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 - 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 - THES A1 - Ghasemi, Hamid T1 - Stochastic optimization of fiber reinforced composites considering uncertainties N2 - Briefly, the two basic questions that this research is supposed to answer are: 1. Howmuch fiber is needed and how fibers should be distributed through a fiber reinforced composite (FRC) structure in order to obtain the optimal and reliable structural response? 2. How do uncertainties influence the optimization results and reliability of the structure? Giving answer to the above questions a double stage sequential optimization algorithm for finding the optimal content of short fiber reinforcements and their distribution in the composite structure, considering uncertain design parameters, is presented. In the first stage, the optimal amount of short fibers in a FRC structure with uniformly distributed fibers is conducted in the framework of a Reliability Based Design Optimization (RBDO) problem. Presented model considers material, structural and modeling uncertainties. In the second stage, the fiber distribution optimization (with the aim to further increase in structural reliability) is performed by defining a fiber distribution function through a Non-Uniform Rational BSpline (NURBS) surface. The advantages of using the NURBS surface as a fiber distribution function include: using the same data set for the optimization and analysis; high convergence rate due to the smoothness of the NURBS; mesh independency of the optimal layout; no need for any post processing technique and its non-heuristic nature. The output of stage 1 (the optimal fiber content for homogeneously distributed fibers) is considered as the input of stage 2. The output of stage 2 is the Reliability Index (b ) of the structure with the optimal fiber content and distribution. First order reliability method (in order to approximate the limit state function) as well as different material models including Rule of Mixtures, Mori-Tanaka, energy-based approach and stochastic multi-scales are implemented in different examples. The proposed combined model is able to capture the role of available uncertainties in FRC structures through a computationally efficient algorithm using all sequential, NURBS and sensitivity based techniques. The methodology is successfully implemented for interfacial shear stress optimization in sandwich beams and also for optimization of the internal cooling channels in a ceramic matrix composite. Finally, after some changes and modifications by combining Isogeometric Analysis, level set and point wise density mapping techniques, the computational framework is extended for topology optimization of piezoelectric / flexoelectric materials. T3 - ISM-Bericht // Institut für Strukturmechanik, Bauhaus-Universität Weimar - 2016,1 KW - Optimization KW - Fiber Reinforced Composite KW - Finite Element Method KW - Isogeometric Analysis KW - Flexoelectricity KW - Finite-Elemente-Methode KW - Optimierung Y1 - 2016 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:gbv:wim2-20161117-27042 ER - TY - JOUR A1 - Shirazi, A. H. N. A1 - Mohebbi, Farzad A1 - Azadi Kakavand, M. R. A1 - He, B. A1 - Rabczuk, Timon T1 - Paraffin Nanocomposites for Heat Management of Lithium-Ion Batteries: A Computational Investigation JF - JOURNAL OF NANOMATERIALS N2 - Lithium-ion (Li-ion) batteries are currently considered as vital components for advances in mobile technologies such as those in communications and transport. Nonetheless, Li-ion batteries suffer from temperature rises which sometimes lead to operational damages or may even cause fire. An appropriate solution to control the temperature changes during the operation of Li-ion batteries is to embed batteries inside a paraffin matrix to absorb and dissipate heat. In the present work, we aimed to investigate the possibility of making paraffin nanocomposites for better heat management of a Li-ion battery pack. To fulfill this aim, heat generation during a battery charging/discharging cycles was simulated using Newman’s well established electrochemical pseudo-2D model. We couple this model to a 3D heat transfer model to predict the temperature evolution during the battery operation. In the later model, we considered different paraffin nanocomposites structures made by the addition of graphene, carbon nanotubes, and fullerene by assuming the same thermal conductivity for all fillers. This way, our results mainly correlate with the geometry of the fillers. Our results assess the degree of enhancement in heat dissipation of Li-ion batteries through the use of paraffin nanocomposites. Our results may be used as a guide for experimental set-ups to improve the heat management of Li-ion batteries. KW - Batterie KW - Wärmeleitfähigkeit Y1 - 2016 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:gbv:wim2-20170411-31141 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 - 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 - 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 - 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 - 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 - 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 -