Two-Scale Optimization of Graded Lattice Structures respecting Buckling on Micro- and Macroscale

Interest in components with detailed structures increased with the progress in advanced manufacturing techniques in recent years. Parts with graded lattice elements can provide interesting mechanical, thermal, and acoustic properties compared to parts where only coarse features are included. One of these improvements is better global buckling resistance of the component. However, thin features are prone to local buckling. Normally, analyses with high computational effort are conducted on high-resolution finite element meshes to optimize parts with good global and local stability. Until recently, works focused only on either global or local buckling behavior. We use two-scale optimization based on asymptotic homogenization of elastic properties and local buckling behavior to reduce the effort of full-scale analyses. For this, we present an approach for concurrent local and global buckling optimization of parameterized graded lattice structures. It is based on a worst-case model for the homogenized buckling load factor, which acts as a safeguard against pure local buckling. Cross-modes residing on both scales are not detected. We support our theory with numerical examples and validations on dehomogenized designs, which show the capabilities of our method, and discuss the advantages and limitations of the worst-case model.Comment: submitted to Structural and Multidisciplinary Optimizatio

A review on feature-mapping methods for structural optimization

Acknowledgments We thank Dr. Lukas Pflug from the Department of Mathematics at the Friedrich-Alexander-Universität Erlangen-Nürnberg (FAU), Germany, for fruitful discussion and support. The initiative for this review goes back to critical yet constructive comments by Prof. Kurt Maute, from the University of Colorado Boulder, USA. We also thank Prof. Horea Ilies from the University of Connecticut, USA, for guidance and insight into some of the geometric aspects of this work. The first author acknowledges support by Deutsche Forschungsgemeinschaft (DFG) in the framework of the collaborative research center CRC 814 (subproject C2). The third author thanks the support of the US National Science Foundation, award CMMI-1634563.Peer reviewedPreprintPostprin

Pion and Kaon Distribution Amplitudes from lattice QCD: towards the continuum limit

We present the current status of a non-perturbative lattice calculation of the moments of the pion and kaon distribution amplitudes by the RQCD collaboration. Our investigation is carried out using $N_f=2+1$ dynamical, non-perturbatively O(a)-improved Wilson fermions on the CLS ensembles with 5 different lattice spacings and pion masses down to the physical pion mass. A combined continuum and chiral extrapolation to the physical point is performed along two independent quark mass trajectories simultaneously. We employ momentum smearing in order to decrease the contamination by excited states and increase statistical precision.Comment: Proceedings of the 36th Annual International Symposium on Lattice Field Theory - LATTICE201

Light-cone distribution amplitudes of the baryon octet

We present results of the first ab initio lattice QCD calculation of the normalization constants and first moments of the leading twist distribution amplitudes of the full baryon octet, corresponding to the small transverse distance limit of the associated S-wave light-cone wave functions. The P-wave (higher twist) normalization constants are evaluated as well. The calculation is done using $N_f=2+1$ flavors of dynamical (clover) fermions on lattices of different volumes and pion masses down to 222 MeV. Significant SU(3) flavor symmetry violation effects in the shape of the distribution amplitudes are observed.Comment: Update to the version published in JHE

Light-cone distribution amplitudes of octet baryons from lattice QCD

We present lattice QCD results for the wave function normalization constants and the first moments of the distribution amplitudes for the lowest-lying baryon octet. The analysis is based on a large number of $N_f=2+1$ ensembles comprising multiple trajectories in the quark mass plane including physical pion (and kaon) masses, large volumes, and, most importantly, five different lattice spacings down to $a=0.039\,\mathrm{fm}$. This allows us to perform a controlled extrapolation to the continuum and infinite volume limits by a simultaneous fit to all available data. We demonstrate that the formerly observed violation of flavor symmetry breaking constraints can, indeed, be attributed to discretization effects that vanish in the continuum limit

Pion distribution amplitude from Euclidean correlation functions: Exploring universality and higher-twist effects

Building upon our recent study [G. S. Bali et al., Eur. Phys. J. C 78, 217 (2018)], we investigate the feasibility of calculating the pion distribution amplitude from suitably chosen Euclidean correlation functions at large momentum. We demonstrate in this work the advantage of analyzing several correlation functions simultaneously and extracting the pion distribution amplitude from a global fit. This approach also allows us to study higher-twist corrections, which are a major source of systematic error. Our result for the higher-twist parameter delta(pi)(2) is in good agreement with estimates from QCD sum rules. Another novel element is the use of all-to-all propagators, calculated using stochastic estimators, which enables an additional volume average of the correlation functions, thereby reducing statistical errors

