Publications of Eduardo Felipe Fernandez Sanchez
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See detailTopology Optimization for Large-Scale Additive Manufacturing: Generating designs tailored to the deposition nozzle size
Fernandez Sanchez, Eduardo Felipe ULiege; Ayas, Can; Langelaar, Matthijs et al

in Virtual and Physical Prototyping (2021), 16:2

Additive Manufacturing (AM) processes intended for large-scale components deposit large volumes of material to shorten process duration. This reduces the resolution of the AM process, which is typically ... [more ▼]

Additive Manufacturing (AM) processes intended for large-scale components deposit large volumes of material to shorten process duration. This reduces the resolution of the AM process, which is typically defined by the deposition nozzle size. If the resolution limitation is not considered when designing for Large-Scale Additive Manufacturing (LSAM), difficulties can arise in the manufacturing process, which may require the adaptation of deposition parameters. This work incorporates the nozzle size constraint into Topology Optimisation (TO) in order to generate optimised designs suitable to the process resolution. This article proposes and compares two methods, which are based on existing TO techniques that enable control of minimum and maximum member size, and of minimum cavity size. The first method requires the minimum and maximum member size to be equal to the deposition nozzle size, thus design features of uniform width are obtained. The second method defines the size of solid members sufficiently small for the resulting structure to resemble a structural skeleton, which can be interpreted as the deposition path. Through filtering and projection techniques, the thin structures are thickened according to the chosen nozzle size. Thus, a topology tailored to the deposition nozzle size is obtained along with a deposition proposal. The methods are demonstrated and assessed using 2D and 3D benchmark problems. [less ▲]

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See detailAnalytical relationships for imposing minimum length scale inthe robust Topology Optimization formulation
Trillet, Denis ULiege; Duysinx, Pierre ULiege; Fernandez Sanchez, Eduardo Felipe ULiege

in Structural and Multidisciplinary Optimization (2021), 64

When using the robust topology optimization formulation in the density framework, the minimum size of the solid and void phases must be imposed implicitly through the parameters that define the density ... [more ▼]

When using the robust topology optimization formulation in the density framework, the minimum size of the solid and void phases must be imposed implicitly through the parameters that define the density filter and the smoothed Heaviside projection. Finding these parameters can be time consuming and cumbersome, hindering a general code implementation of the robust formulation. Motivated by this issue, in this article we provide analytical expressions that explicitly relate the minimum length scale and the parameters that define it. The expressions are validated on a density-based framework. To facilitate the reproduction of results, MATLAB codes are provided. [less ▲]

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See detailTopology Optimization Including Additive Manufacturing Constraints
Fernandez Sanchez, Eduardo Felipe ULiege

Doctoral thesis (2020)

The development of new materials and new manufacturing techniques have experienced a rapid development in the past few decades, and today designers have access to a large set of processes and materials to ... [more ▼]

The development of new materials and new manufacturing techniques have experienced a rapid development in the past few decades, and today designers have access to a large set of processes and materials to fabricate their designs. However, the conventional trial-and-error or other empirical design methods have become cumbersome and inefficient, while technological design tools such as topology optimization have become a breakthrough in design. Topology optimization supports the structural design by generating innovative concepts with high performance to weight ratio. The design tool usually proposes highly complex geometries that are difficult or even impossible to manufacture by conventional manufacturing processes. Fortunately, new Additive Manufacturing (AM) techniques provide a greater free-form freedom and enable the production of highly efficient, yet complex, optimized designs. Nonetheless, even the most advanced AM processes have their technological limitations. For instance, it is difficult to print parts with very small details or very large dimensions. It is also difficult to print parts with insufficient mechanical support during the layer-by-layer deposition process. Likewise, processes that deposit large volumes of material present difficulties related to the deposition path. This thesis introduces manufacturing constraints in density-based topology optimization in order to improve the manufacturability of the optimized designs. Specifically, geometrical restrictions are addressed aiming at imposing minimum member size, minimum cavity size, maximum member size, minimum separation distance between solid members, and minimum part inclination to reduce the use of sacrificial support material. The minimum size of the parts is imposed through filtering techniques. The maximum size is controlled using local volume restrictions, which are gathered into a single global constraint using aggregation functions. The minimum gap between solid members is also imposed through local volume restrictions, but these are applied in regions whose geometry enables to control the separation distance between parts and not their maximum size. The minimum inclination of the parts is imposed through local constraints that compare the surface slope with a critical baseline. The research is conducted within the density-based topology optimization framework and implemented in open-access codes suitable for solving 2D and 3D large-scale design problems. The assessed constraints demonstrate the ability to influence directly and indirectly the components manufacturability. For example, it is noted that the maximum size restriction can be used to address some limitations of processes depositing large volumes of material, such as the Wire Arc Additive Manufacturing (WAAM). In addition, the proposed methods show the ability to produce solutions with low amounts of intermediate densities and well-defined surfaces, which facilitates the interpretation and manufacture of the optimized designs. In particular cases, designs may feature such reduced complexity that they can even be manufactured by conventional manufacturing processes. [less ▲]

