@article{KrausCrişanWittor, author = {Kraus, Matthias and Cri{\c{s}}an, Nicolae-Andrei and Wittor, Bj{\"o}rn}, title = {Stability Study of Cantilever-Beams - Numerical Analysis and Analytical Calculation (LTB)}, series = {ce/papers}, volume = {2021}, journal = {ce/papers}, number = {Volume 4, issue 2-4}, publisher = {Ernst \& Sohn, a Wiley brand}, address = {Berlin}, doi = {10.1002/cepa.1539}, url = {http://nbn-resolving.de/urn:nbn:de:gbv:wim2-20220112-45637}, pages = {2199 -- 2206}, abstract = {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).}, subject = {Tr{\"a}ger}, language = {en} } @article{IbanezKraus, author = {Ibanez, Stalin and Kraus, Matthias}, title = {A Numerical Approach for Plastic Cross Cross-Sectional Analyses of Steel Members}, series = {ce/papers}, volume = {2021}, journal = {ce/papers}, number = {Volume 4, issue 2-4}, publisher = {Ernst \& Sohn, a Wiley brand}, address = {Berlin}, doi = {10.1002/cepa.1527}, url = {http://nbn-resolving.de/urn:nbn:de:gbv:wim2-20220112-45622}, pages = {2098 -- 2106}, abstract = {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.}, subject = {Stahlkonstruktion}, language = {en} } @article{LegatiukWeiszPatrault, author = {Legatiuk, Dmitrii and Weisz-Patrault, Daniel}, title = {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}, series = {Computational Methods and Function Theory}, volume = {2021}, journal = {Computational Methods and Function Theory}, publisher = {Springer}, address = {Heidelberg}, doi = {10.1007/s40315-021-00403-7}, url = {http://nbn-resolving.de/urn:nbn:de:gbv:wim2-20210805-44763}, pages = {1 -- 23}, abstract = {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.}, subject = {Angewandte Mathematik}, language = {en} } @article{ReichertOlneyLahmer, author = {Reichert, Ina and Olney, Peter and Lahmer, Tom}, title = {Combined approach for optimal sensor placement and experimental verification in the context of tower-like structures}, series = {Journal of Civil Structural Health Monitoring}, volume = {2021}, journal = {Journal of Civil Structural Health Monitoring}, number = {volume 11}, publisher = {Heidelberg}, address = {Springer}, doi = {10.1007/s13349-020-00448-7}, url = {http://nbn-resolving.de/urn:nbn:de:gbv:wim2-20210804-44701}, pages = {223 -- 234}, abstract = {When it comes to monitoring of huge structures, main issues are limited time, high costs and how to deal with the big amount of data. In order to reduce and manage them, respectively, methods from the field of optimal design of experiments are useful and supportive. Having optimal experimental designs at hand before conducting any measurements is leading to a highly informative measurement concept, where the sensor positions are optimized according to minimal errors in the structures' models. For the reduction of computational time a combined approach using Fisher Information Matrix and mean-squared error in a two-step procedure is proposed under the consideration of different error types. The error descriptions contain random/aleatoric and systematic/epistemic portions. Applying this combined approach on a finite element model using artificial acceleration time measurement data with artificially added errors leads to the optimized sensor positions. These findings are compared to results from laboratory experiments on the modeled structure, which is a tower-like structure represented by a hollow pipe as the cantilever beam. Conclusively, the combined approach is leading to a sound experimental design that leads to a good estimate of the structure's behavior and model parameters without the need of preliminary measurements for model updating.}, subject = {Strukturmechanik}, language = {en} } @article{Lahmer, author = {Lahmer, Tom}, title = {FEM-Based determination of real and complex elastic, dielectric, and piezoelectric moduli in piezoceramic materials}, series = {IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control}, journal = {IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control}, doi = {10.25643/bauhaus-universitaet.3608}, url = {http://nbn-resolving.de/urn:nbn:de:gbv:wim2-20171030-36083}, abstract = {We propose an enhanced iterative scheme for the precise reconstruction of piezoelectric material parameters from electric impedance and mechanical displacement measurements. It is based on finite-element simulations of the full three-dimensional piezoelectric equations, combined with an inexact Newton or nonlinear Landweber iterative inversion scheme. We apply our method to two piezoelectric materials and test its performance. For the first material, the manufacturer provides a full data set; for the second one, no material data set is available. For both cases, our inverse scheme, using electric impedance measurements as input data, performs well.}, subject = {Finite-Elemente-Methode}, language = {en} } @article{VuBacNguyenXuanChenetal., author = {Vu-Bac, N. and Nguyen-Xuan, Hung and Chen, Lei and Lee, C.K. and Zi, Goangseup and Zhuang, Xiaoying and Liu, G.R. and Rabczuk, Timon}, title = {A phantom-node method with edge-based strain smoothing for linear elastic fracture mechanics}, series = {Journal of Applied Mathematics}, journal = {Journal of Applied Mathematics}, doi = {10.1155/2013/978026}, url = {http://nbn-resolving.de/urn:nbn:de:gbv:wim2-20170426-31676}, abstract = {This paper presents a novel numerical procedure based on the combination of an edge-based smoothed finite element (ES-FEM) with a phantom-node method for 2D linear elastic fracture mechanics. In the standard phantom-node method, the cracks are formulated by adding phantom nodes, and the cracked element is replaced by two new superimposed elements. This approach is quite simple to implement into existing explicit finite element programs. The shape functions associated with discontinuous elements are similar to those of the standard finite elements, which leads to certain simplification with implementing in the existing codes. The phantom-node method allows modeling discontinuities at an arbitrary location in the mesh. The ES-FEM model owns a close-to-exact stiffness that is much softer than lower-order finite element methods (FEM). Taking advantage of both the ES-FEM and the phantom-node method, we introduce an edge-based strain smoothing technique for the phantom-node method. Numerical results show that the proposed method achieves high accuracy compared with the extended finite element method (XFEM) and other reference solutions.