The Experts below are selected from a list of 819 Experts worldwide ranked by ideXlab platform
Alessandro Reali - One of the best experts on this subject based on the ideXlab platform.
-
multi level bezier extraction for hierarchical local refinement of isogeometric analysis
Computer Methods in Applied Mechanics and Engineering, 2018Co-Authors: Davide Dangella, Stefan Kollmannsberger, E Rank, Alessandro RealiAbstract:Abstract One of the main topics of research on Isogeometric Analysis is local refinement. Among the various techniques currently studied and developed, one of the most appealing, referred to as hierarchical B-Splines, consists of defining a suitable set of basis functions on different hierarchical levels. This strategy can also be improved, for example to recover partition of unity, resorting to a truncation operation, giving rise to the so-called truncated hierarchical B-Splines. Despite its conceptual simplicity, implementing the hierarchical definition of shape functions into an existing code can be rather involved. In this work we present a simple way to bring the hierarchical isogeometric concept closer to a standard finite element formulation. Practically speaking, the hierarchy of functions and Knot spans is flattened into a sequence of elements being equipped with a standard single-level basis. In fact, the proposed multi-level extraction is a generalization of the classical Bezier extraction and analogously offers a standard element structure to the hierarchical overlay of functions. Moreover, this approach is suitable for an extension to non-linear problems and for a parallel implementation. The multi-level extraction is presented as a general concept that can be applied to different kinds of refinements and basis functions. Finally, few basic algorithms to compute the local multi-level extraction operator for Knot Insertion on spline spaces are outlined and compared, and some numerical examples are presented.
Clemens V Verhoosel - One of the best experts on this subject based on the ideXlab platform.
-
Isogeometric analysis for modelling of failure in advanced composite materials
Numerical Modelling of Failure in Advanced Composite Materials, 2015Co-Authors: Jjc Joris Remmers, Clemens V Verhoosel, Rene De BorstAbstract:Isogeometric analysis (IGA) has recently received much attention in the computational mechanics community. The basic idea is to use splines as the basis functions for finite-element calculations. This enables the integration of computer-aided design and numerical analysis and allows for an exact representation of complex, curved geometries. Another feature of isogeometric basis functions, their higher-order continuity, is even more important for the development of shell and continuum shell elements to analyse structural stability and damage in thin-walled composite structures. The higher-order shape functions can be used to implement relatively straightforward but powerful shell elements. In addition, these shape functions contribute to a better representation of stresses in continuum elements. Finally, interfaces and delaminations can be modelled by reducing the order of the isogeometric shape functions by Knot-Insertion. In this chapter, we will give an overview of the recent developments in IGA for shell and continuum shell formulations.
-
an isogeometric approach to cohesive zone modeling
International Journal for Numerical Methods in Engineering, 2011Co-Authors: Clemens V Verhoosel, Rene De Borst, Michael A Scott, Thomas J R HughesAbstract:The possibility of enhancing a B-spline basis with discontinuities by means of Knot Insertion makes isogeometric finite elements a suitable candidate for modeling discrete cracks. In this contribution we use isogeometric finite elements to discretize the cohesive zone formulation for failure in materials. In the case of a pre-defined interface, non-uniform rational B-splines are used to obtain an efficient discretization. In the case that propagating cracks are considered, T-splines are found to be more suitable, due to their ability to generate localized discontinuities. Various numerical simulations demonstrate the suitability of the isogeometric approach to cohesive zone modeling.
Malcolm A. Sabin - One of the best experts on this subject based on the ideXlab platform.
