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- ItemTopology optimization subject to additive manufacturing constraints(Berlin ; Heidelberg : Springer, 2021) Ebeling-Rump, Moritz; Hömberg, Dietmar; Lasarzik, Robert; Petzold, ThomasIn topology optimization the goal is to find the ideal material distribution in a domain subject to external forces. The structure is optimal if it has the highest possible stiffness. A volume constraint ensures filigree structures, which are regulated via a Ginzburg–Landau term. During 3D printing overhangs lead to instabilities. As a remedy an additive manufacturing constraint is added to the cost functional. First order optimality conditions are derived using a formal Lagrangian approach. With an Allen-Cahn interface propagation the optimization problem is solved iteratively. At a low computational cost the additive manufacturing constraint brings about support structures, which can be fine tuned according to demands and increase stability during the printing process.
- ItemCompact differential-fed planar filtering antennas(Basel : MDPI AG, 2019) Hassan, Emadeldeen; Martynenko, Denys; Wadbro, Eddie; Fischer, Gunter; Berggren, MartinThis paper proposes novel low-profile differential-fed planar antennas with embedded sharp frequency selectively. The antennas are compact and easy to integrate with differential devices without matching baluns. The antenna design is formulated as a topology optimization problem, where requirements on impedance bandwidth, directivity, and filtering are used as the design objectives. The optimized antennas operate over the frequency band 6.0-8.5 GHz. The antennas have reflection coefficients below -15 dB, cross-polarization levels below -42 dB, a maximum gain of 6.0 ± 0.5 dB, and a uniform directivity over more than 130° beamwidth angle in the frequency band of interest. In addition, the antennas exhibit sharp roll-off between the operational band and frequencies around the 5.8GHz WiFi band and the 10 GHz X-band. One antenna has been fabricated with a good match between simulation and measurement results. © 2019 by the authors. Licensee MDPI, Basel, Switzerland.
- ItemDesign of thin micro-architectured panels with extension-bending coupling effects using topology optimization(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2021) Agnelli, Filippo; Nika, Grigor; Constantinescu, AndreiWe design thin micro-architectured panels with programmable macroscopic behaviour using inverse homogenization, the Hadamard shape derivative, and a level set method in the diffuse interface context. The optimally designed microstructures take into account the extension-bending effect in addition to in-plane stiffness and out-of-plane bending stiffness. Furthermore, we present numerical examples of optimal microstructures that attain different targets for different volume fractions and interpret the physical significance of the extension-bending coupling. The simultaneous control of the in-plane, out-of-plane and their coupled behaviour enables to shift a flat panel into a dome or saddle shaped structure under the action of an in-plane loading. Moreover, the obtained unit cells are elementary blocks to create three-dimensional objects with shape-morphing capabilities.
- ItemStochastic topology optimisation with hierarchical tensor reconstruction(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2016) Eigel, Martin; Neumann, Johannes; Schneider, Reinhold; Wolf, SebastianA novel approach for risk-averse structural topology optimization under uncertainties is presented which takes into account random material properties and random forces. For the distribution of material, a phase field approach is employed which allows for arbitrary topological changes during optimization. The state equation is assumed to be a high-dimensional PDE parametrized in a (finite) set of random variables. For the examined case, linearized elasticity with a parametric elasticity tensor is used. Instead of an optimization with respect to the expectation of the involved random fields, for practical purposes it is important to design structures which are also robust in case of events that are not the most frequent. As a common risk-aware measure, the Conditional Value at Risk (CVaR) is used in the cost functional during the minimization procedure. Since the treatment of such high-dimensional problems is a numerically challenging task, a representation in the modern hierarchical tensor train format is proposed. In order to obtain this highly efficient representation of the solution of the random state equation, a tensor completion algorithm is employed which only required the pointwise evaluation of solution realizations. The new method is illustrated with numerical examples and compared with a classical Monte Carlo sampling approach.
- ItemA PDE-constrained optimization approach for topology optimization of strained photonic devices(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2017) Adam, Lukáš; Hintermüller, Michael; Surowiec, Thomas M.Recent studies have demonstrated the potential of using tensile-strained, doped Germanium as a means of developing an integrated light source for (amongst other things) future microprocessors. In this work, a multi-material phase-field approach to determine the optimal material configuration within a so-called Germanium-on-Silicon microbridge is considered. Here, an optimal configuration is one in which the strain in a predetermined minimal optical cavity within the Germanium is maximized according to an appropriately chosen objective functional. Due to manufacturing requirements, the emphasis here is on the cross-section of the device; i.e. a socalled aperture design. Here, the optimization is modeled as a non-linear optimization problem with partial differential equation (PDE) and manufacturing constraints. The resulting problem is analyzed and solved numerically. The theory portion includes a proof of existence of an optimal topology, differential sensitivity analysis of the displacement with respect to the topology, and the derivation of first and second-order optimality conditions. For the numerical experiments, an array of first and second-order solution algorithms in function-space are adapted to the current setting, tested, and compared. The numerical examples yield designs for which a significant increase in strain (as compared to an intuitive empirical design) is observed.