On the implementation and effectiveness of morphological close-open and open-close filters for topology optimization

© 2016, Springer-Verlag Berlin Heidelberg. This note reconsiders the morphological close-open and open-close filters for topology optimization introduced in an earlier paper (Sigmund Struct Multidiscip Optim 33(4–5):401–424 (2007)). Close-open and open-close filters are defined as the sequential application of four dilation or erosion filters. In the original paper, these filters were proposed in order to provide length scale control in both the solid and the void phase. However, it was concluded that the filters were not useful in practice due to the computational cost of the sensitivity analysis. In this note, it is shown that the computational cost is much lower if the sensitivity analysis for each erosion or dilation step is performed sequentially. Unfortunately, it is also found that the close-open and open-close filters do not have the expected effect in terms of length scale control: each close or open operation ruins the effect of the preceding filters, resulting in a design with a minimum length scale in either the solid phase or the void phase, but not both.status: publishe

The impact of uncertain dynamic soil characteristics on the prediction of ground vibrations

De laatste jaren zijn verschillende numerieke modellen ontwikkeld voor de voorspelling van grondtrillingen in de bebouwde omgeving. Deze modellen beschrijven de trillingsbron, de transmissie van golven door de grond, en de respons van het gebouw. De transmissie van golven door de grond wordt bepaald door de dynamische grondkarakteristieken. De cruciale parameters zijn de dynamische glijdingsmodulus en de materiaaldempingsverhouding van de grond. Deze eigenschappen worden bepaald door middel van in situ proeven of laboratoriumproeven. De volledige karakterisatie van de ruimtelijke variatie van de grondkarakteristieken is echter praktisch onmogelijk. Als gevolg hiervan zijn de grondkarakteristieken onzeker. In de thesis wordt de invloed van deze onzekerheid op de voorspelling van grondtrillingen bestudeerd. De focus ligt op de dynamische glijdingsmodulus. Er wordt een probabilistische aanpak gevolgd waarbij de variatie van de glijdingsmodulus met de diepte gemodelleerd wordt als een stochastisch proces. De variatie van de glijdingsmodulus in horizontale richting wordt genegeerd. De glijdingsmodulus wordt bepaald door middel van de spectrale analyse van oppervlaktegolven (Spectral Analysis of Surface Waves, SASW). Dit gebeurt op basis van een Bayesiaans schema. De a priori informatie over de glijdingsmodulus, die beschikbaar is voor de uitvoering van de SASW-proef, wordt gecombineerd met de experimentele resultaten van de SASW-proef ter bepaling van een a posteriori stochastisch grondmodel. Het a posteriori stochastische grondmodel wordt bemonsterd met behulp van een Markovketen-Monte Carlomethode. Zo wordt een ensemble van grondprofielen bekomen die in overeenstemming zijn met de resultaten van de SASW-proef. Dit ensemble wordt bestudeerd om de resolutie van de SASW-proef te beoordelen. Vervolgens wordt de voorspelling van grondtrillingen beschouwd. De trillingen aan het grondoppervlak ten gevolge van een hamerimpact op een kleine fundering worden voorspeld. Dit gebeurt aan de hand van een Monte Carlomethode, uitgaande van het ensemble van grondprofielen dat afgeleid is van de SASW-proef. Er wordt vastgesteld dat de variabiliteit van de trillingsvoorspellingen afhankelijk is van de frequentie. Bij lage frequenties volstaat de resolutie van de SASW-proef en blijft de variabiliteit van de respons beperkt. Bij hogere frequenties heeft de onzekerheid op de glijdingsmodulus een invloed op de voorspellingen en neemt de variabiliteit toe.status: publishe

Determination of the dynamic soil characteristics at the NGES

Analysis of the field data collected at the National Geotechnical Experimentation Site (NGES) at Texas A&M University (TAMU) is outlined. Data have been collected along two measurement lines from two and multi-sensor arrays using a variety of sources. The data from each measurement line are processed separately. The STA/LTA procedure is applied in order to determine the P-waves arrival time. The P-wave velocity profile is determined by solving an inverse problem, where the difference between the theoretical arrival time, corresponding to a horizontally layered halfspace, with the experimental arrival time is minimized. The classical SASW method as well as the frequency-wavenumber analysis are used to determine the experimental dispersion curve. The dispersion curve is subsequently inverted to determine the S-wave velocity profile, using the a priori determined P-wave velocity profile. The width of peaks of the response in the frequency-wavenumber domain is used to determine the experimental attenuation curve. The attenuation curve is finally inverted to give the material damping ratio profile, while the already determined P- and S-wave velocity profiles are fixed in the inversion procedure. The determined soil profile is finally used to make a comparison between the theoretical and experimental frequency-wavenumber spectrum. The correspondence with experimental results is good. © 2011 ASCE.status: publishe

Robust topology optimization of structures with imperfect geometry based on geometric nonlinear analysis

