@article{Zhang,
  author    = {Zhang, Yongzheng},
  title     = {Nonlocal dynamic Kirchhoff plate formulation based on nonlocal operator method},
  series = {Engineering with Computers},
  volume    = {2022},
  journal   = {Engineering with Computers},
  publisher = {Springer},
  address   = {London},
  doi       = {10.1007/s00366-021-01587-1},
  url       = {http://nbn-resolving.de/urn:nbn:de:gbv:wim2-20220209-45849},
  pages     = {1 -- 35},
  abstract  = {In this study, we propose a nonlocal operator method (NOM) for the dynamic analysis of (thin) Kirchhoff plates. The nonlocal Hessian operator is derived based on a second-order Taylor series expansion. The NOM does not require any shape functions and associated derivatives as 'classical' approaches such as FEM, drastically facilitating the implementation. Furthermore, NOM is higher order continuous, which is exploited for thin plate analysis that requires C1 continuity. The nonlocal dynamic governing formulation and operator energy functional for Kirchhoff plates are derived from a variational principle. The Verlet-velocity algorithm is used for the time discretization. After confirming the accuracy of the nonlocal Hessian operator, several numerical examples are simulated by the nonlocal dynamic Kirchhoff plate formulation.},
  subject      = {Angewandte Mathematik},
  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{GuerlebeckLegatiukNilssonetal.,
  author    = {G{\"u}rlebeck, Klaus and Legatiuk, Dmitrii and Nilsson, Henrik and Smarsly, Kay},
  title     = {Conceptual modelling: Towards detecting modelling errors in engineering applications},
  series = {Mathematical Methods in Applied Sciences},
  journal   = {Mathematical Methods in Applied Sciences},
  doi       = {10.1002/mma.5934},
  url       = {http://nbn-resolving.de/urn:nbn:de:gbv:wim2-20200110-40614},
  pages     = {1 -- 10},
  abstract  = {Rapid advancements of modern technologies put high demands on mathematical modelling of engineering systems. Typically, systems are no longer "simple" objects, but rather coupled systems involving multiphysics phenomena, the modelling of which involves coupling of models that describe different phenomena. After constructing a mathematical model, it is essential to analyse the correctness of the coupled models and to detect modelling errors compromising the final modelling result. Broadly, there are two classes of modelling errors: (a) errors related to abstract modelling, eg, conceptual errors concerning the coherence of a model as a whole and (b) errors related to concrete modelling or instance modelling, eg, questions of approximation quality and implementation. Instance modelling errors, on the one hand, are relatively well understood. Abstract modelling errors, on the other, are not appropriately addressed by modern modelling methodologies. The aim of this paper is to initiate a discussion on abstract approaches and their usability for mathematical modelling of engineering systems with the goal of making it possible to catch conceptual modelling errors early and automatically by computer assistant tools. To that end, we argue that it is necessary to identify and employ suitable mathematical abstractions to capture an accurate conceptual description of the process of modelling engineering systems.},
  subject      = {Angewandte Mathematik},
  language  = {en}
}
@article{ZhangNanthakumarLahmeretal.,
  author    = {Zhang, Chao and Nanthakumar, S.S. and Lahmer, Tom and Rabczuk, Timon},
  title     = {Multiple cracks identification for piezoelectric structures},
  series = {International Journal of Fracture},
  journal   = {International Journal of Fracture},
  pages     = {1 -- 19},
  abstract  = {Multiple cracks identification for piezoelectric structures},
  subject      = {Angewandte Mathematik},
  language  = {en}
}
@article{NguyenTuanKoenkeBettziecheetal.,
  author    = {Nguyen-Tuan, Long and K{\"o}nke, Carsten and Bettzieche, Volker and Lahmer, Tom},
  title     = {Numerical modeling and validation for 3D coupled-nonlinear thermo-hydro-mechanical problems in masonry dams},
  series = {Computers \& Structures},
  journal   = {Computers \& Structures},
  pages     = {143 -- 154},
  abstract  = {Numerical modeling and validation for 3D coupled-nonlinear thermo-hydro-mechanical problems in masonry dams},
  subject      = {Angewandte Mathematik},
  language  = {en}
}
@article{AchenbachLahmerMorgenthal,
  author    = {Achenbach, Marcus and Lahmer, Tom and Morgenthal, Guido},
  title     = {Global Sensitivity Analysis of Reinforced Concrete Walls Subjected to Standard Fire - A Comparison of Methods},
  series = {14th International Probabilistic Workshop},
