TY - JOUR A1 - Legatiuk, Dmitrii A1 - Weisz-Patrault, Daniel T1 - Coupling of Complex Function Theory and Finite Element Method for Crack Propagation Through Energetic Formulation: Conformal Mapping Approach and Reduction to a Riemann–Hilbert Problem JF - Computational Methods and Function Theory N2 - In this paper we present a theoretical background for a coupled analytical–numerical approach to model a crack propagation process in two-dimensional bounded domains. The goal of the coupled analytical–numerical approach is to obtain the correct solution behaviour near the crack tip by help of the analytical solution constructed by using tools of complex function theory and couple it continuously with the finite element solution in the region far from the singularity. In this way, crack propagation could be modelled without using remeshing. Possible directions of crack growth can be calculated through the minimization of the total energy composed of the potential energy and the dissipated energy based on the energy release rate. Within this setting, an analytical solution of a mixed boundary value problem based on complex analysis and conformal mapping techniques is presented in a circular region containing an arbitrary crack path. More precisely, the linear elastic problem is transformed into a Riemann–Hilbert problem in the unit disk for holomorphic functions. Utilising advantages of the analytical solution in the region near the crack tip, the total energy could be evaluated within short computation times for various crack kink angles and lengths leading to a potentially efficient way of computing the minimization procedure. To this end, the paper presents a general strategy of the new coupled approach for crack propagation modelling. Additionally, we also discuss obstacles in the way of practical realisation of this strategy. KW - Angewandte Mathematik KW - Finite-Elemente-Methode KW - Rissausbreitung KW - Modellierung KW - Bruchmechanik KW - fracture mechanics KW - crack propagation KW - coupling KW - energetic approach Y1 - 2021 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:gbv:wim2-20210805-44763 UR - https://link.springer.com/article/10.1007/s40315-021-00403-7 VL - 2021 SP - 1 EP - 23 PB - Springer CY - Heidelberg ER - TY - JOUR A1 - Kraus, Matthias A1 - Crişan, Nicolae-Andrei A1 - Wittor, Björn T1 - Stability Study of Cantilever-Beams – Numerical Analysis and Analytical Calculation (LTB) JF - ce/papers N2 - According to Eurocode, the computation of bending strength for steel cantilever beams is a straightforward process. The approach is based on an Ayrton-Perry formula adaptation of buckling curves for steel members in compression, which involves the computation of an elastic critical buckling load for considering the instability. NCCI documents offer a simplified formula to determine the critical bending moment for cantilevers beams with symmetric cross-section. Besides the NCCI recommendations, other approaches, e.g. research literature or Finite-Element-Analysis, may be employed to determine critical buckling loads. However, in certain cases they render different results. Present paper summarizes and compares the abovementioned analytical and numerical approaches for determining critical loads and it exemplarily analyses corresponding cantilever beam capacities using numerical approaches based on plastic zones theory (GMNIA). KW - Träger KW - Stahl KW - Biegefestigkeit KW - Finite-Elemente-Methode KW - Stahlträger KW - Knicklast KW - Freiträgerkapazität KW - Eurocode Y1 - 2021 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:gbv:wim2-20220112-45637 UR - https://onlinelibrary.wiley.com/doi/full/10.1002/cepa.1539 VL - 2021 IS - Volume 4, issue 2-4 SP - 2199 EP - 2206 PB - Ernst & Sohn, a Wiley brand CY - Berlin ER - TY - JOUR A1 - Ibanez, Stalin A1 - Kraus, Matthias T1 - A Numerical Approach for Plastic Cross Cross-Sectional Analyses of Steel Members JF - ce/papers N2 - Global structural analyses in civil engineering are usually performed considering linear-elastic material behavior. However, for steel structures, a certain degree of plasticization depending on the member classification may be considered. Corresponding plastic analyses taking material nonlinearities into account are effectively realized using numerical methods. Frequently applied finite elements of two and three-dimensional models evaluate the plasticity at defined nodes using a yield surface, i.e. by a yield condition, hardening rule, and flow rule. Corresponding calculations are connected to a large numerical as well as time-consuming effort and they do not rely on the theoretical background of beam theory, to which the regulations of standards mainly correspond. For that reason, methods using beam elements (one-dimensional) combined with cross-sectional analyses are commonly applied for steel members in terms of plastic zones theories. In these approaches, plasticization is in general assessed by means of axial stress only. In this paper, more precise numerical representation of the combined stress states, i.e. axial and shear stresses, is presented and results of the proposed approach are validated and discussed. KW - Stahlkonstruktion KW - Plastizität KW - Strukturanalyse KW - Stahlbauteil KW - Axialspannung KW - Finite-Elemente-Methode Y1 - 2021 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:gbv:wim2-20220112-45622 UR - https://onlinelibrary.wiley.com/doi/full/10.1002/cepa.1527 VL - 2021 IS - Volume 4, issue 2-4 SP - 2098 EP - 2106 PB - Ernst & Sohn, a Wiley brand CY - Berlin ER -