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See detailAn aggregation strategy of maximum size constraints in density-based topology optimization
Fernandez Sanchez, Eduardo Felipe ULiege; Collet, Maxime; Alarcon Soto, Pablo ULiege et al

in Structural and Multidisciplinary Optimization (2019)

The maximum size constraint restricts the amount of material within a test region in each point of the design domain, leading to a highly constrained problem. In this work, the local constraints are ... [more ▼]

The maximum size constraint restricts the amount of material within a test region in each point of the design domain, leading to a highly constrained problem. In this work, the local constraints are gathered into a single one using aggregation functions. The challenge of this task is presented in detail, as well as the proposed strategy to address it. The latter is validated on different test problems as the compliance minimization, the minimum thermal compliance, and the compliant mechanism design. These are implemented in the MATLAB software for 2D design domains. As final validation, a 3D compliance minimization problem is also shown. The study includes two well-known aggregation functions, p-mean and p-norm. The comparison of these functions allows a deeper understanding about their behavior. For example, it is shown that they are strongly dependent on the distribution and amount of data. In addition, a new test region is proposed for the maximum size constraint which, in 2D, is a ring instead of a circle around the element under analysis. This slightly change reduces the introduction of holes in the optimized designs, which can contribute to improve manufacturability of maximum size–constrained components. [less ▲]

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See detailAn overhang constraint adaptable to a proper building orientation
Fernandez Sanchez, Eduardo Felipe ULiege; Yang, Kaike; Koutla, Ioanna ULiege et al

in World Congress of Structural and Multidisciplinary Optimization (WCSMO13), May 20-24, 2019, Beijing, China. (2019, May 20)

In additive manufacturing processes, the critical overhang angle of downward facing surfaces limits printability of parts. To consider this limitation of the process in topology optimization, several ... [more ▼]

In additive manufacturing processes, the critical overhang angle of downward facing surfaces limits printability of parts. To consider this limitation of the process in topology optimization, several approaches have been proposed in the literature. Most of them operate with a user-defined building direction, thus, if the orientation is not appropriate, structural performance could be drastically compromised. This work aims to reduce the dependence of the user on the definition of the building direction. We make use of a gradient-based constraint due to the low computation cost it demands in comparison to layer-by-layer approaches. The method is demonstrated on 2D and 3D examples. [less ▲]

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See detailMisalignment topology optimization with manufacturing constraints
Bauduin, Simon ULiege; Alarcon Soto, Pablo ULiege; Fernandez Sanchez, Eduardo Felipe ULiege et al

Conference (2019, May)

Topology optimization design problems aims at the minimization of an objective function while satisfying various constraints. Since Bendsøe and Kikuchi (1988) topology optimization has mostly been based ... [more ▼]

Topology optimization design problems aims at the minimization of an objective function while satisfying various constraints. Since Bendsøe and Kikuchi (1988) topology optimization has mostly been based on “compliance formulation” as it provides solutions where the displacements are globally controlled. However, this formulation doesn’t take into account special design requirements over local displacements or even relative displacements such as the misalignment between two gear axes. This point is of paramount importance to achieve the best efficiency in many mechanical transmission devices. Although critical in practical engineering designs, this question is especially challenging as very few contributions exist on the subject. Coupling topology optimization with the misalignment minimization can provide promising results once right formulation can be identified. At first, the misalignment can be expressed in various ways. A few formulations have been tested on a simple case study composed of two gear axes to be align. This allowed us to choose a promising expression for the misalignment and furthermore to investigate its efficiency on 2D test cases consisting of a simplified one-stage-reduction box and a simplified differential. The objective is to minimize the misalignment between two beams representing the gears engaged with each other. The formulations have been implemented in our in-house MATLAB code. Different issues have been highlighted and solved. The first basic implementation leads to unclear optimized material distributions as well as non-converged solutions. Optimization results have been investigated and new design formulations have been elaborated to tackle the various issues. We have showed that imposing a constraint on the measure of non-discreteness is able to enforce black-and-white solution with actual engineering meaning. The second issue is a possible disconnection of the structure coming from an ill-posed nature of the optimization problem as only local constraints are taken into account and no global performance of the problem is required. This issue is partly tackled by imposing a constraint on the measure of discreteness, but another natural way is to introduce an additional constraint on the global compliance of the component. According to our numerical experiments, the proposed formulation is able to yield optimized solutions that make sense from an engineering point of view in 2D but also in 3D applications. Presently we are also introducing manufacturing constraints such as minimum/maximum size and minimum gap to further improve the manufacturability of the optimized solutions. The 3D academic torsion problem (see below) illustrates the effectiveness of the proposed formulation including misalignment in a 3D case. The presentation will be illustrated with several industrial applications. [less ▲]