  journal   = {14th International Probabilistic Workshop},
  pages     = {97 -- 106},
  abstract  = {Global Sensitivity Analysis of Reinforced Concrete Walls Subjected to Standard Fire—A Comparison of Methods},
  subject      = {Angewandte Mathematik},
  language  = {en}
}
@article{GoebelLahmerOsburg,
  author    = {G{\"o}bel, Luise and Lahmer, Tom and Osburg, Andrea},
  title     = {Uncertainty analysis in multiscale modeling of concrete based on continuum micromechanics},
  series = {European Journal of Mechanics-A/Solids},
  journal   = {European Journal of Mechanics-A/Solids},
  abstract  = {Uncertainty analysis in multiscale modeling of concrete based on continuum micromechanics},
  subject      = {Angewandte Mathematik},
  language  = {en}
}
@article{AlaladeNguyenTuanWuttkeetal.,
  author    = {Alalade, Muyiwa and Nguyen-Tuan, Long and Wuttke, Frank and Lahmer, Tom},
  title     = {Damage identification in gravity dams using dynamic coupled hydro-mechanical XFEM},
  series = {International Journal of Mechanics and Materials in Design},
  journal   = {International Journal of Mechanics and Materials in Design},
  doi       = {10.25643/bauhaus-universitaet.3596},
  pages     = {1 -- 19},
  abstract  = {Damage identification in gravity dams using dynamic coupled hydro-mechanical XFEM.},
  subject      = {Angewandte Mathematik},
  language  = {en}
}
@article{ZhangWangLahmeretal.,
  author    = {Zhang, Chao and Wang, Cuixia and Lahmer, Tom and He, Pengfei and Rabczuk, Timon},
  title     = {A dynamic XFEM formulation for crack identification},
  series = {International Journal of Mechanics and Materials in Design},
  journal   = {International Journal of Mechanics and Materials in Design},
  pages     = {427 -- 448},
  abstract  = {A dynamic XFEM formulation for crack identification},
  subject      = {Angewandte Mathematik},
  language  = {en}
}
@article{NguyenTuanLahmerDatchevaetal.,
  author    = {Nguyen-Tuan, Long and Lahmer, Tom and Datcheva, Maria and Stoimenova, Eugenia and Schanz, Tom},
  title     = {A novel parameter identification approach for buffer elements involving complex coupled thermo-hydro-mechanical analyses},
  series = {Computers and Geotechnics},
  journal   = {Computers and Geotechnics},
  pages     = {23 -- 32},
  abstract  = {A novel parameter identification approach for buffer elements involving complex coupled thermo-hydro-mechanical analyses},
  subject      = {Angewandte Mathematik},
  language  = {en}
}
@article{VuBacLahmerZhuangetal.,
  author    = {Vu-Bac, N. and Lahmer, Tom and Zhuang, Xiaoying and Nguyen-Thoi, T. and Rabczuk, Timon},
  title     = {A software framework for probabilistic sensitivity analysis for computationally expensive models},
  series = {Advances in Engineering Software},
  journal   = {Advances in Engineering Software},
  pages     = {19 -- 31},
  abstract  = {A software framework for probabilistic sensitivity analysis for computationally expensive models},
  subject      = {Angewandte Mathematik},
  language  = {en}
}
@article{NanthakumarLahmerZhuangetal.,
  author    = {Nanthakumar, S.S. and Lahmer, Tom and Zhuang, Xiaoying and Park, Harold S. and Rabczuk, Timon},
  title     = {Topology optimization of piezoelectric nanostructures},
  series = {Journal of the Mechanics and Physics of Solids},
  journal   = {Journal of the Mechanics and Physics of Solids},
  pages     = {316 -- 335},
  abstract  = {Topology optimization of piezoelectric nanostructures},
  subject      = {Angewandte Mathematik},
  language  = {en}
}
@article{GhorashiLahmerBagherzadehetal.,
  author    = {Ghorashi, Seyed Shahram and Lahmer, Tom and Bagherzadeh, Amir Saboor and Zi, Goangseup and Rabczuk, Timon},
  title     = {A stochastic computational method based on goal-oriented error estimation for heterogeneous geological materials},
  series = {Engineering Geology},
  journal   = {Engineering Geology},
  abstract  = {A stochastic computational method based on goal-oriented error estimation for heterogeneous geological materials},
  subject      = {Angewandte Mathematik},
  language  = {en}
}
@article{NanthakumarLahmerZhuangetal.,
  author    = {Nanthakumar, S.S. and Lahmer, Tom and Zhuang, Xiaoying and Zi, Goangseup and Rabczuk, Timon},
  title     = {Detection of material interfaces using a regularized level set method in piezoelectric structures},
  series = {Inverse Problems in Science and Engineering},
  journal   = {Inverse Problems in Science and Engineering},
  pages     = {153 -- 176},
  abstract  = {Detection of material interfaces using a regularized level set method in piezoelectric structures},
  subject      = {Angewandte Mathematik},
  language  = {en}
}
@article{LahmerBockHildebrandetal.,
