Seamless integration of design and Kirchhoff–Love shell analysis using analysis-suitable unstructured T-splines

Casquero, Hugo; Wei, Xiaodong; Toshniwal, Deepesh; Li, Angran; Hughes, Thomas J.R.; Kiendl, Josef; Zhang, Yongjie

doi:10.1016/j.cma.2019.112765

Cited by 84 publications

(36 citation statements)

References 87 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…We compare and summarize the convergence plots of the two geometric On the other hand, it is worth mentioning that adaptive mesh refinement is usually the method of choice to recover optimal convergence for problems with irregular solutions. In IGA, T-splines [51][52][53][54], hierarchical B-splines [55][56][57][58][59], and locally-refinable B-splines [60,61] are typical examples in this family of methods.…”

Section: L-shaped Domainmentioning

confidence: 99%

Immersed boundary-conformal isogeometric method for linear elliptic problems

et al. 2021

Self Cite

View full text Add to dashboard Cite

We present a novel isogeometric method, namely the Immersed Boundary-Conformal Method (IBCM), that features a layer of discretization conformal to the boundary while employing a simple background mesh for the remaining domain. In this manner, we leverage the geometric flexibility of the immersed boundary method with the advantages of a conformal discretization, such as intuitive control of mesh resolution around the boundary, higher accuracy per degree of freedom, automatic satisfaction of interface kinematic conditions, and the ability to strongly impose Dirichlet boundary conditions. In the proposed method, starting with a boundary representation of a geometric model, we extrude it to obtain a corresponding conformal layer. Next, a given background B-spline mesh is cut with the conformal layer, leading to two disconnected regions: an exterior region and an interior region. Depending on the problem of interest, one of the two regions is selected to be coupled with the conformal layer through Nitsche’s method. Such a construction involves Boolean operations such as difference and union, which therefore require proper stabilization to deal with arbitrarily cut elements. In this regard, we follow our precedent work called the minimal stabilization method (Antolin et al in SIAM J Sci Comput 43(1):A330–A354, 2021). In the end, we solve several 2D benchmark problems to demonstrate improved accuracy and expected convergence with IBCM. Two applications that involve complex geometries are also studied to show the potential of IBCM, including a spanner model and a fiber-reinforced composite model. Moreover, we demonstrate the effectiveness of IBCM in an application that exhibits boundary-layer phenomena.

show abstract

Section: L-shaped Domainmentioning

confidence: 99%

Immersed boundary-conformal isogeometric method for linear elliptic problems

et al. 2021

Self Cite

View full text Add to dashboard Cite

show abstract

“…Along this direction, simultaneously fulfilling the requirements from both design and analysis is a significant challenge. Numerous methods have been developed over the past few years, but among them, only a few constructions can achieve optimal convergence rates in IGA, such as geometrically smooth multipatch construction, 21,22 degenerated Bézier construction, 23‐25 manifold‐based construction, 26 and blended C 0 construction for unstructured hexahedral meshes 27 . A common simplification in all these constructions is to adopt uniform parameterization around extraordinary vertices, that is, the surrounding knot intervals are assumed to be the same.…”

Section: Introductionmentioning

confidence: 99%

Tuned hybrid nonuniform subdivision surfaces with optimal convergence rates

Wei

Zhang

et al. 2021

Numerical Meth Engineering

Self Cite

View full text Add to dashboard Cite

This article presents an enhanced version of our previous work, hybrid nonuniform subdivision (HNUS) surfaces, to achieve optimal convergence rates in isogeometric analysis (IGA). We introduce a parameter λ (14<λ<1) to control the rate of shrinkage of irregular regions, so the method is called tuned hybrid nonuniform subdivision (tHNUS). Thus, HUNS is a special case of tHNUS when λ=12. While introducing λ in hybrid subdivision significantly complicates the theoretical proof of G1 continuity around extraordinary vertices, reducing λ can recover optimal convergence rates when tHNUS functions are used as a basis in IGA. From the geometric point of view, tHNUS retains comparable shape quality as HNUS under nonuniform parameterization. Its basis functions are refinable and the geometric mapping stays invariant during refinement. Moreover, we prove that a tHNUS surface is globally G1‐continuous. From the analysis point of view, tHNUS basis functions form a nonnegative partition of unity, are globally linearly independent, and their spline spaces are nested. In the end, we numerically demonstrate that tHNUS basis functions can achieve optimal convergence rates for the Poisson's problem with nonuniform parameterization around extraordinary vertices.

show abstract

“…Isogeometric analysis (IGA), introduced by Hughes et al [1], was originally proposed to bridge the gap between computer-aided geometric design (CAGD) models, which are often constructed using non-uniform rational B-splines (NURBS) [2] and recently using other spline technologies [3][4][5][6][7][8][9][10][11][12][13][14][15][16], and their corresponding physics-based computational approximation models that are frequently based on Lagrange polynomial representations for the geometry and solution spaces. The essential concept of IGA is to employ the same basis functions that are used in design for numerical analysis.…”

Section: Introductionmentioning

confidence: 99%

Blended isogeometric Kirchhoff–Love and continuum shells

Liu

Johnson

Rajanna

et al. 2021

Computer Methods in Applied Mechanics and Engineering

View full text Add to dashboard Cite

The computational modeling of thin-walled structures based on isogeometric analysis (IGA), non-uniform rational B-splines (NURBS), and Kirchhoff-Love (KL) shell formulations has attracted significant research attention in recent years. While these methods offer numerous benefits over the traditional finite element approach, including exact representation of the geometry, naturally satisfied high-order continuity within each NURBS patch, and computationally efficient rotation-free formulations, they also present a number of challenges in modeling real-world engineering structures of considerable complexity. Specifically, these NURBS-based engineering models are usually comprised of numerous patches, with discontinuous derivatives, nonconforming discretizations, and non-watertight connections at their interfaces. Moreover, the analysis of such structures often requires the full stress and strain tensors (i.e., including the transverse normal and shear components) for subsequent failure analysis and remaining life prediction. Despite the efficiency provided by the KL shell, the formulation cannot accurately predict the response in the transverse directions due to its kinematic assumptions. In this work, a penalty-based formulation for the blended coupling of KL and continuum shells is presented. The proposed approach embraces both the computational efficiency of KL shells and the availability of the full-scale stress/strain tensors of continuum shells where needed by modeling critical structural components using continuum shells and other components using KL shells. The proposed method enforces the displacement and rotational continuities in a variational manner and is applicable to non-conforming and non-smooth interfaces. The efficacy of the developed method is demonstrated through a number of benchmark studies with a variety of analysis configurations, including linear and nonlinear analyses, matching and non-matching discretizations, and isotropic and composite materials. Finally, an aircraft horizontal stabilizer is considered to demonstrate the applicability of the proposed blended shells to real-world engineering structures of significant complexity. c

show abstract

Seamless integration of design and Kirchhoff–Love shell analysis using analysis-suitable unstructured T-splines

Cited by 84 publications

References 87 publications

Immersed boundary-conformal isogeometric method for linear elliptic problems

Immersed boundary-conformal isogeometric method for linear elliptic problems

Tuned hybrid nonuniform subdivision surfaces with optimal convergence rates

Blended isogeometric Kirchhoff–Love and continuum shells

Contact Info

Product

Resources

About