An isogeometric design-through-analysis methodology based on adaptive hierarchical refinement of NURBS, immersed boundary methods, and T-spline CAD surfaces

Schillinger, Dominik; Dedè, Luca; Scott, Michael A.; Evans, John A.; Borden, Michael J.; Rank, Ernst; Hughes, Thomas J.R.

doi:10.1016/j.cma.2012.03.017

Cited by 436 publications

(326 citation statements)

References 83 publications

Supporting

Mentioning

313

Contrasting

Unclassified

Order By: Relevance

“…Thomas et al [59] developed a generalization of such technique. In recent years, the application of the T-spline in the IGA framework to different areas has been developed [60][61][62][63][64]. In the context of IGA-BEM Scott et al [58] extended the analysissuitable T-spline to unstructured meshes for elastostatic problems and developed a collocation procedure based on a generalization of the Grenville abscissae.…”

Section: Introductionmentioning

confidence: 99%

A 3d Isogeometrical Boundary Element Analysis for Non-Linear Gravity Wave Propagation

Maestre¹,

Pallarès²,

Cuesta³

2016

Proceedings of the VII European Congress on Computational Methods in Applied Sciences and Engineering (ECCOMAS Congress 2016)

View full text Add to dashboard Cite

Abstract. In this paper we describe a three-dimensional Isogeometric BEM in the time domain based on the T-spline and Non Uniform Rational B-Splines (NURBS) basis to study the free surface behavior. Traditionally, the Lagrange polynomials have been used to discretize the geometry and the BEMs variables. The Lagrange basis are discontinues across the elements although the physical variables are continuous. In dynamics problems with high mesh distortions this approach can produce numerical instabilities that can be quickly propagated. This problem could be overcome using T-spline or NURB basis. The main advantages of this approach are: (1) the control of the continuity and smoothness of the T-spline and NURBS basis, which makes the model numerically stable without the need of artificial smooth techniques;(2) the high order geometrical approximation by non-rational splines;(3) the refinement capabilities without affecting the geometry and BEM's variables; and (4) the direct integration with computer aid geometrical design tools. We use the concept of the Bézier extraction operation which provides an element point of view of the T-Spline and NURBS similar to the traditional finite element. The boundary integral Equation is solved at each time step by the GMRES algorithm and the time marching scheme is performed with a fourth-order Runge-Kutta method to update the model. Additionally, the hydrodynamic force is calculated by an auxiliary boundary equation. Some numerical benchmark examples are analysed to show the accuracy and the stability of the method 7967 J. Maestre, J. Pallarés and I. Cuesta

show abstract

Section: Introductionmentioning

confidence: 99%

A 3d Isogeometrical Boundary Element Analysis for Non-Linear Gravity Wave Propagation

Maestre¹,

Pallarès²,

Cuesta³

2016

Proceedings of the VII European Congress on Computational Methods in Applied Sciences and Engineering (ECCOMAS Congress 2016)

View full text Add to dashboard Cite

show abstract

“…Inserting the flux approximation (13) into (11), relating the result to the left-hand side of (15) and summing over the two subdomains K i yields the following primal formulation: (16) where l(v) = 0 in our example. For a compact notation, we use the jump operator for scalar quantities as…”

Section: Variational Formulationmentioning

confidence: 99%

“…The final form of the non-symmetric Nitsche method is the primal formulation of (10) and (11), which can be obtained by relating σ h and τ to u h and v. To this end, we first consider integration by parts…”

Section: Variational Formulationmentioning

confidence: 99%

“…We note that there also exist methods for the isogeometric analysis of volumetric geometries defined by Brep surfaces, e.g., based on embedded domain methods [10,11] or boundary element methods [12,13]. From a technology viewpoint, the latter three components of the above list profit from significant progress in both isogeometric analysis and embedded domain methods in recent years.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

A parameter-free variational coupling approach for trimmed isogeometric thin shells

2016

Self Cite

View full text Add to dashboard Cite

The non-symmetric variant of Nitsche's method was recently applied successfully for variationally enforcing boundary and interface conditions in non-boundary-fitted discretizations. In contrast to its symmetric variant, it does not require stabilization terms and therefore does not depend on the appropriate estimation of stabilization parameters. In this paper, we further consolidate the non-symmetric Nitsche approach by establishing its application in isogeometric thin shell analysis, where variational coupling techniques are of particular interest for enforcing interface conditions along trimming curves. To this end, we extend its variational formulation within Kirchhoff-Love shell theory, combine it with the finite cell method, and apply the resulting framework to a range of representative shell problems based on trimmed NURBS surfaces. We demonstrate that the non-symmetric variant applied in this context is stable and can lead to the same accuracy in terms of displacements and stresses as its symmetric counterpart. Based on our numerical evidence, the non-symmetric Nitsche method is a viable parameter-free alternative to the symmetric variant in elastostatic shell analysis.

show abstract

“…As a result, exact geometry is introduced into the analysis. The smooth basis can then be leveraged in analysis [5,6,7] and lead to innovative approaches to model design [8,9,10], analysis [11,12,13,14], optimization [15], and adaptivity [16,17,18,19,20].…”

Section: Introductionmentioning

confidence: 99%

Robust Poisson Surface Reconstruction

Estellers

Scott

Tew

et al. 2015

Lecture Notes in Computer Science

View full text Add to dashboard Cite

Abstract. We propose a method to reconstruct surfaces from oriented point clouds with non-uniform sampling and noise by formulating the problem as a convex minimization that reconstructs the indicator function of the surface's interior. Compared to previous models, our reconstruction is robust to noise and outliers because it substitutes the leastsquares fidelity term by a robust Huber penalty; this allows to recover sharp corners and avoids the shrinking bias of least squares. We choose an implicit parametrization to reconstruct surfaces of unknown topology and close large gaps in the point cloud. For an efficient representation, we approximate the implicit function by a hierarchy of locally supported basis elements adapted to the geometry of the surface. Unlike ad-hoc bases over an octree, our hierarchical B-splines from isogeometric analysis locally adapt the mesh and degree of the splines during reconstruction. The hierarchical structure of the basis speeds-up the minimization and efficiently represents clustered data. We also advocate for convex optimization, instead isogeometric finite-element techniques, to efficiently solve the minimization and allow for non-differentiable functionals. Experiments show state-of-the-art performance within a more flexible framework.

show abstract

An isogeometric design-through-analysis methodology based on adaptive hierarchical refinement of NURBS, immersed boundary methods, and T-spline CAD surfaces

Cited by 436 publications

References 83 publications

A 3d Isogeometrical Boundary Element Analysis for Non-Linear Gravity Wave Propagation

A 3d Isogeometrical Boundary Element Analysis for Non-Linear Gravity Wave Propagation

A parameter-free variational coupling approach for trimmed isogeometric thin shells

Robust Poisson Surface Reconstruction

Contact Info

Product

Resources

About