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See detailMartian dust storm impact on atmospheric H 2 O and D/H observed by ExoMars Trace Gas Orbiter
Vandaele, A. C.; Korablev, O.; Daerden, F. et al

in Nature (2019), 568

Global dust storms on Mars are rare 1,2 but can affect the Martian atmosphere for several months. They can cause changes in atmospheric dynamics and inflation of the atmosphere 3 , primarily owing to ... [more ▼]

Global dust storms on Mars are rare 1,2 but can affect the Martian atmosphere for several months. They can cause changes in atmospheric dynamics and inflation of the atmosphere 3 , primarily owing to solar heating of the dust 3 . In turn, changes in atmospheric dynamics can affect the distribution of atmospheric water vapour, with potential implications for the atmospheric photochemistry and climate on Mars 4 . Recent observations of the water vapour abundance in the Martian atmosphere during dust storm conditions revealed a high-altitude increase in atmospheric water vapour that was more pronounced at high northern latitudes 5,6 , as well as a decrease in the water column at low latitudes 7,8 . Here we present concurrent, high-resolution measurements of dust, water and semiheavy water (HDO) at the onset of a global dust storm, obtained by the NOMAD and ACS instruments onboard the ExoMars Trace Gas Orbiter. We report the vertical distribution of the HDO/H 2 O ratio (D/H) from the planetary boundary layer up to an altitude of 80 kilometres. Our findings suggest that before the onset of the dust storm, HDO abundances were reduced to levels below detectability at altitudes above 40 kilometres. This decrease in HDO coincided with the presence of water-ice clouds. During the storm, an increase in the abundance of H 2 O and HDO was observed at altitudes between 40 and 80 kilometres. We propose that these increased abundances may be the result of warmer temperatures during the dust storm causing stronger atmospheric circulation and preventing ice cloud formation, which may confine water vapour to lower altitudes through gravitational fall and subsequent sublimation of ice crystals 3 . The observed changes in H 2 O and HDO abundance occurred within a few days during the development of the dust storm, suggesting a fast impact of dust storms on the Martian atmosphere. © 2019, The Author(s), under exclusive licence to Springer Nature Limited. [less ▲]

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See detailNo detection of methane on Mars from early ExoMars Trace Gas Orbiter observations
Korablev, O.; Vandaele, A. C.; Montmessin, F. et al

in Nature (2019), 568

The detection of methane on Mars has been interpreted as indicating that geochemical or biotic activities could persist on Mars today 1 . A number of different measurements of methane show evidence of ... [more ▼]

The detection of methane on Mars has been interpreted as indicating that geochemical or biotic activities could persist on Mars today 1 . A number of different measurements of methane show evidence of transient, locally elevated methane concentrations and seasonal variations in background methane concentrations 2–5 . These measurements, however, are difficult to reconcile with our current understanding of the chemistry and physics of the Martian atmosphere 6,7 , which—given methane’s lifetime of several centuries—predicts an even, well mixed distribution of methane 1,6,8 . Here we report highly sensitive measurements of the atmosphere of Mars in an attempt to detect methane, using the ACS and NOMAD instruments onboard the ESA-Roscosmos ExoMars Trace Gas Orbiter from April to August 2018. We did not detect any methane over a range of latitudes in both hemispheres, obtaining an upper limit for methane of about 0.05 parts per billion by volume, which is 10 to 100 times lower than previously reported positive detections 2,4 . We suggest that reconciliation between the present findings and the background methane concentrations found in the Gale crater 4 would require an unknown process that can rapidly remove or sequester methane from the lower atmosphere before it spreads globally. [less ▲]