-
A.: NURBS with extraordinary points: Highdegree, non-uniform, rational subdivision schemes
2016Co-Authors: Thomas J. Cashman, Neil A. Dodgson, Ursula H. Augsdörfer, Malcolm A. SabinAbstract:The same control mesh subdivided in three different configurations. In regular regions, the degree 3 surface (b) is C2, and the degree 7 surfaces (c) and (d) are C6. No previous subdivision scheme can generate the surface (d). The Knot intervals modified to give (d) are shown in (a); the red interval is ten times greater than the unmarked intervals, and the green interval is four times greater. Comparing (d) with (c), note that in this case the non-uniform intervals change the whole surface, because the influence of a Knot interval grows with degree. We present a subdivision framework that adds extraordinary vertices to NURBS of arbitrarily high degree. The surfaces can represent any odd degree NURBS patch exactly. Our rules handle non-uniform Knot vectors, and are not restricted to midpoint Knot Insertion. In the absence of multiple Knots at extraordinary points, the limit surfaces have bounded curvature
-
NURBS with Extraordinary Points: High-degree, Non-uniform, Rational Subdivision Schemes
2010Co-Authors: Thomas J. Cashman, Ursula H. Augsdörfer, Neil A. Dodgson, Malcolm A. SabinAbstract:The same control mesh subdivided in three different configurations. In regular regions, the degree 3 surface (b) is C2, and the degree 7 surfaces (c) and (d) are C6. No previous subdivision scheme can generate the surface (d). The Knot intervals modified to give (d) are shown in (a); the red interval is ten times greater than the unmarked intervals, and the green interval is four times greater. Comparing (d) with (c), note that in this case the non-uniform intervals change the whole surface, because the influence of a Knot interval grows with degree. We present a subdivision framework that adds extraordinary vertices to NURBS of arbitrarily high degree. The surfaces can represent any odd degree NURBS patch exactly. Our rules handle non-uniform Knot vectors, and are not restricted to midpoint Knot Insertion. In the absence of multiple Knots at extraordinary points, the limit surfaces have bounded curvature
-
NURBS with extraordinary points: high-degree, non-uniform, rational subdivision schemes
ACM Transactions on Graphics, 2009Co-Authors: Thomas J. Cashman, Ursula H. Augsdörfer, Neil A. Dodgson, Malcolm A. SabinAbstract:We present a subdivision framework that adds extraordinary vertices to NURBS of arbitrarily high degree. The surfaces can represent any odd degree NURBS patch exactly. Our rules handle non-uniform Knot vectors, and are not restricted to midpoint Knot Insertion. In the absence of multiple Knots at extraordinary points, the limit surfaces have bounded curvature.
-
Non-uniform BSpline subdivision using refine and smooth
Springer, 2007Co-Authors: Thomas J. Cashman, Neil A. Dodgson, Malcolm A. SabinAbstract:Abstract. Subdivision surfaces would be useful in a greater number of applications if an arbitrary-degree, non-uniform scheme existed that was a generalisation of NURBS. As a step towards building such a scheme, we investigate non-uniform analogues of the Lane-Riesenfeld ‘refine and smooth ’ subdivision paradigm. We show that the assumptions made in constructing such an analogue are critical, and conclude that Schaefer’s global Knot Insertion algorithm is the most promising route for further investigation in this area.
Joris J. C. Remmers - One of the best experts on this subject based on the ideXlab platform.
-
Efficient modelling of delamination growth using adaptive isogeometric continuum shell elements
Computational Mechanics, 2020Co-Authors: Camiel Adams, Martin Fagerström, Joris J. C. RemmersAbstract:The computational efficiency of CAE tools for analysing failure progression in large layered composites is key. In particular, efficient approximation and solution methods for delamination modelling are crucial to meet today’s requirements on virtual development lead times. For that purpose, we present here an adaptive continuum shell element based on the isogeometric analysis framework, suitable for the modelling of arbitrary delamination growth. To achieve an efficient procedure, we utilise that, in isogeometric analysis, the continuity of the approximation field easily can be adapted via so-called Knot Insertion. As a result, the current continuum shell provides a basis for an accurate but also computationally efficient prediction of delamination growth in laminated composites. Results show that the adaptive modelling framework works well and that, in comparison to a fully resolved model, the adaptive approach gives significant time savings even for simple analyses where major parts of the domain exhibit delamination growth.
Remmers Joris - One of the best experts on this subject based on the ideXlab platform.
