TY - JOUR A1 - Zhang, Yongzheng A1 - Ren, Huilong T1 - Implicit implementation of the nonlocal operator method: an open source code JF - Engineering with computers N2 - In this paper, we present an open-source code for the first-order and higher-order nonlocal operator method (NOM) including a detailed description of the implementation. The NOM is based on so-called support, dual-support, nonlocal operators, and an operate energy functional ensuring stability. The nonlocal operator is a generalization of the conventional differential operators. Combined with the method of weighed residuals and variational principles, NOM establishes the residual and tangent stiffness matrix of operate energy functional through some simple matrix without the need of shape functions as in other classical computational methods such as FEM. NOM only requires the definition of the energy drastically simplifying its implementation. The implementation in this paper is focused on linear elastic solids for sake of conciseness through the NOM can handle more complex nonlinear problems. The NOM can be very flexible and efficient to solve partial differential equations (PDEs), it’s also quite easy for readers to use the NOM and extend it to solve other complicated physical phenomena described by one or a set of PDEs. Finally, we present some classical benchmark problems including the classical cantilever beam and plate-with-a-hole problem, and we also make an extension of this method to solve complicated problems including phase-field fracture modeling and gradient elasticity material. KW - Strukturmechanik KW - Nonlocal operator method KW - Operator energy functional KW - Implicit KW - Dual-support KW - Variational principle KW - Taylor series expansion KW - Stiffness matrix Y1 - 2022 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:gbv:wim2-20220216-45930 UR - https://link.springer.com/article/10.1007/s00366-021-01537-x VL - 2022 SP - 1 EP - 35 PB - Springer CY - London ER - TY - JOUR A1 - Zhang, Chao A1 - Nanthakumar, S.S. A1 - Lahmer, Tom A1 - Rabczuk, Timon T1 - Multiple cracks identification for piezoelectric structures JF - International Journal of Fracture N2 - Multiple cracks identification for piezoelectric structures KW - Angewandte Mathematik KW - Stochastik KW - Strukturmechanik Y1 - 2017 SP - 1 EP - 19 ER - TY - JOUR A1 - Nguyen-Tuan, Long A1 - Könke, Carsten A1 - Bettzieche, Volker A1 - Lahmer, Tom T1 - Numerical modeling and validation for 3D coupled-nonlinear thermo-hydro-mechanical problems in masonry dams JF - Computers & Structures N2 - Numerical modeling and validation for 3D coupled-nonlinear thermo-hydro-mechanical problems in masonry dams KW - Angewandte Mathematik KW - Stochastik KW - Strukturmechanik Y1 - 2017 SP - 143 EP - 154 ER - TY - JOUR A1 - Achenbach, Marcus A1 - Lahmer, Tom A1 - Morgenthal, Guido T1 - Global Sensitivity Analysis of Reinforced Concrete Walls Subjected to Standard Fire - A Comparison of Methods JF - 14th International Probabilistic Workshop N2 - Global Sensitivity Analysis of Reinforced Concrete Walls Subjected to Standard Fire—A Comparison of Methods KW - Angewandte Mathematik KW - Stochastik KW - Strukturmechanik Y1 - 2017 SP - 97 EP - 106 ER - TY - JOUR A1 - Göbel, Luise A1 - Lahmer, Tom A1 - Osburg, Andrea T1 - Uncertainty analysis in multiscale modeling of concrete based on continuum micromechanics JF - European Journal of Mechanics-A/Solids N2 - Uncertainty analysis in multiscale modeling of concrete based on continuum micromechanics KW - Angewandte Mathematik KW - Stochastik KW - Strukturmechanik Y1 - 2017 ER - TY - JOUR A1 - Zhang, Chao A1 - Wang, Cuixia A1 - Lahmer, Tom A1 - He, Pengfei A1 - Rabczuk, Timon T1 - A dynamic XFEM formulation for crack identification JF - International Journal of Mechanics and Materials in Design N2 - A dynamic XFEM formulation for crack identification KW - Angewandte Mathematik KW - Stochastik KW - Strukturmechanik Y1 - 2016 SP - 427 EP - 448 ER - TY - JOUR A1 - Nguyen-Tuan, Long A1 - Lahmer, Tom A1 - Datcheva, Maria A1 - Stoimenova, Eugenia A1 - Schanz, Tom T1 - A novel parameter identification approach for buffer elements involving complex coupled thermo-hydro-mechanical analyses JF - Computers and Geotechnics N2 - A novel parameter identification approach for buffer elements involving complex coupled thermo-hydro-mechanical analyses KW - Angewandte Mathematik KW - Stochastik KW - Strukturmechanik Y1 - 2016 SP - 23 EP - 32 ER - TY - JOUR A1 - Vu-Bac, N. A1 - Lahmer, Tom A1 - Zhuang, Xiaoying A1 - Nguyen-Thoi, T. A1 - Rabczuk, Timon T1 - A software framework for probabilistic sensitivity analysis for computationally expensive models JF - Advances in Engineering Software N2 - A software framework for probabilistic sensitivity analysis for computationally expensive models KW - Angewandte Mathematik KW - Stochastik KW - Strukturmechanik Y1 - 2016 