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See detailConstraints Aggregation in Topology Optimization
Fernandez Sanchez, Eduardo Felipe ULiege; Collet, Maxime ULiege; Bauduin, Simon ULiege et al

Scientific conference (2018, September 17)

A vast amount of the methods that address local design requirements introduce a wide set of constraints within the optimization problem. This local formulation calls for the use of aggregation functions ... [more ▼]

A vast amount of the methods that address local design requirements introduce a wide set of constraints within the optimization problem. This local formulation calls for the use of aggregation functions in order to avoid the computational burden on the optimizer. This step of collecting the constraints within a few representative ones seems as a simple implementation detail coming at the final stage of the formulation. Therefore it is often neglected in the discussion. However if this aggregation step is not well treated the success of the whole method may be compromised, and in many cases the simplest part of the constraint becomes time-consuming or even, the hardest point of the formulation. Aggregation functions are built to be smooth and differentiable approximations of the max function. In addition their sensitivity information should be smooth in order to be used in efficient continuous optimization algorithms. They have also to catch accurately the most critical constraints to mimic the locally constrained problem. The classical application is in the field of stress constraints, where a large amount of contributions have been made on the subject. Most of the research contributes with new aggregation techniques, which are adapted to the context of topology optimization with stress constraints. However, to tailor high quality global manufacturing constraints, we need to make further progress in the understanding of the aggregation functions when used in the topology optimization. To this end, we perform a deep theoretical investigation and a quantitative numerical assessment of the behavior of these functions when being used in different formulations of manufacturing and mechanical constraints. Specifically, we focus the study on p-mean and p–norm functions within the framework of density methods. We include in the analysis methods to introduce: i) maximum size control, ii) minimum gap between solid members, iii) minimum size, iii) overhang control for additive manufacturing and iv) stress constraints. Some important observations obtained from this study are: p-norm depends on the amount of data that is being aggregated, making it more unstable under mesh refinement. On the other hand, p-mean is less dependent on mesh modifications but it is likely to produce results that do not satisfy every local constraint. In addition, by looking at the sensitivities it is possible to have an insight of the nonlinearity of a method. [less ▲]

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See detailCritical Plane approach for fatigue resistance using stress-based topology optimization
Collet, Maxime ULiege; Bauduin, Simon ULiege; Fernandez Sanchez, Eduardo Felipe ULiege et al

Conference (2018, September 17)

Fatigue is responsible for almost 80% of the overall breakages in mechanical components (Oest(2017)). Such a failure phenomenon must be prevented as soon as the early stage of design. Since the seminal ... [more ▼]

Fatigue is responsible for almost 80% of the overall breakages in mechanical components (Oest(2017)). Such a failure phenomenon must be prevented as soon as the early stage of design. Since the seminal works by Augut Wöhler, see Schültz(1996), the literature counts various methods able to prevent fatigue failure (Schijve(2003)). In the automotive industry, the components undergo a high number of cycles leading to consider the stresses as variables into the fatigue criteria. Topology optimization has become a valuable tool used to propose preliminary designs as attested by several commercial software on the market. Combining fatigue design with a stress-based topology optimization procedure is therefore natural. In this work, the coupling of the Dang Van criterion (Dang Van et al(1989), Dang Van(2010)) within a topology optimization code is investigated to provide fatigue resistant layouts. The choice of the Dang Van criterion is encouraged by its wide usage in the automotive industry (Koutiri(2011)). The former is based on the concept of critical plane in the vicinity of which plastic yielding occurs. With the hypothesis of reaching the elastic shakedown state, the criterion establishes that crack initiation is prevented if the microscopic stress state remains below a prescribed threshold. Following the framework proposed by Dang Van (Dang Van(1989)), the fatigue failure procedure is introduced into a density-based topology optimization code embedding stress constraints. The first step of the procedure is to construct the microscopic stress using a regular finite element analysis and evaluate a damage value in the sense of Dang Van. A sub-optimization routine is necessary to solve a min-max problem in order to find the residual stress tensor to construct the microscopic stresses (Mandel et al(1977), Bernasconi(2002)). This sub-optimization might be time consuming and must be dealt with care. In a second step, this work shows how the fatigue resistance procedure is implemented into a density-based topology optimization using stress constraints and in particular how the sensitivity analysis is performed using the adjoint approach (Tortorelli and Michaleris(1994)). The optimization process is carried out with the Method of Moving Assymptotes (Svanberg(1987)) along the qp-relaxation (Bruggi(2008)) to overcome the singularity phenomenon of the stress constraints. The proposed optimization framework is evaluated in terms of its numerical performances and is compared to classical results obtained by a regular stress-based topology optimization on several benchmarks. [less ▲]