-
AN ADAPTIVE ISOGEOMETRIC CONTINUUM SHELL ELEMENT FOR EFFICIENT MODELLING OF DELAMINATION GROWTH
2019Co-Authors: Adams Camiel, Fagerstr\uf6m Martin, Remmers JorisAbstract:To accurately predict damage growth in large, thin-walled composite structures, it is required\ua0to have models that are both valid and computational efficient. In this respect, isogeometric\ua0continuum shell elements provide an interesting option. First of all, the higher order\ua0continuity achieved via isogeometric analysis yields an increased in-plane smoothness that enable\ua0the use of larger shell elements. In addition, the high in-plane continuity also leads to that\ua0in-plane derivatives of in-plane stresses are continuous across element edges, thereby allowing\ua0for element-local recovery procedures for the prediction of out-of-plane stresses [2, 3].\ua0Furthermore, as shown by Hosseini et al. [1], it is in an isogeometric continuum shell modelling framework rather straightforward to modify the through-thickness kinematics to incorporate\ua0weak and strong discontinuities. By introducing weak discontinuities at ply interfaces,\ua0the through-thickness strain discontinuities at these locations are explicitly accounted for. This\ua0enables a much better 3D strain and stress prediction, something which is key for a good estimation\ua0of the amount of intralaminar damage. By introducing strong discontinuities, the element\ua0is also capable to represent initiation and growth of one or several delamination cracks.In the current contribution, we extend the shell formulation from [1] into an adaptive continuum\ua0shell that allows for an update of the through-thickness kinematics at any required time\ua0instant during the simulation. The adaptivity is facilitated by that the through-thickness kinematical\ua0enrichment can be achieved by so-called ”Knot Insertion”, a step which can be fully\ua0automated due to the hierarchical nature of the isogeometric approximation functions.As a result, the current shell provides a good basis for an accurate but also computationally\ua0efficient prediction of the progressive failure in laminates, without a-priory knowledge of\ua0where damage will occur. Results show that the adaptive modelling framework works well,\ua0both to predict the full 3D stress states in multiaxial laminates, but also to capture growth of\ua0delaminations. Furthermore, in comparison to a fully resolved model, the adaptive approach\ua0gives significant time savings even for simple analyses where significant parts of the domain\ua0exhibit delamination growth. This implies that computational efforts (time and memory) can be\ua0considerably reduced when using this adaptive concept in large-scale analyses where damage develop only in a confined, but initially unknown area of the structure.[1] S. Hosseini, J.J.C. Remmers, C.V. Verhoosel, and R. de Borst (2015) Int. J. Numer. Meth.Eng., 102, 159–179.[2] M. Fagerstr\uf6m and J.J.C Remmers (2017) Adaptive modelling of delmination growth usingisogeometric continuum shell elements. Proc. ICCM21, Xian, China.[3] J.-E. Dufour, P. Antolin, G. Sangalli, F. Auricchio, A. Reali (2018) Composites Part B:Engineering, 138, 12-18
-
Adaptive modelling of delamination growth using isogeometric continuum shell elements
2017Co-Authors: Fagerstr\uf6m Martin, Remmers JorisAbstract:As a means to decrease the complexity and size of numerical models for the simulation of progressive failure in composite laminates, and thereby also the computational time required for the simulations, we here propose an adaptive continuum shell element model based on the concept of Isogeometric Analysis. The concept based is based on the approach presented by Hosseini et al. [1], but in contrast to their work, in which delamination interfaces are predefined, we here address the need to handle successive introduction of new discontinuities in an automated fashion.The formulation adopts T-spline basis functions for the discretisation of the shell mid-surface, whereas a higher-order B-spline functions are used for the interpolation in the thickness direction. A discontinuity can be incorporated in this latter function by so-called Knot-Insertion to account for ply interfaces (weak discontinuities) and delaminations (strong discontinuities). In order to automatically enhance the element, various stress-based criteria using element local improved interlaminar stresses can be used. However, for such a stress based approach, the prediction of the through-thickness variation of out-of-plane stress components needs to be improved if a coarse shell approximation is used (the so-called lumped state explained below). For this purpose, we propose and demonstrate the capability of a reconstruction technique based on the classical strategy of integrating the momentum balance equations. Due to the nature of the isogeometric analysis approximation and its higher order displacement smoothness over element edges, this reconstruction can be performed element-wise. This possibility to do an element-wise reconstruction is a strength compared to traditional shell elements, based on Lagrange approximations for the displacement field, for which displacement approximation derivatives (and thereby stresses) are non-smooth. In this way, the isogeometric continuum element can be used in an even more efficient fashion, allowing for the detailed analysis of large, thin-walled composite structures
-
Adaptive modelling of delamination growth using isogeometric continuum shell elements
2017Co-Authors: Fagerstr\uf6m Martin, Remmers JorisAbstract:A key to successful modelling of the complex progressive failure in layered composite materials is to have computationally efficient models and methods which can be adapted to the predominant failure mechanisms in each specific loading case. In particular, efficient approximation and solution methods for delamination modelling is crucial, since "high-fidelity" FE models with many elements through the component thickness interconnected with cohesive interface elements leads to unfeasible simulation times and memory requirements. For that purpose, several papers have been published that present alternative methods for modelling concepts which support laminate failure analyses requiring only one shell element through the thickness and where arbitrary delamination propagation is accounted for only in areas where it is needed, cf. Brouzoulis and Fagerstr\uf6m, Hosseini et al. and McElroy .The proposed new concepts however need to be further developed before they can be readily applied to solve engineering problems in which delamination cracks can initiate