}, subject = {Finite-Elemente-Methode}, language = {en} } @article{TalebiZiSilanietal., author = {Talebi, Hossein and Zi, Goangseup and Silani, Mohammad and Samaniego, Esteban and Rabczuk, Timon}, title = {A simple circular cell method for multilevel finite element analysis}, series = {Journal of Applied Mathematics}, journal = {Journal of Applied Mathematics}, doi = {10.1155/2012/526846}, url = {http://nbn-resolving.de/urn:nbn:de:gbv:wim2-20170426-31639}, abstract = {A simple multiscale analysis framework for heterogeneous solids based on a computational homogenization technique is presented. The macroscopic strain is linked kinematically to the boundary displacement of a circular or spherical representative volume which contains the microscopic information of the material. The macroscopic stress is obtained from the energy principle between the macroscopic scale and the microscopic scale. This new method is applied to several standard examples to show its accuracy and consistency of the method proposed.}, subject = {Finite-Elemente-Methode}, language = {en} } @article{MortazaviPereiraJiangetal., author = {Mortazavi, Bohayra and Pereira, Luiz Felipe C. and Jiang, Jin-Wu and Rabczuk, Timon}, title = {Modelling heat conduction in polycrystalline hexagonal boron-nitride films}, series = {Scientific Reports}, journal = {Scientific Reports}, doi = {10.1038/srep13228}, url = {http://nbn-resolving.de/urn:nbn:de:gbv:wim2-20170425-31534}, abstract = {We conducted extensive molecular dynamics simulations to investigate the thermal conductivity of polycrystalline hexagonal boron-nitride (h-BN) films. To this aim, we constructed large atomistic models of polycrystalline h-BN sheets with random and uniform grain configuration. By performing equilibrium molecular dynamics (EMD) simulations, we investigated the influence of the average grain size on the thermal conductivity of polycrystalline h-BN films at various temperatures. Using the EMD results, we constructed finite element models of polycrystalline h-BN sheets to probe the thermal conductivity of samples with larger grain sizes. Our multiscale investigations not only provide a general viewpoint regarding the heat conduction in h-BN films but also propose that polycrystalline h-BN sheets present high thermal conductivity comparable to monocrystalline sheets.}, subject = {W{\"a}rmeleitf{\"a}higkeit}, language = {en} } @article{BanihaniRabczukAlmomani, author = {Banihani, Suleiman and Rabczuk, Timon and Almomani, Thakir}, title = {POD for real-time simulation of hyperelastic soft biological tissue using the point collocation method of finite spheres}, series = {Mathematical Problems in Engineering}, journal = {Mathematical Problems in Engineering}, doi = {10.1155/2013/386501}, url = {http://nbn-resolving.de/urn:nbn:de:gbv:wim2-20170413-31203}, abstract = {The point collocation method of finite spheres (PCMFS) is used to model the hyperelastic response of soft biological tissue in real time within the framework of virtual surgery simulation. The proper orthogonal decomposition (POD) model order reduction (MOR) technique was used to achieve reduced-order model of the problem, minimizing computational cost. The PCMFS is a physics-based meshfree numerical technique for real-time simulation of surgical procedures where the approximation functions are applied directly on the strong form of the boundary value problem without the need for integration, increasing computational efficiency. Since computational speed has a significant role in simulation of surgical procedures, the proposed technique was able to model realistic nonlinear behavior of organs in real time. Numerical results are shown to demonstrate the effectiveness of the new methodology through a comparison between full and reduced analyses for several nonlinear problems. It is shown that the proposed technique was able to achieve good agreement with the full model; moreover, the computational and data storage costs were significantly reduced.}, subject = {Chirurgie}, language = {en} } @article{AtaollahiOshkourTalebiSeyedShirazietal., author = {Ataollahi Oshkour, Azim and Talebi, Hossein and Seyed Shirazi, Seyed Farid and Bayat, Mehdi and Yau, Yat Huang and Tarlochan, Faris and Abu Osman, Noor Azuan}, title = {Comparison of various functionally graded femoral prostheses by finite element analysis}, series = {Scientific World Journal}, journal = {Scientific World Journal}, doi = {10.1155/2014/807621}, url = {http://nbn-resolving.de/urn:nbn:de:gbv:wim2-20170413-31194}, abstract = {This study is focused on finite element analysis of a model comprising femur into which a femoral component of a total hip replacement was implanted. The considered prosthesis is fabricated from a functionally graded material (FGM) comprising a layer of a titanium alloy bonded to a layer of hydroxyapatite. The elastic modulus of the FGM was adjusted in the radial, longitudinal, and longitudinal-radial directions by altering the volume fraction gradient exponent. Four cases were studied, involving two different methods of anchoring the prosthesis to the spongy bone and two cases of applied loading. The results revealed that the FG prostheses provoked more SED to the bone. The FG prostheses carried less stress, while more stress was induced to the bone and cement. Meanwhile, less shear interface stress was stimulated to the prosthesis-bone interface in the noncemented FG prostheses. The cement-bone interface carried more stress compared to the prosthesis-cement interface. Stair climbing induced more harmful effects to the implanted femur components compared to the normal walking by causing more stress. Therefore, stress shielding, developed stresses, and interface stresses in the THR components could be adjusted through the controlling stiffness of the FG prosthesis by managing volume fraction gradient exponent.}, subject = {Finite-Elemente-Methode}, language = {en} }