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See detailImposing minimum gap distance in topology optimization through maximum size constraints
Fernandez Sanchez, Eduardo Felipe ULiege; Collet, Maxime ULiege; Bauduin, Simon ULiege et al

Conference (2018, May 02)

Maximum size constraints in topology optimization increase the complexity of the designs. It introduces extra channels and cavities that hinder the manufacturability of the component. In this work the ... [more ▼]

Maximum size constraints in topology optimization increase the complexity of the designs. It introduces extra channels and cavities that hinder the manufacturability of the component. In this work the show some contributions to improve the manufacturability of designs that include a maximum size control in topology optimization. [less ▲]

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See detailOVERHANGING CONSTRAINTS IN ADDITIVE MANUFACTURINGUSING TWODIFFERENT TOOLS
Bauduin, Simon ULiege; Collet, Maxime; Fernandez Sanchez, Eduardo Felipe ULiege et al

Poster (2018)

As the manufacturing methods undergo huge evolution thanks to the emergence of additive manufacturing techniques, the interest of a coupling with the topology optimization problem is highly demanded by ... [more ▼]

As the manufacturing methods undergo huge evolution thanks to the emergence of additive manufacturing techniques, the interest of a coupling with the topology optimization problem is highly demanded by industries (such as automotive and aerospace). The challenges are still numerous around such coupling and this work focuses on the overhanging problem related to the metalic additive manufacturing technics(LBM and EBM). To tackle the problem various research directions are investigated and compared to another. [less ▲]

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See detailMISALIGNMENT TOPOLOGY OPTMIZATION
Bauduin, Simon ULiege; Alarcon Soto, Pablo ULiege; Fernandez Sanchez, Eduardo Felipe ULiege et al

Conference (2018)

Topology optimization problems aims at the minimization of an objective function while satisfying various constraints. This objective function has been based on “compliance formulation” since Bendsøe and ... [more ▼]

Topology optimization problems aims at the minimization of an objective function while satisfying various constraints. This objective function has been based on “compliance formulation” since Bendsøe and Kikuchi (1988) as it provides solutions where the displacements are globally controlled. However, this formulation doesn’t take into account special needs over local displacements or even relative displacements such as the misalignment between two gears. This point is of paramount importance to achieve the best efficiency. Although critical, this domain is especially challenging as very few contributions exist on the subject. Coupling topology optimization with the misalignment minimization can provide promising results once chosen the right formulation. The misalignment can be expressed in various ways. In this work a small amount of formulations were tested on a simple case study composed of two axes to be align. This allowed us to choose a promising expression for the misalignment and furthermore to investigate its efficiency on a 2D problem. The former consists of a box clamped on both sides where a load is applied in its center. The objective is to minimize the misalignment between two horizontal bars located at the middle of each clamped edges. This optimization problem was implemented in our in-house MATLAB code. Different issues were already highlighted during this simple test. The first one was an unclear optimized material distribution as well as a non-converged solution. This typical result of topology optimization has been investigated throughout the years and interesting methods were developed to tackle this issue. For our case study we have chosen to impose a constraint on the measure of discreteness in our optimization formulation to impose a more black-and-white solution with actual engineering meaning. The second issue was a disconnection of the structure coming from an ill-posed optimization formulation as only local constraints are taken into account and no global performance of the problem is required. This issue is furthermore emphasized by imposing a constraint on the measure of discreteness. Thusly a natural way to deal with it is to introduce a constraint on the global compliance of the solution. According to our tests we obtained interesting and engineering meaningful solutions on a 2D case. Our formulation of misalignment and our side constraints were furthermore also tested on a 3D torsion problem. [less ▲]

