@article{ChauDinhZiLeeetal.,
  author    = {Chau-Dinh, T. and Zi, Goangseup and Lee, P.S. and Song, Jeong-Hoon and Rabczuk, Timon},
  title     = {Phantom-node method for shell models with arbitrary cracks},
  series = {Computers \& Structures},
  journal   = {Computers \& Structures},
  doi       = {10.1016/j.compstruc.2011.10.021},
  abstract  = {A phantom-node method is developed for three-node shell elements to describe cracks. This method can treat arbitrary cracks independently of the mesh. The crack may cut elements completely or partially. Elements are overlapped on the position of the crack, and they are partially integrated to implement the discontinuous displacement across the crack. To consider the element containing a crack tip, a new kinematical relation between the overlapped elements is developed. There is no enrichment function for the discontinuous displacement field. Several numerical examples are presented to illustrate the proposed method.},
  subject      = {Angewandte Mathematik},
  language  = {en}
}
@article{ShiraziMohebbiAzadiKakavandetal.,
  author    = {Shirazi, A. H. N. and Mohebbi, Farzad and Azadi Kakavand, M. R. and He, B. and Rabczuk, Timon},
  title     = {Paraffin Nanocomposites for Heat Management of Lithium-Ion Batteries: A Computational Investigation},
  series = {JOURNAL OF NANOMATERIALS},
  journal   = {JOURNAL OF NANOMATERIALS},
  doi       = {10.1155/2016/2131946},
  url       = {http://nbn-resolving.de/urn:nbn:de:gbv:wim2-20170411-31141},
  abstract  = {Lithium-ion (Li-ion) batteries are currently considered as vital components for advances in mobile technologies such as those in communications and transport. Nonetheless, Li-ion batteries suffer from temperature rises which sometimes lead to operational damages or may even cause fire. An appropriate solution to control the temperature changes during the operation of Li-ion batteries is to embed batteries inside a paraffin matrix to absorb and dissipate heat. In the present work, we aimed to investigate the possibility of making paraffin nanocomposites for better heat management of a Li-ion battery pack. To fulfill this aim, heat generation during a battery charging/discharging cycles was simulated using Newman's well established electrochemical pseudo-2D model. We couple this model to a 3D heat transfer model to predict the temperature evolution during the battery operation. In the later model, we considered different paraffin nanocomposites structures made by the addition of graphene, carbon nanotubes, and fullerene by assuming the same thermal conductivity for all fillers. This way, our results mainly correlate with the geometry of the fillers. Our results assess the degree of enhancement in heat dissipation of Li-ion batteries through the use of paraffin nanocomposites. Our results may be used as a guide for experimental set-ups to improve the heat management of Li-ion batteries.},
  subject      = {Batterie},
  language  = {en}
}
@article{TalebiSamaniegoSamaniegoetal.,
  author    = {Talebi, Hossein and Samaniego, C. and Samaniego, Esteban and Rabczuk, Timon},
  title     = {On the numerical stability and mass-lumping schemes for explicit enriched meshfree methods},
  series = {International Journal for Numerical Methods in Engineering},
  journal   = {International Journal for Numerical Methods in Engineering},
  doi       = {10.1002/nme.3275},
  pages     = {1009 -- 1027},
  abstract  = {Meshfree methods (MMs) such as the element free Galerkin (EFG)method have gained popularity because of some advantages over other numerical methods such as the finite element method (FEM). A group of problems that have attracted a great deal of attention from the EFG method community includes the treatment of large deformations and dealing with strong discontinuities such as cracks. One efficient solution to model cracks is adding special enrichment functions to the standard shape functions such as extended FEM, within the FEM context, and the cracking particles method, based on EFG method. It is well known that explicit time integration in dynamic applications is conditionally stable. Furthermore, in enriched methods, the critical time step may tend to very small values leading to computationally expensive simulations. In this work, we study the stability of enriched MMs and propose two mass-lumping strategies. Then we show that the critical time step for enriched MMs based on lumped mass matrices is of the same order as the critical time step of MMs without enrichment. Moreover, we show that, in contrast to extended FEM, even with a consistent mass matrix, the critical time step does not vanish even when the crack directly crosses a node.},
  subject      = {Angewandte Mathematik},
  language  = {en}
}
@article{ChakrabortyAnitescuZhuangetal.,
  author    = {Chakraborty, Ayan and Anitescu, Cosmin and Zhuang, Xiaoying and Rabczuk, Timon},
  title     = {Domain adaptation based transfer learning approach for solving PDEs on complex geometries},
  series = {Engineering with Computers},
  volume    = {2022},
  journal   = {Engineering with Computers},
  doi       = {10.1007/s00366-022-01661-2},
  url       = {http://nbn-resolving.de/urn:nbn:de:gbv:wim2-20220811-46776},
  pages     = {1 -- 20},
