Boundary element based multiresolution shape optimisation in electrostatics

Lecture Notes in Computational Science and Engineering

Bandara

2015

Self Cite

We review our recent work on multiresolution shape optimisation and present its application to elastic solids, electrostatic field equations and thin-shells. In the spirit of isogeometric analysis the geometry of the domain is described with subdivision surfaces and different resolutions of the same surface are used for optimisation and analysis. The analysis is performed using a sufficiently fine control mesh with a fixed resolution. During shape optimisation the geometry is updated starting with the coarsest control mesh and then moving on to increasingly finer control meshes. The transfer of data between the geometry and analysis representations is accomplished with subdivision refinement and coarsening operators. Moreover, we discretise elastic solids with the immersed finite element method, electrostatic field equations with the boundary element method and thin-shells with the subdivision finite element technique. In all three discretisation techniques there is no need to generate and maintain an analysis-suitable volume discretisation.

“…For more details we refer to [3,4]. Instead of using least squares fitting the coarsening matrix R can also be defined based on quasi-interpolation [23] or smoothing [41].…”

Section: Multiresolution Editingmentioning

confidence: 99%

Section: Multiresolution Shape Optimisationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Multiresolution Shape Optimisation with Subdivision Surfaces

Lecture Notes in Computational Science and Engineering

Bandara

2015

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“…In that exploratory work Loop subdivision and non-gradient based optimisation algorithms were used. More recently the proposed multiresolution approach has been applied to other types of optimisation problems, namely electrostatic shape optimisation of high-voltage devices [27] and shape optimisation of volumetric solids [28]. The electrostatic simulations are performed with the boundary element method and the solid simulations with a the voxelbased immersed finite element method.…”

Section: Introductionmentioning

confidence: 99%

Isogeometric shape optimisation of shell structures using multiresolution subdivision surfaces

Bandara

2018

Computer-Aided Design

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We introduce the isogeometric shape optimisation of thin shell structures using subdivision surfaces. Both triangular Loop and quadrilateral Catmull-Clark subdivision schemes are considered for geometry modelling and finite element analysis. A gradientbased shape optimisation technique is implemented to minimise compliance, i.e. to maximise stiffness. Different control meshes describing the same surface are used for geometry representation, optimisation and finite element analysis. The finite element analysis is performed with subdivision basis functions corresponding to a sufficiently fine control mesh. During iterative shape optimisation the geometry is updated starting from the coarsest control mesh and proceeding to increasingly finer control meshes. The proposed approach is applied to three optimisation examples, namely a catenary, roof over a rectangular domain and freeform architectural shell roof. The influence of the geometry description and the used subdivision scheme on the obtained optimised curved geometries are investigated in detail.

“…In addition, high‐order BEM discretisations are generally accepted as superior over equivalent low‐order discretisations for acoustic problems. () Several isogeometric BEM approaches have already been developed based on NURBS,() T‐splines,() and subdivision surfaces …”

Section: Introductionmentioning

confidence: 99%

Isogeometric FEM‐BEM coupled structural‐acoustic analysis of shells using subdivision surfaces

Liu

Majeed

Numerical Meth Engineering

et al. 2018

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Summary We introduce a coupled finite and boundary element formulation for acoustic scattering analysis over thin‐shell structures. A triangular Loop subdivision surface discretisation is used for both geometry and analysis fields. The Kirchhoff‐Love shell equation is discretised with the finite element method and the Helmholtz equation for the acoustic field with the boundary element method. The use of the boundary element formulation allows the elegant handling of infinite domains and precludes the need for volumetric meshing. In the present work, the subdivision control meshes for the shell displacements and the acoustic pressures have the same resolution. The corresponding smooth subdivision basis functions have the C1 continuity property required for the Kirchhoff‐Love formulation and are highly efficient for the acoustic field computations. We verify the proposed isogeometric formulation through a closed‐form solution of acoustic scattering over a thin‐shell sphere. Furthermore, we demonstrate the ability of the proposed approach to handle complex geometries with arbitrary topology that provides an integrated isogeometric design and analysis workflow for coupled structural‐acoustic analysis of shells.