Explicit dynamic isogeometric B-Rep analysis of penalty-coupled trimmed NURBS shells

Leidinger, L.F.; Breitenberger, M.; Bauer, Anna; Hartmann, Stefan; Wüchner, Roland; Bletzinger, Kai‐Uwe; Duddeck, Fabian; Song, L.

doi:10.1016/j.cma.2019.04.016

Cited by 53 publications

(31 citation statements)

References 58 publications

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“…While the following section will present an applicability of penalty method to implicit MPM, the technique has never been used in explicit MPM. However, it was used to couple trimmed B-Rep patches through weak enforcement in explicit IBRA by [73]. The formulation of penalty method in explicit MPM should not differ substantially from the current work, but the usage of smaller time step might be necessary to provide stability of the boundary imposition.…”

Section: Nonconforming Boundary Enforcementmentioning

confidence: 98%

Nonconforming Dirichlet boundary conditions in implicit material point method by means of penalty augmentation

et al. 2021

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In many geomechanics applications, material boundaries are subjected to large displacements and deformation. Under these circumstances, the application of boundary conditions using particle methods, such as the material point method (MPM), becomes a challenging task since material boundaries do not coincide with the background mesh. This paper presents a formulation of penalty augmentation to impose nonhomogeneous, nonconforming Dirichlet boundary conditions in implicit MPM. The penalty augmentation is implemented utilizing boundary particles, which can move either according to or independently from the material deformation. Furthermore, releasing contact boundary condition, as well as the capability to accommodate slip boundaries, is introduced in the current work. The accuracy of the proposed method is assessed in both 2D and 3D cases, by convergence analysis reaching the analytical solution and by comparing the results of nonconforming and classical grid-conforming simulations.

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Section: Nonconforming Boundary Enforcementmentioning

confidence: 98%

Nonconforming Dirichlet boundary conditions in implicit material point method by means of penalty augmentation

et al. 2021

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“…Coming up with benchmark problems of increasing geometric complexity to evaluate the performance of different IGA techniques is a required task in the near future. These benchmarks would enable not only comparisons between different types of analysis-suitable splines that handle EPs [45,50,48,59,60], but also comparisons with non-boundary-fitted methods that deal with trimmed NURBS representations [21,22,23,24,25,26].…”

Section: Appendix a Casteljau Algorithmmentioning

confidence: 99%

“…The lack of a conforming parameterization in trimmed NURBS representations rules out the use of standard boundary-fitted methods. To circumvent this issue, nonboundary-fitted methods have been developed in recent years [21,22,23,24,25,26] * . SubD and T-splines have a conforming parameterization, but they are not directly analysis suitable.…”

Section: Introductionmentioning

confidence: 99%

Analysis-suitable unstructured T-splines: Multiple extraordinary points per face

Wei,

Li,

Qian

et al. 2021

Preprint

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Analysis-suitable T-splines (AST-splines) are a promising candidate to achieve a seamless integration between the design and the analysis of thin-walled structures in industrial settings. In this work, we generalize AST-splines to allow multiple extraordinary points within the same face. This generalization drastically increases the flexibility to build geometries using AST-splines; e.g., much coarser meshes can be generated to represent a certain geometry. The AST-spline spaces detailed in this work have C 1 inter-element continuity near extraordinary points and C 2 inter-element continuity elsewhere. We mathematically show that AST-splines with multiple extraordinary points per face are linearly independent and their polynomial basis functions form a non-negative partition of unity. We numerically show that AST-splines with multiple extraordinary points per face lead to optimal convergence rates for second-and fourth-order linear elliptic problems. To illustrate a possible isogeometric framework that is already available, we design the B-pillar and the side outer panel of a car using T-splines with the commercial software Autodesk Fusion360, import the control nets into our in-house code to build AST-splines, and import the Bézier extraction information into the commercial software LS-DYNA to solve eigenvalue problems. The results are compared with conventional finite elements. Good agreement is found, but conventional finite elements require significantly more degrees of freedom to reach a converged solution than AST-splines.

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“…Thus, isogeometric KL shells [39][40][41][42][43][44][45][46][47] have gained popularity in the simulation and analysis community due to their computationally efficient rotation-free formulation and model simplification into the midsurface representation. The formulations have been previously demonstrated as an effective solution for the analysis of complex problems [48][49][50][51][52][53][54][55][56][57][58][59][60][61], including wind turbine blades [62][63][64][65][66][67][68][69][70][71][72] and heart valves [73][74][75][76][77][78][79][80][81]. While computational efficiency is an important factor in numerical analysis, KL shells have limited accuracy in predicting the transverse stress and strain states.…”

Section: Introductionmentioning

confidence: 99%

“…The work of Lei et al [95] coupled surfaces by virtually inserting control points to make the interface matching and subsequently applying linear constraints to the virtually matched interface, and similar approaches have been reported [96]; however, these methods are limited in terms of patch configurations and cannot be applied to non-smooth patch interfaces. Instead of enforcing rotational continuity through explicit geometric constraints, a more general penalty formulation based on including the penalty contribution in the principle of virtual work was proposed [48] and later extended to Reissner-Mindlin shells [97]. Nevertheless, this method restricted the rotation at the patch boundary to be less than 90 • and has limited applicability in large displacement 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

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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

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Explicit dynamic isogeometric B-Rep analysis of penalty-coupled trimmed NURBS shells

Cited by 53 publications

References 58 publications

Nonconforming Dirichlet boundary conditions in implicit material point method by means of penalty augmentation

Nonconforming Dirichlet boundary conditions in implicit material point method by means of penalty augmentation

Analysis-suitable unstructured T-splines: Multiple extraordinary points per face

Blended isogeometric Kirchhoff–Love and continuum shells

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