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    <title language="eng">Systematic assessment of isogeometric sheet metal forming simulations based on trimmed, multi-patch NURBS models in LS-DYNA</title>
    <abstract language="eng">Isogeometric sheet metal forming simulation is a numerical simulation technique that is used to predict the behavior of sheet metal parts during the forming process [1] and tries to tighten the link with the Computer Aided Design (CAD) description. This technique uses the isogeometric analysis (IGA) approach, which combines the well-established framework of traditional finite element analysis (FEA) and the power of non-uniform rational B-splines (NURBS). In contrast to the approach in a “classical” FEA framework, IGA directly uses the ansatzspace of the CAD geometry for analysis, which opens the possibility to work directly on the exact geometry. Furthermore, the smoothness of the NURBS basis functions results in a more accurate simulation [2].&#13;
A powerful method to reduce the computational effort is adaptive mesh refinement, that has been developed and optimized for sheet metal forming applications over several years for standard Finite Elements. However, it remains an open question how an efficient local adaptive mesh refinement strategy can be implemented for complex industrial sheet metal forming simulations based on trimmed NURBS models, which are typically the description in Boundary Representation (B-Rep) CAD-models [3]. First investigations for explicit dynamics have been made in [4].&#13;
&#13;
In this contribution, a detailed comparison between FEA and IGA sheet metal forming applications is conducted. The state of the art for FEA and IGA will be contrasted and the need for an efficient adaptive mesh refinement strategy will be discussed. The goal of our research is to develop an efficient adaptive mesh refinement strategy for isogeometric sheet metal forming simulations in LS-DYNA. This will contribute to closing the efficiency gap between IGA and FEA in explicit dynamics, accelerate the product development process and enable the application of IGA in industrial sheet metal forming simulations.</abstract>
    <parentTitle language="eng">14th European LS-DYNA Conference, October 18 and 19, 2023, Baden-Baden, Germany</parentTitle>
    <identifier type="urn">urn:nbn:de:bvb:898-opus4-68228</identifier>
    <identifier type="doi">10.35096/othr/pub-6822</identifier>
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    <licence>Keine Lizenz - Es gilt das deutsche Urheberrecht: § 53 UrhG</licence>
    <author>Christoph Hollweck</author>
    <author>Lukas Leidinger</author>
    <author>Stefan Hartmann</author>
    <author>Liping Li</author>
    <author>Marcus Wagner</author>
    <author>Roland Wüchner</author>
    <collection role="institutes" number="FAKMB">Fakultät Maschinenbau</collection>
    <collection role="othforschungsschwerpunkt" number="16316">Produktion und Systeme</collection>
    <thesisPublisher>Ostbayerische Technische Hochschule Regensburg</thesisPublisher>
    <file>https://opus4.kobv.de/opus4-oth-regensburg/files/6822/LSDYNA_Conference_presentation.pdf</file>
    <file>https://opus4.kobv.de/opus4-oth-regensburg/files/6822/2023-LS-DYNA-template-paper_CH3.pdf</file>
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    <publishedYear>2026</publishedYear>
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    <pageNumber>36</pageNumber>
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    <volume>450</volume>
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    <publisherName>Elsevier</publisherName>
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    <title language="eng">An analysis of the critical time step size for explicit dynamics using trimmed B-splines, LR-splines, and THB-splines</title>
    <abstract language="eng">Isogeometric analysis (IGA) combined with explicit dynamics is increasingly used in academia and has already been successfully applied in industrial simulations, including crash and sheet-metal forming. Since explicit schemes are only conditionally stable, accurate estimation of the critical time step is essential for both stability and efficiency. Adaptive mesh refinement is widely used to balance accuracy and computational cost. In IGA, THB- and LR-splines break the tensor-product structure of standard B-splines and enable local refinement, but their effect on the critical time step under trimming has not been systematically studied - a key requirement for reliable time step estimation.&#13;
We investigate the critical time step in explicit dynamic simulations using trimmed B-splines, LR-splines, and THB-splines, based on a lumped mass matrix obtained by simple row summation. One-dimensional bar, two-dimensional membrane, and trimmed shell models are analyzed to determine how trimming and local refinement influence element and system eigenfrequencies, which directly control the stable time step. Refined boundary elements in open knot vectors are identified as the main bottleneck. Trimming these elements can increase the stable time step, though certain trimming configurations introduce new restrictions.&#13;
Results show that LR- and THB-splines impose time step constraints similar to B-splines, making them equally suitable for explicit simulations. We also present a general method for computing element-wise Bézier extraction operators for LR- and THB-splines, enabling straightforward integration into standard finite element solvers. The findings are validated through nonlinear sheet-metal forming simulations in LS-DYNA using shells discretized with trimmed B-, LR-, and THB-splines. This represents the first such application and demonstrates their practical feasibility for industrial use.</abstract>
    <parentTitle language="eng">Computer Methods in Applied Mechanics and Engineering</parentTitle>
    <identifier type="issn">0045-7825</identifier>
    <identifier type="doi">10.1016/j.cma.2025.118656</identifier>
    <note>Corresponding author der OTH Regensburg: Christoph Hollweck</note>
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