chen

Zhu

et al. 2017

Computer Methods in Applied Mechanics and Engineering

211

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Three dimensional (3D) topology optimization problems always involve huge numbers of Degrees of Freedom (DOFs) in finite element analysis (FEA) and design variables in numerical optimization, respectively. This will inevitably lead to large computational efforts in the solution process. In the present paper, an efficient and explicit topology optimization approach which can reduce not only the number of design variables but also the number of degrees of freedom in FEA is proposed based on the Moving Morphable Voids (MMVs) solution framework. This is achieved by introducing a set of geometry parameters (e.g., control points of B-spline surfaces) to describe the boundary of a structure explicitly and removing the unnecessary DOFs from the FE model at every step of numerical optimization. Numerical examples demonstrate that the proposed approach does can overcome the bottleneck problems associated with a 3D topology optimization problem in a straightforward way and enhance the solution efficiency significantly.

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Section: Discussionmentioning

confidence: 99%

Explicit three dimensional topology optimization via Moving Morphable Void (MMV) approach

Zhang

Chen

Zhu

et al. 2017

Computer Methods in Applied Mechanics and Engineering

211

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“…Moreover, situations usually arise when the approximation used for the field variables must be refined locally, whilst keeping the same (coarser) geometrical approximation. This is the case in shape optimization [54,31,30], or for problems with singularities, boundary layers or steep gradients.…”

Section: Contributionmentioning

confidence: 99%

Weakening the tight coupling between geometry and simulation in isogeometric analysis: From sub‐ and super‐geometric analysis to Geometry‐Independent Field approximaTion (GIFT)

Atroshchenko

Tomar

et al. 2018

Numerical Meth Engineering

106

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This paper presents an approach to generalize the concept of isogeometric analysis by allowing different spaces for the parameterization of the computational domain and for the approximation of the solution field. The method inherits the main advantage of isogeometric analysis, ie, preserves the original exact computer-aided design geometry (for example, given by nonuniform rational B-splines), but allows pairing it with an approximation space, which is more suitable/flexible for analysis, for example, T-splines, LR-splines, (truncated) hierarchical B-splines, and PHT-splines. This generalization offers the advantage of adaptive local refinement without the need to reparameterize the domain, and therefore without weakening the link with the computer-aided design model. We demonstrate the use of the method with different choices of geometry and field spaces and show that, despite the failure of the standard patch test, the optimum convergence rate is achieved for nonnested spaces.

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“…[38,39]) and general curved structures (e.g., in Refs. [40][41][42][43][44][45]). The ease of achieving multiple resolutions, and the high order shape functions of IGA, also promote the development of topology optimization, e.g., in Refs.…”

Section: Introductionmentioning

confidence: 99%

An isogeometric numerical study of partially and fully implicit schemes for transient adjoint shape sensitivity analysis

2020

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In structural design optimization involving transient responses, time integration scheme plays a crucial role in sensitivity analysis because it affects the accuracy and stability of transient analysis. In this work, the influence of time integration scheme is studied numerically for the adjoint shape sensitivity analysis of two benchmark transient heat conduction problems within the framework of isogeometric analysis. It is found that (i) the explicit approach (β = 0) and semi-implicit approach with β < 0.5 impose a strict stability condition of the transient analysis;(ii) the implicit approach (β = 1) and semi-implicit approach with β > 0.5 are generally preferred for their unconditional stability; and (iii) Crank-Nicolson type approach (β = 0.5) may induce a large error for large time-step sizes due to the oscillatory solutions. The numerical results also show that the time-step size does not have to be chosen to satisfy the critical conditions for all of the eigen-frequencies. It is recommended to use β % 0:75 for unconditional stability, such that the oscillation condition is much less critical than the Crank-Nicolson scheme, and the accuracy is higher than a fully implicit approach.

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Shape optimization directly from CAD: An isogeometric boundary element approach using T-splines

Cited by 127 publications

References 82 publications

Explicit three dimensional topology optimization via Moving Morphable Void (MMV) approach

Explicit three dimensional topology optimization via Moving Morphable Void (MMV) approach

Weakening the tight coupling between geometry and simulation in isogeometric analysis: From sub‐ and super‐geometric analysis to Geometry‐Independent Field approximaTion (GIFT)

An isogeometric numerical study of partially and fully implicit schemes for transient adjoint shape sensitivity analysis

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