Topologieoptimierung intelligenter piezoelektrischer Wandler

Numerical topology optimization based on the ersatz material model is very attractive in the research community and industry. Large scale nonlinear problems can be solved efficiently through the availability of appropriate optimizers, often resulting in non-intuitive solutions. However, topology optimization has not yet been established in the design of practical sensors and actuators. To this end we perform a thorough analysis and discussion of two exemplary piezoelectric devices, a single-frequency loudspeaker and a cantilevered energy harvester. With respect to the loudspeaker a broad range of objective functions is compared and discussed, culminating in a fully coupled piezoelectric-mechanical-acoustic near field topology optimization problem. Piezoelectric strain cancellation and acoustic short circuits need to be balanced with structural resonance in order to obtain close to resonance performance for almost arbitrary target frequencies. Providing appropriate initial designs proved to be essential for robust optimization. Cantilevered piezoelectric energy harvesters have been subject to various optimization approaches. However these have generally been based on reduced model assumptions. We present topology optimization of a realistic cantilevered energy harvester model. It proved to be necessary to use advanced topology optimization techniques, stress constraints to enforce practically feasible designs and Heaviside filtering for void features size control and for obtaining a black and white design pattern. To the best of our knowledge, this is the first time that dynamic piezoelectric stress constraints have been formulated for topology optimization. The obtained result is mechanism-based and interpretable to manufacture. This appears to be a novel finding in the field of cantilevered piezoelectric energy harvesting design. Performing numerical experiments, we were surprised to observe pronounced piezoelectric self-penalization, which means optimal black and white solutions without penalizing design interpolation and additional constraints beside box constraints on the design variable. This phenomenon is only rarely and briefly described in the literature. Within this thesis we perform initial heuristic steps in the analysis of the self-penalization phenomenon, which indeed appears in many different topology optimization problems. Once self-penalization is rigorously understood, our vision is to find methods supporting the self-penalizing effect and to obtain solutions potentially closer to the original problem than constrained and penalized ersatz problems. To this end we present oscillation constraints, a feature size control with independent solid and void feature size without enforcing intermediate pseudo material.Numerische Topologieoptimierung mittels des Ersatzmaterialmodells ist sowohl in der Forschung als auch im industriellem Einsatz etabliert. Mittels passender Optimierer können auch umfangreiche nichtlineare Probleme effizient gelöst werden, wobei oft überraschende und nicht-intuitive Lösungen entstehen. In der Entwicklung von Wandlern für den realen Einsatz konnte sich die Topologieoptimierung jedoch noch nicht etablieren und soll aus diesem Grund innerhalb dieser Arbeit an zwei exemplarischen piezoelektrischen Wandlern erprobt werden. Es handelt sich um einen monofrequenten piezoelektrischen Lautsprechers und einen Balken-Energy Harvesters. Die jeweiligen Probleme werden detailliert diskutiert und analysiert. Die Lautsprecheroptimierung wird für verschiedene Zielfunktionen durchgeführt. Es stellt sich heraus, dass für ein vollständig gekoppeltes Piezoelektrik-Mechanik-Akustik-Problem eine akustische Nahfeldoptimierung notwendig ist. Piezoelektrische Dehnungsauslöschungen und akustische Kurzschlüsse müssen mit strukturellen Resonanzmoden ausbalanciert werden. Dann ist es jedoch für fast beliebige Frequenzen möglich, Schallleistungen vergleichbar zum Resonanzfall zu erreichen. Hierzu sind jedoch zweckmäßig konstruierte Startwerte notwendig. Piezoelekrische Balken-Energy Harvester wurden bisher mit verschiedenen Ansätzen optimiert, jedoch in der Regel auf Basis reduzierter Modellannahmen. In dieser Arbeit stellen wie die Topologieoptimierung eines realistischen Balken-Energy Harvesters vor. Es stellt sich heraus, dass der Einsatz von State of the Art Methoden der Topologieoptimierung notwendig ist. Um baubare Ergebnisse zu erzielen, müssen die auftretenden Spannungen auf einen zulässigen Wert beschränkt werden. Mittels eines Heaviside-Filters wird die Lochgröße gesteuert und ein kontrastreiches Topologieergebnis erzielt. Dynamische piezoelektrische Spannungsbedingungen werden somit zum ersten Mal im Rahmen der Topologieoptimierung angewandt. Das Optimierungsergebnis basiert auf einem interpretierbaren Mechanismus und stellt somit eine neues Designprinzip im Bereich piezoelektrischer Balken-Energy Harvester dar. Bei den numerischen Berechnungen konnten wir überraschenderweise eine deutliche piezoelektrische Selbstpenalisierung beobachten. Dies bezeichnet eine 0-1 Lösung, ohne dass eine Penalisierung der Interpolationsfunktion des Designs bzw. zusätzliche Nebenbedingungen angewendet werden. Designschranken sind natürlich notwendig. Es handelt sich um ein nur selten beschriebenes Phänomen. Im Rahmen dieser Arbeit unternehmen wir erste heuristische Schritte zur Analyse des Phänomens der Selbstpenalisierung. Das Phänomen tritt bei einer Reine von Topologieoptimierungsproblemen auf. Die Vision ist, dass, wenn Selbstpenalisierung rigoros verstanden ist, Methoden gefunden werden die die Selbstpenalisierung unterstützen. Unter Umständen können so Lösungen gefunden werden, die näher am Originalproblem liegen als am penalisierten Ersatzproblem. Zu diesem Zweck wird auch eine neue Nebenbedingung zur Beschränkung der Variation des Designs vorgestellt. Dies erlaubt die getrennte Vorgabe für minimale Strukturgrößen im Material und für Löcher