SP - 19 EP - 31 ER - TY - JOUR A1 - Nanthakumar, S.S. A1 - Lahmer, Tom A1 - Zhuang, Xiaoying A1 - Park, Harold S. A1 - Rabczuk, Timon T1 - Topology optimization of piezoelectric nanostructures JF - Journal of the Mechanics and Physics of Solids N2 - Topology optimization of piezoelectric nanostructures KW - Angewandte Mathematik KW - Stochastik KW - Strukturmechanik Y1 - 2016 SP - 316 EP - 335 ER - TY - JOUR A1 - Ghorashi, Seyed Shahram A1 - Lahmer, Tom A1 - Bagherzadeh, Amir Saboor A1 - Zi, Goangseup A1 - Rabczuk, Timon T1 - A stochastic computational method based on goal-oriented error estimation for heterogeneous geological materials JF - Engineering Geology N2 - A stochastic computational method based on goal-oriented error estimation for heterogeneous geological materials KW - Angewandte Mathematik KW - Stochastik KW - Strukturmechanik Y1 - 2016 ER - TY - JOUR A1 - Nanthakumar, S.S. A1 - Lahmer, Tom A1 - Zhuang, Xiaoying A1 - Zi, Goangseup A1 - Rabczuk, Timon T1 - Detection of material interfaces using a regularized level set method in piezoelectric structures JF - Inverse Problems in Science and Engineering N2 - Detection of material interfaces using a regularized level set method in piezoelectric structures KW - Angewandte Mathematik KW - Stochastik KW - Strukturmechanik Y1 - 2016 SP - 153 EP - 176 ER - TY - JOUR A1 - Lahmer, Tom A1 - Bock, Sebastian A1 - Hildebrand, Jörg A1 - Gürlebeck, Klaus T1 - Non-destructive identification of residual stresses in steel under thermal loadings JF - Inverse Problems in Science and Engineering N2 - Non-destructive identification of residual stresses in steel under thermal loadings KW - Angewandte Mathematik KW - Stochastik KW - Strukturmechanik Y1 - 2016 SP - 1 EP - 17 ER - TY - JOUR A1 - Nguyen-Tuan, Long A1 - Lahmer, Tom A1 - Datcheva, Maria A1 - Schanz, Tom T1 - Global and local sensitivity analyses for coupled thermo‐hydro‐mechanical problems JF - International Journal for Numerical and Analytical Methods in Geomechanics N2 - Global and local sensitivity analyses for coupled thermo‐hydro‐mechanical problems KW - Angewandte Mathematik KW - Stochastik KW - Strukturmechanik Y1 - 2016 ER - TY - JOUR A1 - Marzban, Samira A1 - Lahmer, Tom T1 - Conceptual implementation of the variance-based sensitivity analysis for the calculation of the first-order effects JF - Journal of Statistical Theory and Practice N2 - Conceptual implementation of the variance-based sensitivity analysis for the calculation of the first-order effects KW - Angewandte Mathematik KW - Stochastik KW - Strukturmechanik Y1 - 2016 SP - 589 EP - 611 ER - TY - JOUR A1 - Nanthakumar, S.S. A1 - Lahmer, Tom A1 - Rabczuk, Timon T1 - Detection of multiple flaws in piezoelectric structures using XFEM and level sets JF - International Journal for Numerical Methods in Engineering N2 - Detection of multiple flaws in piezoelectric structures using XFEM and level sets KW - Angewandte Mathematik KW - Stochastik KW - Strukturmechanik Y1 - 2016 SP - 960 ER - TY - JOUR A1 - Lahmer, Tom A1 - Nguyen-Tuan, Long A1 - Könke, Carsten A1 - Bettzieche, Volker T1 - Thermo-hydro-mechanische 3-D-Simulation von Staumauern‐Modellierung und Validierung JF - WASSERWIRTSCHAFT N2 - Thermo-hydro-mechanische 3-D-Simulation von Staumauern‐Modellierung und Validierung KW - Angewandte Mathematik KW - Stochastik KW - Strukturmechanik Y1 - 2016 SP - 27 EP - 30 ER - TY - JOUR A1 - Lahmer, Tom A1 - Ilg, J. A1 - Lerch, Reinhard T1 - Variance-based sensitivity analyses of piezoelectric models JF - Computer Modeling in Engineering & Sciences N2 - Variance-based sensitivity analyses of piezoelectric models KW - Angewandte Mathematik KW - Stochastik KW - Strukturmechanik Y1 - 2015 SP - 105 EP - 126 ER - TY - JOUR A1 - Zhao, Jun-Hua A1 - Lu, Lixin A1 - Zhang, Zhiliang A1 - Guo, Wanlin A1 - Rabczuk, Timon T1 - Continuum modeling of the cohesive energy for the interfaces between _lms, spheres, coats and substrates JF - Computational Materials Science N2 - Continuum modeling of the cohesive energy for the interfaces between _lms, spheres, coats and substrates KW - Angewandte Mathematik KW - Strukturmechanik Y1 - 2015 SP - 432 EP - 438 ER - TY - JOUR A1 - Ben, S. A1 - Zhao, Jun-Hua A1 - Zhang, Yancheng A1 - Rabczuk, Timon T1 - The interface strength and debonding for composite structures: review and recent developments JF - Composite Structures N2 - The interface strength and debonding for composite structures: review and recent developments KW - Angewandte Mathematik KW - Strukturmechanik Y1 - 2015 ER - TY - JOUR A1 - Zhao, Jun-Hua A1 - Jia, Yue A1 - Wei, Ning A1 - Rabczuk, Timon T1 - Binding energy and mechanical stability of two parallel and crossing carbon nanotubes JF - Journal of Applied Mechanics N2 - Binding energy and mechanical stability of two parallel and crossing carbon nanotubes KW - Angewandte Mathematik KW - Strukturmechanik Y1 - 2015 ER -