TY - JOUR A1 - Zhang, Yongzheng T1 - Nonlocal dynamic Kirchhoff plate formulation based on nonlocal operator method JF - Engineering with Computers N2 - 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. KW - Angewandte Mathematik KW - nonlocal operator method KW - nonlocal Hessian operator KW - operator energy functional KW - dual-support KW - variational principle Y1 - 2022 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:gbv:wim2-20220209-45849 UR - https://link.springer.com/article/10.1007/s00366-021-01587-1 VL - 2022 SP - 1 EP - 35 PB - Springer CY - London ER - 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 - Gürlebeck, Klaus A1 - Legatiuk, Dmitrii A1 - Nilsson, Henrik A1 - Smarsly, Kay T1 - Conceptual modelling: Towards detecting modelling errors in engineering applications JF - Mathematical Methods in Applied Sciences N2 - 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. KW - Angewandte Mathematik KW - Angewandte Informatik KW - Ingenieurwissenschaften KW - Modellierung KW - engineering KW - abstraction KW - modelling KW - formal approaches KW - type theory Y1 - 2019 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:gbv:wim2-20200110-40614 UR - https://onlinelibrary.wiley.com/doi/abs/10.1002/mma.5934 SP - 1 EP - 10 ER - TY - JOUR A1 - Alalade, Muyiwa A1 - Nguyen-Tuan, Long A1 - Wuttke, Frank A1 - Lahmer, Tom T1 - Damage identification in gravity dams using dynamic coupled hydro-mechanical XFEM JF - International Journal of Mechanics and Materials in Design N2 - Damage identification in gravity dams using dynamic coupled hydro-mechanical XFEM. KW - Angewandte Mathematik KW - Stochastik KW - Strukturmechanik Y1 - 2017 U6 - http://dx.doi.org/10.25643/bauhaus-universitaet.3596 SP - 1 EP - 19 ER - TY - JOUR A1 - Kaltenbacher, Barbara A1 - Lahmer, Tom A1 - Mohr, Marcus A1 - Kaltenbacher, Manfred T1 - PDE based determination of piezoelectric material tensors JF - European Journal of Applied Mathematics N2 - PDE based determination of piezoelectric material tensors. KW - Angewandte Mathematik KW - Stochastik KW - Strukturmechanik Y1 - 2006 U6 - http://dx.doi.org/10.25643/bauhaus-universitaet.3595 SP - 383 EP - 416 ER - TY - JOUR A1 - Lahmer, Tom A1 - Kaltenbacher, Manfred A1 - Kaltenbacher, Barbara A1 - Lerch, Reinhard A1 - Leder, Erich T1 - Fem-based determination of real and complex elastic, dielectric, and piezoelectric moduli in piezoceramic materials JF - IEEE transactions on ultrasonics, ferroelectrics, and frequency control N2 - Fem-based determination of real and complex elastic, dielectric, and piezoelectric moduli in piezoceramic materials. KW - Angewandte Mathematik KW - Stochastik KW - Strukturmechanik Y1 - 2008 U6 - http://dx.doi.org/10.25643/bauhaus-universitaet.3594 ER - TY - JOUR A1 - Lahmer, Tom A1 - Kaltenbacher, Barbara A1 - Schulz, V. T1 - Optimal measurement selection for piezoelectric material tensor identification JF - Inverse Problems in Science and Engineering N2 - Optimal measurement selection for piezoelectric material tensor identification. KW - Angewandte Mathematik KW - Stochastik KW - Strukturmechanik Y1 - 2008 U6 - http://dx.doi.org/10.25643/bauhaus-universitaet.3593 SP - 369 EP - 387 ER - TY - JOUR A1 - Lahmer, Tom T1 - Modified Landweber iterations in a multilevel algorithm applied to inverse problems in piezoelectricity JF - Journal of Inverse and Ill-posed Problems N2 - Modified Landweber iterations in a multilevel algorithm applied to inverse problems in piezoelectricity KW - Angewandte Mathematik KW - Stochastik KW - Strukturmechanik Y1 - 2009 SP - 585 EP - 593 ER - TY - JOUR A1 - Hauck, A. A1 - Lahmer, Tom A1 - Kaltenbacher, Manfred T1 - Enhanced homogenization technique for magnetomechanical systems using the generalized finite element method JF - COMPEL: The international journal for computation and mathematics in electrical and electronic engineering N2 - Enhanced homogenization technique for magnetomechanical systems using the generalized finite element method KW - Angewandte Mathematik KW - Stochastik KW - Strukturmechanik Y1 - 2009 SP - 935 EP - 947 ER - TY - JOUR A1 - Lahmer, Tom A1 - Könke, Carsten A1 - Bettzieche, Volker T1 - Optimal positioning of sensors for the monitoring of water dams JF - WASSERWIRTSCHAFT N2 - Optimal positioning of sensors for the monitoring of water dams KW - Angewandte Mathematik KW - Stochastik KW - Strukturmechanik Y1 - 2010 SP - 16 EP - 19 ER -