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See detailImposing minimum and maximum member size, minimum cavity size, and minimum separation distance between solid members in topology optimization
Fernandez Sanchez, Eduardo Felipe ULiege; Yang, Kai-ke; Koppen, Stijn et al

in Computer Methods in Applied Mechanics and Engineering (2020), 368

This paper focuses on density-based topology optimization and proposes a combined method to simultaneously impose Minimum length scale in the Solid phase (MinSolid), Minimum length scale in the Void phase ... [more ▼]

This paper focuses on density-based topology optimization and proposes a combined method to simultaneously impose Minimum length scale in the Solid phase (MinSolid), Minimum length scale in the Void phase (MinVoid) and Maximum length scale in the Solid phase (MaxSolid). MinSolid and MinVoid mean that the size of solid parts and cavities must be greater than the size of a prescribed circle or sphere. This is ensured through the robust design approach based on eroded, intermediate and dilated designs. MaxSolid seeks to restrict the formation of solid parts larger than a prescribed size, which is imposed through local volume restrictions. In the first part of this article, we show that by proportionally restricting the maximum size of the eroded, intermediate and dilated designs, it is possible to obtain optimized designs satisfying, simultaneously, MinSolid, MinVoid and MaxSolid. However, in spite of obtaining designs with crisp boundaries, some results can be difficult to manufacture due to the presence of multiple rounded cavities, which are introduced by the maximum size restriction with the sole purpose of avoiding thick solid members in the structure. To address this issue, in the second part of this article we propose a new geometric constraint that seeks to control the minimum separation distance between two solid members, also called the Minimum Gap (MinGap). Differently from MinVoid, MinGap introduces large void areas that do not necessarily have to be round. 2D and 3D test cases show that simultaneous control of MinSolid, MinVoid, MaxSolid and MinGap can be useful to improve the manufacturability of maximum size constrained designs. [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

in Structural and Multidisciplinary Optimization (2020), 61(6), 2467-2480

This work aims at introducing misalignment response in the design of mechanical transmission components using topology optimization. Misalignment considerations can be of high importance for various ... [more ▼]

This work aims at introducing misalignment response in the design of mechanical transmission components using topology optimization. Misalignment considerations can be of high importance for various industrial applications as in gearbox or differential, where aligned axes are to be ensured during the usage of the part. Nevertheless, to the authors’ knowledge, no work so far implements such response in a topology optimization framework. In this contribution, misalignment between two spatial vectors is evaluated in various ways using trigonometry and vector functions. The misalignment is formulated through the spatial displacements of the constituent nodes of the objective vectors. The authors choose a formulation among other and implement the later in a 2D topology framework for further investigation on test cases. Issues such as material disconnection, non-discrete solutions or lack of engineering meaning are tackled along this work by the introduction of constraints and parametric studies. A performance test is achieved on a simplified gearbox transmission system to assess the performance between designs with or without misalignment considerations.Manufacturing constraints are introduced to improve the manufacturability of the optimized solution. Subsequently a 3D test case further highlights the usefulness of this contribution. [less ▲]

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See detailLength scale control and building orientation in topology optimization for additive manufacturing
Fernandez Sanchez, Eduardo Felipe ULiege; Duysinx, Pierre ULiege

Conference (2019, September 12)

Additive manufacturing (AM) and topology optimization have allowed a significant progress in the development of highly efficient and lightweight components. However, there are still some technological ... [more ▼]

Additive manufacturing (AM) and topology optimization have allowed a significant progress in the development of highly efficient and lightweight components. However, there are still some technological limitations to account for which prevent the direct link between topology optimization and AM. The goal of this research conducted during the research project AERO+ sponsored by Walloon Region, is to consider manufacturing constraints as soon as the early stage of the design, i.e. during topology optimization, to propose optimized designs that are close to be ready for additive manufacturing, or at least involve a minimum amount of modification. In this context, length scale control has been an active topic of research as it encompasses a wide variety of manufacturing constraints. In the first part of this work, we focus on the maximum size constraint, which introduces void regions into massive zones to prevent the formation of structural features that are thicker than a prescribed size. The formulation does not control the geometry of the introduced cavities which could bring difficulties to manufacturing. For instance, the constraint tends to place structural members with a small separation distance between them, and to significantly increase the amount of closed cavities in the optimized design (Fig. 1). In this work we present two strategies to control the geometry of the cavities in a maximum-size-constrained problem. The first one is based on the robust design approach based on eroded, intermediate and dilated projections. It is shown that restricting the maximum size on all three projections effectively enforces the minimum length scale of the void phase on the blueprint design (Fig. 2). The second strategy is based on the maximum size formulation. It is a constraint that introduces large void regions into massive zones to increase the separation distance between solid members generated by the maximum size constraint. Examples, including both 2D and 3D design domains, indicate that the proposed approaches significantly reduce the quantity of closed cavities and increases the minimum size of those remaining (Fig. 3). By reducing the complexity of the design, those contributions may facilitate manufacturability of maximum-size constrained components. The overhang limitation of AM has been another topic of interest in topology optimization. Several authors have recently proposed methods to avoid the overhanging features in the optimized design. Most of them operate with a user-defined building direction, thus, if the selected orientation is not appropriate, structural performance could be drastically compromised. In the second part of this work we present a gradient-based overhang constraint that intends to follow the best printing direction during the optimization process. The main idea is to evaluate printability for different user-defined building orientations. The least penalizing overhang-constraint is added in the topology optimization problem using aggregation functions. Due to the local nature of the formulation, the method is easily parallelizable and of low computational cost. The method is evaluated on 2D and 3D test cases. [less ▲]

