Ceramic is a material frequently used in industry because of its favorable properties. Common approaches in shape optimization for ceramic structures aim to minimize the tensile stress acting on the component, as it is the main driver for failure. In contrast to this, we follow a more natural approach by minimizing the component's probability of failure under a given tensile load. Since the fundamental work of Weibull, the probabilistic description of the strength of ceramics is standard and has been widely applied. Here, for the first time, the resulting failure probabilities are used as objective functions in PDE constrained shape optimization.To minimize the probability of failure, we choose a gradient based method combined with a first discretize then optimize approach. For discretization finite elements are used. Using the Lagrangian formalism, the shape gradient via the adjoint equation is calculated at low computational cost. * {bolten@math.,hanno.gottschalk@,chahn@,saadi@}uni-wuppertal.de arXiv:1705.05776v1 [math.OC] 16 May 2017 2 BOLTEN, GOTTSCHALK, HAHN AND SAADIThe implementation is verified by comparison of it with a finite difference method applied to a minimal 2d example. Furthermore, we construct shape flows towards an optimal / improved shape in the case of a simple beam and a bended joint.
This work provides a numerical calculation of shape gradients of failure probabilities for mechanical components using a first discretize, then adjoint approach. While deterministic life prediction models for failure mechanisms are not (shape) differentiable, this changes in the case of probabilistic life prediction. The probabilistic, or reliability based, approach thus opens the way for efficient adjoint methods in the design for mechanical integrity. In this work we propose, implement and validate a method for the numerical calculation of the shape gradients of failure probabilities for the failure mechanism low cycle fatigue (LCF), which applies to polycrystalline metal. Numerical examples range from a bended rod to a complex geometry from a turbo charger in 3D.
In the optimization of turbomachinery components, shape sensitivities for fluid dynamical objective functions have been used for a long time. As peak stress is not a differential functional of the shape, such highly efficient procedures so far have been missing for objective functionals that stem from mechanical integrity. This changes, if deterministic lifing criteria are replaced by probabilistic criteria, which have been introduced recently to the field of low cycle fatigue (LCF).Here we present a finite element (FEA) based first discretize, then adjoin approach to the calculation of shape gradients (sensitivities) for the failure probability with regard to probabilistic LCF and apply it to simple and complex geometries, as e.g. a blisk geometry.We review the computation of failure probabilities with a FEA postprocessor and sketch the computation of the relevant quantities for the adjoint method. We demonstrate high accuracy and computational efficiency of the adjoint method compared to finite difference schemes. We discuss implementation details for rotating components with cyclic boundary conditions. Finally, we shortly comment on future development steps and on potential applications in multi criteria optimization.
Eccentrically Braced Frames (EBFs) have been widely used in the last decades and proved their efficiency to resist strong earthquake intensities by providing suitable ductility and lateral stiffness. Using the PBPD method for the design, EBFs can fulfill the target performance objectives under major earthquakes. The most commonly used configurations are the K-shaped and the recent Y-shaped EBFs, which have the advantage that the links are independent of the beam and can be easily replaced after an earthquake without serious damage to the beam and slab. This study focused on the lateral reliability of both systems under seismic loading. Nonlinear static pushover and Incremental Dynamic Analysis (IDA) were performed on 5-story and 10-story K- and Y-shaped EBFs. A series of 14 near- and 7 far-field seismic records were considered to analyze and compare the inter-story drifts of both systems using the Seismostruct software. Moreover, Peak Ground Accelerations (PGA) and the different performance levels were also examined.
Many agent based simulation approaches have been proposed for pedestrian flow. As such models are applied e.g. in evacuation studies, the quality and reliability of such models is of vital interest. Pedestrian trajectories are functional data and thus functional principal component analysis is a natural tool to asses the quality of pedestrian flow models beyond average properties.In this article we conduct functional PCA for the trajectories of pedestrians passing through a bottleneck. In this way it is possible to asses the quality of the models not only on basis of average values but also by considering its fluctuations. We benchmark two agent based models of pedestrian flow against the experimental data using PCA average and stochastic features. * corresponding author Email addresses: m.chraibi@fz-juelich.de (Mohcine Chraibi), tim.ensslen@uni-wuppertal.de (Tim Ensslen), hanno.gottschalk@uni-wuppertal.de (Hanno Gottschalk), saadi@uni-wuppertal.de Functional PCA proves to be an efficient tool to detect deviation between simulation and experiment and to asses quality of pedestrian models.
Mechanical components that are exposed to cyclic mechanical loading fail at loads that are well below the ultimate tensile strength. This process is known as fatigue. The failure time, that is the time when a first crack forms, is highly random. In this work we review some recent developments in the modelling of probabilistic failure times, understood as the time to the formation of a fatigue crack.We also discuss the how probabilistic models can be used in shape design with the design intent of optimizing the component's reliability. We give review a recent existence result for optimal shapes and we discuss continuous and discrete shape derivatives. Another application is optimal service scheduling. The mathematical fields involved range from reliability statistics over stochastic point processes, multiscale modeling, PDEs on variable geometries, shape optimization and numerical analysis to operations research.
During the last two decades, the attention of researchers has been focused on repairing and retrofitting concrete frames to make them more earthquake-resistant. Two methods have been developed to increase the seismic resistance of previously undamaged structures before they are subjected to an earthquake. The first is through the addition of new structural members, such as steel braces and the second is by selectively strengthening structural elements, for instance through steel caging. Seismic response analysis results have been utilized in multi-story RC frames that were designed without seismic design criteria. This study aims to determine whether the retrofitting technique is effective based on comparisons between steel braces, steel cages, and their combinations. The seismic performance is defined by the seismic code for Algeria RPA 2003 according to the latest recommendations. Static nonlinear analysis was used to compare seismic responses of existing non-ductile reinforced concrete RC frames under a variety of retrofit schemes. The results show that retrofitting with steel caging gives excellent performance in terms of ductility and low shear capacity. The retrofitting with steel bracing increased the shear capacity but led to a severe ductility deficiency. The retrofitting structure combined with steel bracing and steel caging shows good performance in shear capacity and ductility. Using the Zipper system (steel bracing) and V system in combination with steel caging gives similar results to the RPA model.
In this paper, numerous experimental tests were carried out to study the behavior of concrete containing glass fibers and confined with glass fiber-reinforced polymer (GFRP). Concrete specimens containing different fiber percentages ( 0.3 wt.%, 0.6 wt.%, 0.9 wt.% or 1.2 wt.%) and with different strengths of concrete (8.5 MPa, 16 MPa and 25 MPa) and different confinement levels (two, four and six layers of GFRP) were used as research parameters. The samples were tested to failure under pure axial compression. The results imply that the confinement effect with GFRP is relatively higher for concrete samples containing glass fiber (GFCC) with a percentage equal to 0.6 wt.%. The theoretical of stress ratios (fcc/fco) estimated by using existing ultimate strength models are found to be close to the experimental results for high strength of GFCC, but not close to the experimental results for low strength of GFCC.
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