  abstract  = {In machine learning, if the training data is independently and identically distributed as the test data then a trained model can make an accurate predictions for new samples of data. Conventional machine learning has a strong dependence on massive amounts of training data which are domain specific to understand their latent patterns. In contrast, Domain adaptation and Transfer learning methods are sub-fields within machine learning that are concerned with solving the inescapable problem of insufficient training data by relaxing the domain dependence hypothesis. In this contribution, this issue has been addressed and by making a novel combination of both the methods we develop a computationally efficient and practical algorithm to solve boundary value problems based on nonlinear partial differential equations. We adopt a meshfree analysis framework to integrate the prevailing geometric modelling techniques based on NURBS and present an enhanced deep collocation approach that also plays an important role in the accuracy of solutions. We start with a brief introduction on how these methods expand upon this framework. We observe an excellent agreement between these methods and have shown that how fine-tuning a pre-trained network to a specialized domain may lead to an outstanding performance compare to the existing ones. As proof of concept, we illustrate the performance of our proposed model on several benchmark problems.},
  subject      = {Maschinelles Lernen},
  language  = {en}
}
@article{IlyaniAkmarKramerRabczuk,
  author    = {Ilyani Akmar, A.B. and Kramer, O. and Rabczuk, Timon},
  title     = {Multi-objective evolutionary optimization of sandwich structures: An evaluation by elitist non-dominated sorting evolution strategy},
  series = {American Journal of Engineering and Applied Sciences},
  journal   = {American Journal of Engineering and Applied Sciences},
  doi       = {10.3844/ajeassp.2015.185.201},
  url       = {http://nbn-resolving.de/urn:nbn:de:gbv:wim2-20170418-31402},
  pages     = {185 -- 201},
  abstract  = {In this study, an application of evolutionary multi-objective optimization algorithms on the optimization of sandwich structures is presented. The solution strategy is known as Elitist Non-Dominated Sorting Evolution Strategy (ENSES) wherein Evolution Strategies (ES) as Evolutionary Algorithm (EA) in the elitist Non-dominated Sorting Genetic algorithm (NSGA-II) procedure. Evolutionary algorithm seems a compatible approach to resolve multi-objective optimization problems because it is inspired by natural evolution, which closely linked to Artificial Intelligence (AI) techniques and elitism has shown an important factor for improving evolutionary multi-objective search. In order to evaluate the notion of performance by ENSES, the well-known study case of sandwich structures are reconsidered. For Case 1, the goals of the multi-objective optimization are minimization of the deflection and the weight of the sandwich structures. The length, the core and skin thicknesses are the design variables of Case 1. For Case 2, the objective functions are the fabrication cost, the beam weight and the end deflection of the sandwich structures. There are four design variables i.e., the weld height, the weld length, the beam depth and the beam width in Case 2. Numerical results are presented in terms of Paretooptimal solutions for both evaluated cases.},
  subject      = {Optimierung},
  language  = {en}
}
@article{ZhangHaoWangetal.,
  author    = {Zhang, Chao and Hao, Xiao-Li and Wang, Cuixia and Wei, Ning and Rabczuk, Timon},
  title     = {Thermal conductivity of graphene nanoribbons under shear deformation: A molecular dynamics simulation},
  series = {Scientific Reports},
  journal   = {Scientific Reports},
  doi       = {10.1038/srep41398},
  url       = {http://nbn-resolving.de/urn:nbn:de:gbv:wim2-20170428-31718},
  abstract  = {Tensile strain and compress strain can greatly affect the thermal conductivity of graphene nanoribbons (GNRs). However, the effect of GNRs under shear strain, which is also one of the main strain effect, has not been studied systematically yet. In this work, we employ reverse nonequilibrium molecular dynamics (RNEMD) to the systematical study of the thermal conductivity of GNRs (with model size of 4 nm × 15 nm) under the shear strain. Our studies show that the thermal conductivity of GNRs is not sensitive to the shear strain, and the thermal conductivity decreases only 12-16\% before the pristine structure is broken. Furthermore, the phonon frequency and the change of the micro-structure of GNRs, such as band angel and bond length, are analyzed to explore the tendency of thermal conductivity. The results show that the main influence of shear strain is on the in-plane phonon density of states (PDOS), whose G band (higher frequency peaks) moved to the low frequency, thus the thermal conductivity is decreased. The unique thermal properties of GNRs under shear strains suggest their great potentials for graphene nanodevices and great potentials in the thermal managements and thermoelectric applications.},
  subject      = {W{\"a}rmeleitf{\"a}higkeit},
  language  = {en}
}
@inproceedings{NguyenThanhRabczuk,
  author    = {Nguyen-Thanh, Nhon and Rabczuk, Timon},
  title     = {A SMOOTHED FINITE ELEMENT METHOD FOR THE STATIC AND FREE VIBRATION ANALYSIS OF SHELLS},
  editor    = {G{\"u}rlebeck, Klaus and K{\"o}nke, Carsten},
  organization    = {Bauhaus-Universit{\"a}t Weimar},
  issn      = {1611-4086},
  doi       = {10.25643/bauhaus-universitaet.2877},
  url       = {http://nbn-resolving.de/urn:nbn:de:gbv:wim2-20170314-28777},
  pages     = {24},
  abstract  = {A four-node quadrilateral shell element with smoothed membrane-bending based on Mindlin-Reissner theory is proposed. The element is a combination of a plate bending and membrane element. It is based on mixed interpolation where the bending and membrane stiffness matrices are calculated on the boundaries of the smoothing cells while the shear terms are approximated by independent interpolation functions in natural coordinates. The proposed element is robust, computationally inexpensive and free of locking. Since the integration is done on the element boundaries for the bending and membrane terms, the element is more accurate than the MITC4 element for distorted meshes. This will be demonstrated for several numerical examples.},
  subject      = {Angewandte Informatik},
  language  = {en}
}