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See detailFatigue resistant designs using stress-based topology optimization
Collet, Maxime ULiege; Bauduin, Simon ULiege; Fernandez Sanchez, Eduardo Felipe ULiege et al

Conference (2017, September 15)

Fatigue is an important mode of failure in mechanical engineering and accounting for it as soon as the early stage of design using topology optimization sounds primordial. Structures undergoing high-cycle ... [more ▼]

Fatigue is an important mode of failure in mechanical engineering and accounting for it as soon as the early stage of design using topology optimization sounds primordial. Structures undergoing high-cycle fatigue can be described by the stress-based approach and then a stress-based topology optimization framework, which has received great interest since almost 20 years because of the innovative designs that can be achieved to answer strength requirements, can be used. Literature reports many good results for shape optimization [Mrzyglod & Zielinsky(2006)] whereas in the eld of topology optimization several authors have shown that considering fatigue in an optimization framework leads to more relevant solutions where fluctuating loads are involved [Holmberg E.(2015), Collet et al(2016), Sv ard(2015)]. The good behaviour of the implementation of an advanced fatigue criterion, i.e. the multiaxial Dang Van criterion [Dang Van et al(1989)] is first investigated in the framework of a density-based topology optimization problem. The choice of this fatigue criterion is justifed by its good applicability in automotive or aeronautic industry as well as its relevancy with respect to experimental results. We present the sensitivity analysis with stress constraints and present some classical benchmarks to illustrate the behaviour of the optimized solution. In a second time, the fatigue resistance is introduced in the well-known microstructural design [Sigmund (2000)] also know as architectured material design which are now considered in mechanical engineering because of their manufacturability thanks to additive manufacturing processes. Ensuring the fatigue resistance of the cellular material will by extension ensure the structural integrity of the overall structure itself. The optimization is performed by using the MMA optimizer [Svanberg(1987)] whereas the singularity phenomenon of the stress constraints is circumvented by using the qp-relaxation [Bruggi(2008)]. Both types of optimization framework are evaluated in term of their numerical performances and are compared to classical results generated by a regular stress-based topology optimization. Finally, the results are 3D-printed to assess for their manufacturability. [less ▲]

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See detailContributions to handle maximum size constraints in density-based topology optimization
Fernandez Sanchez, Eduardo Felipe ULiege; Collet, Maxime ULiege; Bauduin, Simon ULiege et al

Scientific conference (2017, September 14)

The maximum size formulation in topology optimization restricts the amount of material within a test region in each point in the design domain, leading to a highly constrained problem. In this work the ... [more ▼]

The maximum size formulation in topology optimization restricts the amount of material within a test region in each point in the design domain, leading to a highly constrained problem. In this work the local constraints are aggregated into a single one by p-mean and p-norm functions, classically used for stress constraints. Moreover, a new test region is investigated which is a ring instead of the classical circle around the element. These developments were implemented for compliance minimization with the MBB beam test case. Results indicate that p-mean performs better in the maximum size field than p-norm, because it underestimates the most violated constraint. This gives some relaxation to the problem that allows stiffer connections. Similar effect has been observed for the ring-shaped region which reduces the amount of holes that are introduced in the structure, specially in the connection of solid members. In addition, it is shown that the maximum size formulation allows the definition of the minimum gap between solid members which gives designers more control over the geometry. The developments have been illustrated and validated with compliance minimization tests of 2D-domains. [less ▲]

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See detailFatigue resistant designs using stress-based topology optimization
Collet, Maxime ULiege; Bauduin, Simon ULiege; Fernandez Sanchez, Eduardo Felipe ULiege et al

