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 - 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 - TY - JOUR A1 - Lahmer, Tom A1 - Könke, Carsten A1 - Bettzieche, Volker T1 - Optimale Positionierung von Messeinrichtungen an Staumauern zur Bauwerksüberwachung JF - WASSERWIRTSCHAFT N2 - Optimale Positionierung von Messeinrichtungen an Staumauern zur Bauwerksüberwachung KW - Angewandte Mathematik KW - Stochastik KW - Strukturmechanik Y1 - 2010 SP - 16 EP - 16 ER - TY - JOUR A1 - Lahmer, Tom T1 - Crack identification in hydro-mechanical systems with applications to gravity water dams JF - Inverse Problems in Science and Engineering N2 - Crack identification in hydro-mechanical systems with applications to gravity water dams KW - Angewandte Mathematik KW - Stochastik KW - Strukturmechanik Y1 - 2010 SP - 1083 EP - 1101 ER - TY - JOUR A1 - Stein, Peter A1 - Lahmer, Tom A1 - Bock, Sebastian T1 - Synthese und Analyse von gekoppelten Modellen im konstruktiven Ingenieurbau BT - Sonderdruck‐DFG Graduiertenkolleg JF - Bautechnik N2 - Synthese und Analyse von gekoppelten Modellen im konstruktiven Ingenieurbau KW - Angewandte Mathematik KW - Stochastik KW - Strukturmechanik Y1 - 2011 SP - 8 EP - 11 ER -