Efficient modelling of delamination growth using adaptive isogeometric continuum shell elements

Adams, Camiel; Fagerström, Martin; Remmers, Jjc Joris

doi:10.1007/s00466-019-01754-8

Cited by 14 publications

(3 citation statements)

References 24 publications

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“…While computational efficiency is an important factor in numerical analysis, KL shells have limited accuracy in predicting the transverse stress and strain states. This limitation has sparked the development of IGA-based continuum shell and layerwise continuous shell formulations [82][83][84][85][86][87][88][89], which enable other analysis types where stress triaxiality effects cannot be neglected, such as multiaxial fatigue analysis [90] and ductile fracture analysis [91].…”

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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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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“…In particular, IGA has been shown to provide good results when combined with the LW concept (see, e.g., [14,15]). In this context, also 2D isogeometric finite element approaches have been proposed in the literature [16,17], with some of them relying on high-order theories [18] or employing enhanced shell and plate theories [19,20].…”

Section: Introductionmentioning

confidence: 99%

Accurate equilibrium-based interlaminar stress recovery for isogeometric laminated composite Kirchhoff plates

Patton¹,

Antolín²,

Dufour³

et al. 2020

Preprint

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In this paper, we use isogeometric Kirchhoff plates to approximate composite laminates adopting the classical laminate plate theory. Both isogeometric Galerkin and collocation formulations are considered. Within this framework, interlaminar stresses are recovered through an effective post-processing technique based on the direct imposition of equilibrium in strong form, relying on the accuracy and the higher continuity typically granted by isogeometric discretizations. The effectiveness of the proposed approach is proven by extensive numerical tests.

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“…In the context of composite modeling, 2D IGA finite element formulations have been proposed in [30,31], with some of them employing enhanced shell and plate theories [32,33]. Other approaches use a combination of IGA and the Carrera Unified Formulation as in [34].…”

Section: Introductionmentioning

confidence: 99%

Efficient equilibrium-based stress recovery for isogeometric laminated curved structures

Patton¹,

Antolín²,

Kiendl³

et al. 2020

Preprint

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This work focuses on an efficient stress recovery procedure for laminated composite curved structures, which relies on Isogeometric Analysis (IGA) and equilibrium. Using a single element through the thickness in combination with a calibrated layerwise integration rule or a homogenized approach, the 3D solid isogeometric modeling grants an inexpensive and accurate approximation in terms of displacements (and their derivatives) and in-plane stresses, while through-the-thickness stress components are poorly approximated. Applying a further post-processing step, an accurate out-of-plane stress state is also recovered, even from a coarse displacement solution. This is based on a direct integration of the equilibrium equations in strong form, involving high order derivatives of the displacement field. Such a continuity requirement is fully granted by IGA shape function properties. The post-processing step is locally applied, which grants that no additional coupled terms appear in the equilibrium, allowing for a direct reconstruction without the need to further iterate to resolve the out-of-balance momentum equation. Several numerical results show the good performance of this approach particularly for composite stacks with significant radius-to-thickness ratio and number of plies. In particular, in the latter case, where a layerwise technique employing a number of degrees of freedom directly proportional to the number of plies would be much more computationally demanding, the proposed method can be regarded as a very appealing alternative choice.

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Efficient modelling of delamination growth using adaptive isogeometric continuum shell elements

Cited by 14 publications

References 24 publications

Blended isogeometric Kirchhoff–Love and continuum shells

Blended isogeometric Kirchhoff–Love and continuum shells

Accurate equilibrium-based interlaminar stress recovery for isogeometric laminated composite Kirchhoff plates

Efficient equilibrium-based stress recovery for isogeometric laminated curved structures

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