Conference (2017, June 08)

Stress based topology optimization has received great interest since almost 20 years because of the innovative designs that can be achieved to answer strength requirements. Fatigue is an important mode of ... [more ▼]

Stress based topology optimization has received great interest since almost 20 years because of the innovative designs that can be achieved to answer strength requirements. Fatigue is an important mode of failure in mechanical engineering and accounting for it as soon as the early stage of design using topology optimization sounds primordial. Literature reports many good results for shape optimization [Mrzyglod & Zielinsky(2006)] whereas in the field of topology optimization several authors have shown that considering fatigue in an optimization framework leads to more relevant solutions where fluctuating loads are involved [Holmberg E.(2015), Collet et al(2016), Svärd(2015)]. In order to check the good behavior of the implementation, we first investigate the implementation of an advanced fatigue criterion, i.e. the multiaxial Dang Van criterion [Dang Van et al(1989)], in the framework of a density-based topology optimization problem. The choice of this fatigue criterion is justifed by its good applicability in automotive or aeronautic industry as well as its relevancy with respect to experimental results. We present the sensitivity analysis with stress constraints and present some classical benchmarks to illustrate the behavior of the optimized solution. In a second time, we introduce the fatigue resistance in the well-known microstructural design [Sigmund (1999)]. The new additive manufacturing techniques allow to fabricate components exhibiting architectured materials. In this perspective, ensuring the fatigue resistance of the cellular material will by extension ensure the structural integrity of the overall structure itself. Both types of optimization framework are evaluated in term of their numerical performances and are compared to classical results generated by a regular stress-based topology optimization. Finally, the results are 3D-printed to assess for their manufacturability. [less ▲]

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See detailTopology optimization of mechanical components fabricated by additive manufacturing for a Shell Eco Marathon vehicle
Alarcon Soto, Pablo ULiege; Collet, Maxime ULiege; Bauduin, Simon ULiege et al

Conference (2017, June 07)

Since 2004, a team of students and researchers of University of Liege takes part to the Shell Eco Marathon race with a lightweight electric vehicle. The goal of this pedagogical project is to design ... [more ▼]

Since 2004, a team of students and researchers of University of Liege takes part to the Shell Eco Marathon race with a lightweight electric vehicle. The goal of this pedagogical project is to design, fabricate and operate a vehicle exhibiting the least energy consumption. A key factor to reduce the energy consumption is to minimize the vehicle mass. Besides the body structure made of CRFP, engineers have also to focus on the weight reduction of any mechanical parts of the powertrain, transmission and of rolling gear. The combination of topology optimization with additive manufacturing techniques allows to propose innovative designs exhibiting a high performance to weight ratio. Topology optimized designs are often characterized by a high geometrical complexity that is not possible to manufacture without 3D printing. This work presents the CAE design methodology that was developed to combine topology and shape optimization with 3d printing manufacturing. Novel developments both in shape and topology optimization have also been realized for the specific character of these components. The design methodology is illustrated with several applications of components of our new Eco Marathon prototype. They include a support for electric traction motors and different torque arms of the steering mechanism to be implemented in the new 2017 vehicle. The presentation is going to show the different design steps from the specifications and the formulation of the design problem to the 3D-printing of the parts: the topology optimization, interpretation and CAD reconstruction, shape optimization and detailed finite element verification of the solution. The optimization is performed thanks to the commercial software NX-TOPOL and the final CAD design is reconstructed in the CATIA environment software after a smoothing procedure in the NX-CAD environment. We show that the final design can be 3D-printed and a comparison with a design produced using traditional design approach is provided. [less ▲]

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See detailContributions to handle maximum size constraints in density-based topology optimization
Fernandez Sanchez, Eduardo Felipe ULiege; Collet, Maxime ULiege; Bauduin, Simon ULiege et al

in Fiebig, Sierk; Bletzinger, Kai-Uwe; Maute, Kurt (Eds.) et al Advances in Structural and Multidisciplinary Optimization (2017, June 05)