  author    = {Lahmer, Tom and Bock, Sebastian and Hildebrand, J{\"o}rg and G{\"u}rlebeck, Klaus},
  title     = {Non-destructive identification of residual stresses in steel under thermal loadings},
  series = {Inverse Problems in Science and Engineering},
  journal   = {Inverse Problems in Science and Engineering},
  pages     = {1 -- 17},
  abstract  = {Non-destructive identification of residual stresses in steel under thermal loadings},
  subject      = {Angewandte Mathematik},
  language  = {en}
}
@article{NguyenTuanLahmerDatchevaetal.,
  author    = {Nguyen-Tuan, Long and Lahmer, Tom and Datcheva, Maria and Schanz, Tom},
  title     = {Global and local sensitivity analyses for coupled thermo-hydro-mechanical problems},
  series = {International Journal for Numerical and Analytical Methods in Geomechanics},
  journal   = {International Journal for Numerical and Analytical Methods in Geomechanics},
  abstract  = {Global and local sensitivity analyses for coupled thermo-hydro-mechanical problems},
  subject      = {Angewandte Mathematik},
  language  = {en}
}
@article{MarzbanLahmer,
  author    = {Marzban, Samira and Lahmer, Tom},
  title     = {Conceptual implementation of the variance-based sensitivity analysis for the calculation of the first-order effects},
  series = {Journal of Statistical Theory and Practice},
  journal   = {Journal of Statistical Theory and Practice},
  pages     = {589 -- 611},
  abstract  = {Conceptual implementation of the variance-based sensitivity analysis for the calculation of the first-order effects},
  subject      = {Angewandte Mathematik},
  language  = {en}
}
@article{NanthakumarLahmerRabczuk,
  author    = {Nanthakumar, S.S. and Lahmer, Tom and Rabczuk, Timon},
  title     = {Detection of multiple flaws in piezoelectric structures using XFEM and level sets},
  series = {International Journal for Numerical Methods in Engineering},
  journal   = {International Journal for Numerical Methods in Engineering},
  pages     = {960},
  abstract  = {Detection of multiple flaws in piezoelectric structures using XFEM and level sets},
  subject      = {Angewandte Mathematik},
  language  = {en}
}
@article{LahmerNguyenTuanKoenkeetal.,
  author    = {Lahmer, Tom and Nguyen-Tuan, Long and K{\"o}nke, Carsten and Bettzieche, Volker},
  title     = {Thermo-hydro-mechanische 3-D-Simulation von Staumauern-Modellierung und Validierung},
  series = {WASSERWIRTSCHAFT},
  journal   = {WASSERWIRTSCHAFT},
  pages     = {27 -- 30},
  abstract  = {Thermo-hydro-mechanische 3-D-Simulation von Staumauern-Modellierung und Validierung},
  subject      = {Angewandte Mathematik},
  language  = {de}
}
@inproceedings{IgnatovaKirschkeTauscheretal.,
  author    = {Ignatova, Elena and Kirschke, Heiko and Tauscher, Eike and Smarsly, Kay},
  title     = {PARAMETRIC GEOMETRIC MODELING IN CONSTRUCTION PLANNING USING INDUSTRY FOUNDATION CLASSES},
  series = {Digital Proceedings, International Conference on the Applications of Computer Science and Mathematics in Architecture and Civil Engineering : July 20 - 22 2015, Bauhaus-University Weimar},
  booktitle = {Digital Proceedings, International Conference on the Applications of Computer Science and Mathematics in Architecture and Civil Engineering : July 20 - 22 2015, Bauhaus-University Weimar},
  editor    = {G{\"u}rlebeck, Klaus and Lahmer, Tom},
  organization    = {Bauhaus-Universit{\"a}t Weimar},
  issn      = {1611-4086},
  doi       = {10.25643/bauhaus-universitaet.2802},
  url       = {http://nbn-resolving.de/urn:nbn:de:gbv:wim2-20170314-28024},
  pages     = {8},
  abstract  = {One of the most promising and recent advances in computer-based planning is the transition from classical geometric modeling to building information modeling (BIM). Building information models support the representation, storage, and exchange of various information relevant to construction planning. This information can be used for describing, e.g., geometric/physical properties or costs of a building, for creating construction schedules, or for representing other characteristics of construction projects. Based on this information, plans and specifications as well as reports and presentations of a planned building can be created automatically. A fundamental principle of BIM is object parameterization, which allows specifying geometrical, numerical, algebraic and associative dependencies between objects contained in a building information model. In this paper, existing challenges of parametric modeling using the Industry Foundation Classes (IFC) as a federated model for integrated planning are shown, and open research questions are discussed.},
  subject      = {Angewandte Informatik},
  language  = {en}
}