© 2014 Elsevier B.V. Topology optimization often leads to structures consisting of slender elements which are particularly sensitive to geometric imperfections. Such imperfections might affect the structural stability and induce large displacement effects in these slender structures. This paper therefore presents a robust approach to topology optimization which accounts for geometric imperfections and their potentially detrimental influence on the structural stability. Geometric nonlinear effects are incorporated in the optimization by means of a Total Lagrangian finite element formulation in the minimization of end-compliance. Geometric imperfections are modeled as a vector-valued random field in the design domain. The resulting uncertain performance of the design is taken into account by minimizing a weighted sum of the mean and standard deviation of the compliance in the robust optimization problem. These stochastic moments are typically estimated by means of sampling methods such as Monte Carlo simulation. However, these methods require multiple independent nonlinear finite element analyses in each design iteration of the optimization algorithm. An efficient solution algorithm which uses adjoint differentiation in a second-order perturbation method is therefore developed to estimate the stochastic moments during the optimization. Two applications with structures that exhibit different types of structural instabilities are examined. In both cases, it is demonstrated by means of an extensive Monte Carlo simulation that the deterministic design is very sensitive to imperfections, while the design obtained by means of the proposed method is much more robust.publisher: Elsevier articletitle: Robust topology optimization of structures with imperfect geometry based on geometric nonlinear analysis journaltitle: Computer Methods in Applied Mechanics and Engineering articlelink: http://dx.doi.org/10.1016/j.cma.2014.11.028 content_type: article copyright: Copyright © 2014 Elsevier B.V. All rights reserved.status: publishe

The use of SASW tests to determine the material damping ratio in the soil

This paper presents a technique for the determination of the material damping ratio of shallow soil layers. It is based on the Spectral Analysis of Surface Waves (SASW) test. The technique is an alternative to existing methods, where the damping ratio is determined from the spatial decay of the Rayleigh wave. These methods are based on the hypothesis that the response of the soil in the SASW test is due to a single mode surface wave. Therefore, the resulting attenuation curve can become erroneous when higher modes contribute to the soil's response. Moreover, in these methods, the estimate of the attenuation curve is based on an estimate of the geometric spreading function. The latter is computed using the shear wave velocity of the soil, which is determined by inversion of the experimental dispersion curve. Errors in the experimental dispersion curve and in the inversion procedure lead to an erroneous geometric spreading factor and, consequently, experimental attenuation curve. In the proposed technique, the wave field recorded in the SASW test is transformed to the frequency-wavenumber domain by means of a discrete approximation to the Hankel transformation. The resulting (experimental) spectrum exhibits peaks corresponding to the Rayleigh modes. The peak corresponding to the fundamental Rayleigh wave is identified and used to determine the experimental dispersion and attenuation curves and, subsequently, the soil profile. The dispersion curve is derived from the peak's position, while the attenuation curve is derived from its width, using the half-power bandwidth method. In this technique there is no need for calculating the geometric damping. The occurrence of higher Rayleigh modes does not affect the attenuation curve associated with the fundamental Rayleigh wave, as higher modes appear as separate peaks in the $f$-$k$ spectrum and do not interfere with the peak corresponding to the fundamental Rayleigh wave. The method is applied to data collected from a test site Lincent in Belgium.status: publishe

EDT: An ElastoDynamics Toolbox for MATLAB

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EDT: An ElastoDynamics Toolbox for MATLAB

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The generation of hierarchic structures via robust 3D topology optimisation

© 2017 Elsevier Ltd Commonly used building structures often show a hierarchic layout of structural elements. It can be questioned whether such a layout originates from practical considerations, e.g. related to its construction, or that it is (relatively) optimal from a structural point of view. This paper investigates this question by using topology optimisation in an attempt to generate hierarchical structures. As an arbitrarily standard design case, the principle of a traditional timber floor that spans in one direction is used. The optimisation problem is first solved using classical sensitivity and density filtering. This leads indeed to solutions with a hierarchic layout, but they are practically unusable as the floor boarding is absent. A Heaviside projection is therefore considered next, but this does not solve the problem. Finally, a robust approach is followed, and this does result in a design similar to floor boarding supported by timber joists. The robust approach is then followed to study a floor with an opening, two floors that span in two directions, and an eight-level concrete building. It can be concluded that a hierarchic layout of structural elements likely originates from being optimal from a structural point of view. Also clear is that this conclusion cannot be obtained by means of standard topology optimisation based on sensitivity or density filtering (as often found in commercial finite element codes); robust 3D optimisation is required to obtain a usable, constructible (or in the future: 3D printable) structural design, with a crisp black-and-white density distribution.status: publishe

Global Size Optimization of Statically Determinate Trusses Considering Displacement, Member, and Joint Constraints

© 2015 American Society of Civil Engineers. Realistic truss design optimization problems are often governed by practical constraints. Because of the complexity of these constraints, usually only member constraints are taken into account during the optimization, and joint constraints are accounted for in a manual postprocessing step. This paper proposes a method to account for joint constraints in the global discrete size optimization of a steel truss structure. The design of an N-type truss girder is considered first without and then with the joint constraints specified in the Eurocode. To guarantee global optimality in both cases, the optimization problem is reformulated as a mixed-integer linear program. A statically determinate analysis model is adopted so as to ensure that all joint constraints can be reformulated as linear functions. If the joint constraints are not considered in the optimization, a design is obtained where the joints need additional strengthening. This can be done by manually selecting heavier sections, which often leads to a suboptimal result, or by strengthening the joints (e.g., by means of stiffening plates), which has a serious effect on the fabrication cost. If the joint constraints are considered in the optimization, they are automatically satisfied by the final design. The weight of this design is about 15% higher than in the first case. This shows that the joint constraints have a significant effect on the optimal design. If the joint constraints are accounted for in a suboptimal way (e.g., by manually selecting heavier sections), the additional weight may be even higher. Taking into account joint constraints in the optimization leads to a cost reduction at two levels: in terms of engineering cost (no manual postprocessing step is needed) and fabrication cost (using unnecessarily heavy sections and joint strengthening are avoided).status: publishe