The maximum size formulation in topology optimization restricts the amount of material within a test region in each point in the design domain, leading to a highly constrained problem. In this work the ... [more ▼]

The maximum size formulation in topology optimization restricts the amount of material within a test region in each point in the design domain, leading to a highly constrained problem. In this work the local constraints are aggregated into a single one by p-mean and p-norm functions, classically used for stress constraints. Moreover, a new test region is investigated which is a ring instead of the classical circle around the element. These developments were implemented for compliance minimization with the MBB beam test case. Results indicate that p-mean performs better in the maximum size field than p-norm, because it underestimates the most violated constraint. This gives some relaxation to the problem that allows stiffer connections. Similar effect has been observed for the ring-shaped region which reduces the amount of holes that are introduced in the structure, specially in the connection of solid members. In addition, it is shown that the maximum size formulation allows the definition of the minimum gap between solid members which gives designers more control over the geometry. The developments have been illustrated and validated with compliance minimization tests of 2D-domains. [less ▲]

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See detailMicrostructural design using stress–based topology optimization
Collet, Maxime ULiege; Bruggi, Matteo; Noël, Lise ULiege et al

Conference (2016, September 12)

New additive manufacturing techniques break the limitations encountered for years when producing components descending from topology optimization. Classical design procedures focus on macro-structural ... [more ▼]

New additive manufacturing techniques break the limitations encountered for years when producing components descending from topology optimization. Classical design procedures focus on macro-structural optimization to sustain given loads but today innovative manufacturing processes allow considering structures exhibiting tailored microstructures, i.e. the well known microstructural design. The practical applications of structures including material design is mainly motivated by the greater performances that can be achieved compared to classical solutions. Microstructural design has been shown a great interest as attested by recent works. However, stress–based topology optimization has not yet been extensively exploited when addressing microstructural design using numerical homogenization though stress constraints is an important feature and have gained in interest in the field of topology optimization. This contribution investigates the problem of material design enforcing stress constraints within periodic microstructures by considering a representative volume element (RVE) subject to prescribed strain fields. The SIMP approach is adopted as material interpolation law while the optimization problems are solved using a sequential convex programming approach. In particular the well known method of moving asymptotes (MMA) is considered. Numerical homogenization is used to assess the effective elastic properties of the microstructures. The Von Mises stress criterion is used to impose the constraints on the stress level. This work discusses the formulation of a well-posed design problem as well as some numerical issues encountered. The developed solution procedure is first validated by comparison against analytical results, e.g. the single inclusion of Vigdergauz microstructure. [less ▲]

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See detailOverhanging Constraints in Addivitive Manufacturing Using Two Different Tools
Bauduin, Simon ULiege; Collet, Maxime ULiege; Duysinx, Pierre ULiege

Conference (2016, September 12)

Topology optimization is widely used as a design tool for advanced application in mechanical, aerospace and automotive industries. This technique offers an optimal distribution of a predetermined amount ... [more ▼]

Topology optimization is widely used as a design tool for advanced application in mechanical, aerospace and automotive industries. This technique offers an optimal distribution of a predetermined amount of material in a given design space. In the last years, a lot of efforts has been invested into the development of high performance methods such as homogenization, SIMP or BESO. However as the state of the art in manufacturing experiences evolution, a coupling between topology optimization and additive manufacturing is needed. Additive manufacturing has numerous advantages that fits the characteristics of topology optimized designs. It can manufacture highly complex design without high cost increase and furthermore continuous density material of the SIMP method could be manufactured by lattice structures. With all the opportunities given by the additive manufacturing the urge to bind the last one to topology optimization is heavily required. Specific constraints related to manufacturing issues have to be taken into account such as the need of supports structures to ensure a good heat evacuation during the manufacturing process, as well as to hold up overhanging section. Some researches have been done to try to include this constraint in the optimization problem such as Leary and al or Andrew T. Gaynor. However this work focuses on 2 different methods (projection scheme and mechanical approach) to tackle the overhanging problem and compare them . [less ▲]

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