Topology optimization in B-spline space

Qian, Xiaoping

doi:10.1016/j.cma.2013.06.001

Cited by 172 publications

(77 citation statements)

References 33 publications

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“…Because of the close relationship between B‐splines and Bernstein polynomials, we want to clarify the major differences between our method and the B‐spline method of Qian . The first difference lies in the properties of the density field definition itself.…”

Section: Bernstein Basis Polynomialsmentioning

confidence: 99%

“…In the B‐spline approach, the combination of global tensor product construction and required smoothness restricts how we can mesh the domain. In the work of Qian, the domain of interest is embedded in a box‐shaped domain. For complex domain shapes, this method can create some “extra” basis functions in the mesh whose support does not overlap the domain of interest.…”

Section: Bernstein Basis Polynomialsmentioning

confidence: 99%

“…A later work by the Wang et al extends this method using adaptive refinement in both the density field and analysis mesh. An approach proposed by Qian parametrizes the density field using tensor‐product B‐splines. The user controls the order of the spline and the number of knot intervals in each dimension.…”

Section: Introductionmentioning

confidence: 99%

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A density field parametrization for topology optimization using Bernstein elements

Lambe

Czekanski

2018

Numerical Meth Engineering

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Summary A new way of describing the density field in density‐based topology optimization is introduced. The new method uses finite elements constructed from Bernstein polynomials rather than the more common Lagrange polynomials. Use of the Bernstein finite elements allows higher‐order elements to be used in the density‐field interpolation without producing unrealistic density values, ie, values lower than zero or higher than one. Results on several test problems indicate that using the higher‐order Bernstein elements produces optimal designs with sharper estimates of the optimal boundary on coarse design meshes. However, higher‐order elements are also required in the structural analysis to prevent the appearance of unrealistic material distributions. The Bernstein element density interpolation can be combined with adaptive mesh refinement to further improve design accuracy even on design domains with complex geometry.

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Section: Bernstein Basis Polynomialsmentioning

confidence: 99%

Section: Bernstein Basis Polynomialsmentioning

confidence: 99%

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A density field parametrization for topology optimization using Bernstein elements

Lambe

Czekanski

2018

Numerical Meth Engineering

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“…10. This is a classical topology optimization problem of irregular design domain widely studied [21,22,[46][47][48]. Here, the design domain is divided into 90×60 cells and all the supports of CS-RBFs have a 3.5 mm radius.…”

Section: A Cantilever Beam With a Holementioning

confidence: 99%

Stress constrained topology optimization with free-form design domains

Cai

Zhang

2015

Computer Methods in Applied Mechanics and Engineering

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“…In this approach, the voids are represented by coarser mesh while the solids by relatively finer mesh during the process [37,[40][41][42]. 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][45][46]. An efficient approach named multi-resolution topology optimization (MTOP) has been developed where the models for FE analysis and the design optimization are decoupled with different levels of discretization [36].…”

Section: Introductionmentioning

confidence: 99%