## Plenary Lectures

Prof. Manfred Bischoff

**University of Stuttgart, Germany**

Hierarchic Formulations for Static and Dynamic Analysis of Shells

Manfred Bischoff, Bastian Oesterle, Rebecca Thierer, Tarun Kumar Mitruka Vinod Kumar Mitruka, Lisa-Marie Krauss and Ekkehard Ramm

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Sep 19, 2024
9:50-10:50
Kitakyushu International Conference Center, 1F
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Hierarchic shear-deformable shell formulations of Reissner-Mindlin type can be obtained through enrichment of the Kirchhoff-Love shell model. In the context of numerically solving the resulting sets of differential equations this requires C1-continuity of the underlying approximation spaces. However, the advantages of the hierarchic formulations in comparison to standard parametrizations in the context of computational methods are rather appealing, such that taking care of higher continuity may be a prize worth paying.

As the hierarchic concept naturally involves distinct degrees of freedom that are related to the shear deformation, the condition of vanishing transverse shear strain in the thin limit is very simple to fulfil. This means, that the corresponding discretizations are intrinsically free from transverse shear locking. This is true independent of the discretization scheme and has already been verified for isogeometric finite elements, for a meshless formulation with maximum entropy shape functions, as well as for collocation methods. The talk discusses some technical details and presents computational results.

Moreover, the hierarchic structure also provides substantial benefits in the context of dynamics. For explicit time integration, stability requires the time steps to be smaller than a critical time step size that depends on the highest natural frequency of the discretized model. Thus, for shear deformable shell formulations, efficiency is typically limited by the highest transverse shear frequencies, which are often of minor importance for the structural response. Conventional mass scaling methods to increase the critical time step negatively affect the accuracy in the entire frequency spectrum. Hierarchic formulations allow a selective mass scaling of transverse shear frequencies, while bending frequencies remain unaffected. This results in an efficient method that features high accuracy, allows for significantly increased time steps and preserves both linear and angular momentum. In contrast to some existing selective mass scaling methods it also preserves the diagonal structure of lumped mass matrices. Both frequency spectra and the transient behavior in explicit time integration are investigated to demonstrate the features of this intrinsically selective mass scaling concept.

Prof. Ferdinando Auricchio

**University of Pavia, Italy**

Additive Manufacturing: design, production, modeling, computations

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Sep 19, 2024
11:00-12:00
Kitakyushu International Conference Center, 1F
**

Additive Manufacturing (AM) – also known as 3D printing – is taking off in many industrial fields, allowing for new freedom in terms of complex shapes which can be manufactured, opening the door to a new set of design possibilities (but also requirements). On the other hand, AM is a complex physical process, involving thermo-mechanical phenomena at very different scales; accordingly, simulation is fundamental to predict temperature and stress distributions during and after the printing process.

After a short introduction to the technology and possible applications, the presentation will focus on Laser-based Powder Bed Fusion of Metals (PBF-LB/M). A widespread adoption of this technology in many industrial context is yet hindered due to the high stochasticity of the process; in fact, the complex process-structure-property relationships occurring in PBF-LB/M are today not yet fully understood. Therefore, suitable physical and numerical models need to be developed to shed light on these complex phenomena.

It is well known for example that the behavior of lattice structures is not well predicted when computed on the as-designed geometry. Furthermore, due to the inherent variability of PBF-LB/M process parameters, several sources of uncertainty hinder a full understanding of the complex process-structure-property relationships; hence, a control of the source of uncertainties is extremely desired in the modeling and design process.

In the presentation we will highlights some of the interesting applications open by the power of AM but also some limitations due the problems highlighted above.