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Konferenzveröffentlichung
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The logarithmic finite element method
(International Center for Numerical Methods in Engineering (CIMNE), 2018)
The Logarithmic finite element (LogFE) method extends the Ritz-Galerkin method to approximations on a non-linear finite-dimensional manifold in the infinitedimensional solution space. Formulating the interpolant on the logarithmic space allows for a novel treatment of the rotational component of the deformation, and induces a strong coupling between rotations and translations. The Logarithmic finite element method provides
a transformation of the initial configuration that is not restricted to an isoparametric formulation.
Working paper
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Ansatzfunktionen auf dem logarithmischen Raum: die Log-FE-Methode [Abstract]
(2015-09)
Die Logarithmische Finite-Elemente-Methode (Log-FE-Methode) bietet einen neuartigen Ansatz zur Berechnung von FE-Modellen, insbesondere im Rahmen von Multigrid-Verfahren.
In Multigrid-Verfahren wird eine schnelle und robuste Konvergenz insbesondere durch die Entkopplung der Einflüsse der Freiheitsgrade auf den unterschiedlichen Längenskalen erreicht. Das Näherungsverfahren auf dem groben Netz sollte daher auf einer deutlich gröberen Skala arbeiten und (räumlich) hochfrequente Deformationsanteile vermeiden.
Buch
Statik und Einflussfunktionen - vom modernen Standpunkt aus
(2019-01-15)
In dem Buch werden die Grundlagen der klassischen Statik in einer modernen, zeitgemäßen Form dargestellt. Dabei wird auf Präzision und Prägnanz in der Darstellung Wert gelegt. Spezielles Gewicht wird auf Einflussfunktionen gelegt, da diese die Basis der finiten Elemente bilden. Das Rechnen mit finiten Elementen ist, wie in dem Buch gezeigt wird, ein Rechnen mit genäherten Einflussfunktionen. Der Text geht ausführlich auf die Fragen der Modellierung von Tragwerken mit finiten Elementen und der Genauigkeit der numerischen ...
Aufsatz
Introducing the Logarithmic finite element method: a geometrically exact planar Bernoulli beam element
(2016-09-15)
We propose a novel finite element formulation that significantly reduces the number of degrees of freedom necessary to obtain reasonably accurate approximations of the low-frequency component of the deformation in boundary-value problems. In contrast to the standard Ritz–Galerkin approach, the shape functions are defined on a Lie algebra—the logarithmic space—of the deformation function. We construct a deformation function based on an interpolation of transformations at the nodes of the finite element. In the case ...
Konferenzveröffentlichung
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Beyond Ritz-Galerkin: Finite element approximations on a manifold in the configuration space [Abstract]
(Institute of Structural Analysis and Antiseismic Research, School of Civil Engineering, National Technical University of Athens (NTUA), 2016)
An extension of the Ritz-Galerkin method, based on finding approximations on a finite-dimensional manifold of functions (i.e., not a linear subspace) in the infinite-dimensional exact configuration space, will be presented. This new approach is particularly efficient in computing geometrically exact solutions for problems involving large rotations.
Konferenzveröffentlichung
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Coupling atomistic models with continuous finite beam elements [Abstract]
(Institute of Structural Analysis and Antiseismic Research, School of Civil Engineering, National Technical University of Athens (NTUA), 2016)
Concurrent simulations of atomistic (discrete) and continuum models are one key to perform static calculations of large atomistic structures. Occurring ghost forces at the interfaces between discrete (atomistic) and continuous regions are a major challenge for the definition of such interfaces. The so called virtual projection method [1] is a class of force-based a/c schemes which reduce (or even avoid) ghost forces. This class of coupling schemes is able to deal with atomistic models consisting of bonded, multi-body ...
Aufsatz
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Coupled atomistic-continuum simulation of the mechanical properties of single-layered graphene sheets
(2019-11-18)
The purpose of this work is the multiscale modeling of a single-layered graphene sheet. The model is divided into three parts. One is an atomistic domain which is simulated with the atomic-scale finite element method (AFEM). Another is a continuum domain. In this domain, the mechanical properties are investigated by using a finite element based on a nonlocal continuum shell model with a high order strain gradient. To be exact, it is a 4-node 60-generalized degree of freedom (DOF) Mindlin–Reissner finite shell element ...
Konferenzveröffentlichung
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The logarithmic finite element method: Approximation on a manifold in the configuration space
(International Association for Computational IACM, 2018)
Aufsatz
Meshing highly regular structures: The case of super carbon nanotubes of arbitrary order
(2015)
Mesh generation is an important step inmany numerical methods.We present the “HierarchicalGraphMeshing” (HGM)method as a novel approach to mesh generation, based on algebraic graph theory.The HGM method can be used to systematically construct configurations exhibiting multiple hierarchies and complex symmetry characteristics. The hierarchical description of structures provided by the HGM method can be exploited to increase the efficiency of multiscale and multigrid methods. In this paper, the HGM method is employed ...