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 - 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 - 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 - Nanthakumar, S.S. A1 - Lahmer, Tom A1 - Rabczuk, Timon T1 - Detection of flaws in piezoelectric structures using extended FEM JF - International Journal for Numerical Methods in Engineering N2 - Detection of flaws in piezoelectric structures using extended FEM KW - Angewandte Mathematik KW - Stochastik KW - Strukturmechanik Y1 - 2013 SP - 373 EP - 389 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 - 2015 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 - Nanthakumar, S.S. A1 - Lahmer, Tom A1 - Rabczuk, Timon T1 - Detection of multiple flaws in piezoelectric structures using XFEM and level sets JF - Computer Methods in Applied Mechanics and Engineering N2 - Detection of multiple flaws in piezoelectric structures using XFEM and level sets KW - Angewandte Mathematik KW - Stochastik KW - Strukturmechanik Y1 - 2014 SP - 98 EP - 112 ER - TY - THES A1 - Nanthakumar, S.S. T1 - Inverse and optimization problems in piezoelectric materials using Extended Finite Element Method and Level sets T1 - Inverse und Optimierungsprobleme für piezoelektrische Materialien mit der Extended Finite Elemente Methode und Level sets N2 - Piezoelectric materials are used in several applications as sensors and actuators where they experience high stress and electric field concentrations as a result of which they may fail due to fracture. Though there are many analytical and experimental works on piezoelectric fracture mechanics. There are very few studies about damage detection, which is an interesting way to prevent the failure of these ceramics. An iterative method to treat the inverse problem of detecting cracks and voids in piezoelectric structures is proposed. Extended finite element method (XFEM) is employed for solving the inverse problem as it allows the use of a single regular mesh for large number of iterations with different flaw geometries. Firstly, minimization of cost function is performed by Multilevel Coordinate Search (MCS) method. The XFEM-MCS methodology is applied to two dimensional electromechanical problems where flaws considered are straight cracks and elliptical voids. Then a numerical method based on combination of classical shape derivative and level set method for front propagation used in structural optimization is utilized to minimize the cost function. The results obtained show that the XFEM-level set methodology is effectively able to determine the number of voids in a piezoelectric structure and its corresponding locations. The XFEM-level set methodology is improved to solve the inverse problem of detecting inclusion interfaces in a piezoelectric structure. The material interfaces are implicitly represented by level sets which are identified by applying regularisation using total variation penalty terms. The formulation is presented for three dimensional structures and inclusions made of different materials are detected by using multiple level sets. The results obtained prove that the iterative procedure proposed can determine the location and approximate shape of material subdomains in the presence of higher noise levels. Piezoelectric nanostructures exhibit size dependent properties because of surface elasticity and surface piezoelectricity. Initially a study to understand the influence of surface elasticity on optimization of nano elastic beams is performed. The boundary of the nano structure is implicitly represented by a level set function, which is considered as the design variable in the optimization process. Two objective functions, minimizing the total potential energy of a nanostructure subjected to a material volume constraint and minimizing the least square error compared to a target displacement, are chosen for the numerical examples. The numerical examples demonstrate the importance of size and aspect ratio in determining how surface effects impact the optimized topology of nanobeams. Finally a conventional cantilever energy harvester with a piezoelectric nano layer is analysed. The presence of surface piezoelectricity in nano beams and nano plates leads to increase in electromechanical coupling coefficient. Topology optimization of these piezoelectric structures in an energy harvesting device to further increase energy conversion using appropriately modified XFEM-level set algorithm is performed . KW - Finite-Elemente-Methode KW - Piezoelectricity KW - Inverse problems KW - Optimization problems KW - Nanostructures KW - XFEM KW - level set method KW - Surface effects Y1 - 2016 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:gbv:wim2-20161128-27095 ER -