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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 detailNote on Spatial Gradient Operators and Gradient-based Minimum Length Constraints in SIMP Topology Optimization
Yang, Kai-ke; Fernandez Sanchez, Eduardo Felipe ULiege; Niu, Cao et al

in Structural and Multidisciplinary Optimization (2019)

Spatial gradient information of density field in SIMP (Solid Isotropic Material with Penalization) topology optimization is very useful for imposing overhang angle and minimum length (size) manufacturing ... [more ▼]

Spatial gradient information of density field in SIMP (Solid Isotropic Material with Penalization) topology optimization is very useful for imposing overhang angle and minimum length (size) manufacturing constraints or achieving shell-infill optimization. However, the computation of density gradient is an approximation since the design space is discretized. There are several operators for this purpose, which arise from the image processing field. This note compares different gradient operators in the context of SIMP topology optimization method, and suggests a new computation strategy to improve the accuracy of gradient estimation. We take a case study of spatial gradient-based minimum size constraints. New structural indicator functions are proposed to improve the general applicability of previous gradient-based minimum length constraints. This study is carried out in 2D structure examples to validate the methodology. Abstract Spatial gradient information of density field in SIMP (Solid Isotropic Material with Penalization) topology optimization is very useful for imposing overhang angle and minimum length (size) manufacturing constraints or achieving shell-infill optimization. However, the computation of density gradient is an approximation since the design space is discretized. There are several operators for this purpose, which arise from the image processing field. This note compares different gradient operators in the context of SIMP topology optimization method, and suggests a new computation strategy to improve the accuracy of gradient estimation. We take a case study of spatial gradient-based minimum size constraints. New structural indicator functions are proposed to improve the general applicability of previous gradient-based minimum length constraints. This study is carried out in 2D structure examples to validate the methodology. [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 detailImposing Manufacturing Constraints in Topological Optimization of 2D Fuel Cell flow problems using OpenFOAM
Alarcon Soto, Pablo ULiege; Fernandez Sanchez, Eduardo Felipe ULiege; Bauduin, Simon ULiege et al

in Proceedings of the 13th World Congress of Structural and Multidisciplinary Optimization (WCSMO-13) (2019, May)

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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 detailImposing the distance between solid members generated by maximum size constraints in topology optimization
Fernandez Sanchez, Eduardo Felipe ULiege; Duysinx, Pierre ULiege

Poster (2018, October 08)

The combination of topology optimization and additive manufacturing has brought a recent break-through in engineering. Topology optimization aims at generating innovative concepts with high performance to ... [more ▼]

The combination of topology optimization and additive manufacturing has brought a recent break-through in engineering. Topology optimization aims at generating innovative concepts with high performance to weight ratio, but the optimized designs are often difficult to fabricate as-it-is using classical fabrication processes. In the AERO+ research project [1], we focus on metal additive manufacturing processes, and particularly on Electron Beam Melting (EBM) and Selective Layer Manufacturing (SLM) processes. Among others, the maximum size of structural elements has been reported as a manufacturing limitation for these processes mainly due to overheating problems. The maximum size constraint in topology optimization is based on restricting the amount of material within the neighborhood of each point in the design domain [2]. Its role is to split the bulky material during the topology optimization process. The constraint introduces extra structural members in the design, such as bars or sheets, which tend to remain very close to each other. This greatly increases the complexity of the design and therefore of the manufacturing process, as pointed in [3]. This work aims to improve the manufacturability of such designs. To this end, a new constraint is proposed capable of separating the structural members according to the user’s needs. The proposed constraint, as well as the maximum size, restricts the quantity of material within the neighborhood of each point in the design domain. This is achieved by asking for a specific amount of voids within the test region. However, there is a small difference in the involved parameters which allows to separate the structural members instead of constraining their size. For this purpose, the amount of voids to be included within the test region is a function of the distance between bars, as shown in Figure 1. The local constraints are aggregated using the p-mean function in order to avoid the computational overburden on the optimizer. The method is validated for compliance minimization on 2D and 3D design domains (Figure 2 and 3), showing that the proposed constraint is capable of reducing the geometric complexity of designs with maximum size constraints. [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 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 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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