and propagate. For traditional finite element based shell models, such as the one presented by Brouzoulis and Fagerstr\uf6m (based on the eXtended Finite Element Method, XFEM), improved methods to predict the interlaminar stresses are needed for an accurate prediction of delamination initiation, since the transverse stresses predicted directly from the shell solution are of too low accuracy. This was recently done e.g. by Fr\ue4mby et al. who complemented an XFEM shell formulation with a stress recovery approach , performed over a patch of elements, thereby making the model fully adaptive. As for the alternative concept based on an isogeometric approach by Hosseini et al., there is a need to handle successive introduction of new discontinuities by means of Knot-Insertion in an automated fashion. A first step in this direction was taken by the authors in , outlining strategies for how to initiate and propagate delamination cracks using this framework. As a benefit over FE based C0 continuous shells, the necessary improvements of the interlaminar stresses for isogeometric shells can be performed element-wise since in-plane stresses are smooth over element boundaries.In this contribution we focus on the further development of the isogeometric solid-like shell element to allow for an automated Insertion of discontinuities. The formulation adopts NURBS (or T-spline) basis functions for the discretisation of theshell mid-surface, whereas a higher-order B-spline functions are used for the interpolation in the thickness direction. A discontinuity can be incorporated in this latter function by so-called Knot-Insertion to account for ply interfaces (weak discontinuities) and delaminations (strong discontinuities) . In order to automatically enhance the element, various stress-based criteria using element local improved interlaminar stresses are investigated. In this way, the isogeometric continuum element can be used in an even more efficient fashion, allowing for the detailed analysis of large, thin-walled composite structures
-
Adaptive modelling of delamination growth using isogeometric continuum shell elements
2017Co-Authors: Fagerström Martin, Remmers JorisAbstract:A key to successful modelling of the complex progressive failure in layered composite materials is to have computationally efficient models and methods which can be adapted to the predominant failure mechanisms in each specific loading case. In particular, efficient approximation and solution methods for delamination modelling is crucial, since "high-fidelity" FE models with many elements through the component thickness interconnected with cohesive interface elements leads to unfeasible simulation times and memory requirements. For that purpose, several papers have been published that present alternative methods for modelling concepts which support laminate failure analyses requiring only one shell element through the thickness and where arbitrary delamination propagation is accounted for only in areas where it is needed, cf. Brouzoulis and Fagerström, Hosseini et al. and McElroy . The proposed new concepts however need to be further developed before they can be readily applied to solve engineering problems in which delamination cracks can initiate and propagate. For traditional finite element based shell models, such as the one presented by Brouzoulis and Fagerström (based on the eXtended Finite Element Method, XFEM), improved methods to predict the interlaminar stresses are needed for an accurate prediction of delamination initiation, since the transverse stresses predicted directly from the shell solution are of too low accuracy. This was recently done e.g. by Främby et al. who complemented an XFEM shell formulation with a stress recovery approach , performed over a patch of elements, thereby making the model fully adaptive. As for the alternative concept based on an isogeometric approach by Hosseini et al., there is a need to handle successive introduction of new discontinuities by means of Knot-Insertion in an automated fashion. A first step in this direction was taken by the authors in , outlining strategies for how to initiate and propagate delamination cracks using this framework. As a benefit over FE based C0 continuous shells, the necessary improvements of the interlaminar stresses for isogeometric shells can be performed element-wise since in-plane stresses are smooth over element boundaries. In this contribution we focus on the further development of the isogeometric solid-like shell element to allow for an automated Insertion of discontinuities. The formulation adopts NURBS (or T-spline) basis functions for the discretisation of the shell mid-surface, whereas a higher-order B-spline functions are used for the interpolation in the thickness direction. A discontinuity can be incorporated in this latter function by so-called Knot-Insertion to account for ply interfaces (weak discontinuities) and delaminations (strong discontinuities) . In order to automatically enhance the element, various stress-based criteria using element local improved interlaminar stresses are investigated. In this way, the isogeometric continuum element can be used in an even more efficient fashion, allowing for the detailed analysis of large, thin-walled composite structures
-
Strategies for modelling delamination growth using isogeometric continuum shell elements
2016Co-Authors: Remmers Joris, Fagerstr\uf6m MartinAbstract:The computational efficiency of CAE models and methods for analysing failure progression in compositesis important to enable their use in full scale models. In particular, efficient approximation andsolution methods for delamination modelling is crucial to meet today’s requirements on virtual developmentlead times. For that purpose, several papers have been published that present alternative methodsfor modelling concepts which support laminate failure analyses requiring only one shell element throughthe thickness and where arbitrary delamination propagation is accounted for only in areas where it isneeded. The proposed new concepts however need to be further developed before they can bereadily applied to solve engineering problems. As for the alternative concept based on an isogeometricapproach by Hosseini et al., there is a need to handle successive introduction of new discontinuitiesby means of Knot-Insertion in an automated fashion. To this end, better predictions of the throughthe-thickness distribution of out-of-plane stresses are needed. In this paper we focus on the furtherdevelopment of the isogeometric continuum shell element to allow for an automated Insertion of discontinuities
