Publications of Pierre Duysinx
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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 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 detailL'évolution de l'industrie automobile face aux tendances globales de la société
Duysinx, Pierre ULiege

Conference given outside the academic context (2018)

L’évolution de la société est travaillée par les grandes tendances globales de la société telles que la pollution, le réchauffement du climat, mais aussi l’urbanisation, le vieillissement de la population ... [more ▼]

L’évolution de la société est travaillée par les grandes tendances globales de la société telles que la pollution, le réchauffement du climat, mais aussi l’urbanisation, le vieillissement de la population, la digitalisation ou la recherche de la santé. Ces tendances globales permettent de remettre en perspective l’évolution de l’automobile vers les concepts de mobilité, de voiture connectée, de recherche d’efficacité énergétique. L’exposé montre également que les nouvelles évolutions de l’automobile qui se dessinent pour la prochaine décennie porteront également vers l’hyper individualisation et l’amélioration du bien-être et de la santé des passagers. Comprendre ces évolutions permet d’anticiper ces changements et d’y participer au lieu de les subir. [less ▲]

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See detailÉlectriques, hybrides, autonomes… Quelle mobilité pour demain ?
Duysinx, Pierre ULiege

Conference given outside the academic context (2018)

Une vision sur les systèmes de propulsion des véhicules terrestres jusqu'en 2030

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See detailSocietal megatrends and trends in vehicle technologies
Duysinx, Pierre ULiege

Conference given outside the academic context (2018)

The confrence enviions the future trends in automotive technologies at the light of societal megatrends. Different emerging technologies for the vehicle powertrain are envisionned for the next decade ... [more ▼]

The confrence enviions the future trends in automotive technologies at the light of societal megatrends. Different emerging technologies for the vehicle powertrain are envisionned for the next decade: piston engines with natural gas, battery electric vehicles, plug-in hybrid electric vehicles, fuel cells systems. In addition one must also consider the arrival of autonomous driving and of the race for lightweight design of cars. [less ▲]

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See detailThree-dimensional Topology Optimization of Planar Multilayer Busbar
Kuci, Erin; Velasco, Jonathan ULiege; Henrotte, François ULiege et al

Conference (2017, November 17)

This paper addresses the optimal design of three- dimensional planar multilayer busbar, through the general setting of topology optimization. The optimization problem is efficiently solved with a gradient ... [more ▼]

This paper addresses the optimal design of three- dimensional planar multilayer busbar, through the general setting of topology optimization. The optimization problem is efficiently solved with a gradient-based mathematical program- ming algorithm, that exploits a harmonic adjoint variational formulation sensitivity analysis for the harmonic linear mag- netodynamic problem. This formulation can handle topology design variables defined on a finite element mesh [less ▲]

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See detailDesign sensitivity analysis for shape optimization based on the Lie derivative
Kuci, Erin ULiege; Henrotte, François ULiege; Duysinx, Pierre ULiege et al

in Computer Methods in Applied Mechanics and Engineering (2017)

Abstract The paper presents a theoretical framework for the shape sensitivity analysis of systems governed by partial differential equations. The proposed approach, based on geometrical concepts borrowed ... [more ▼]

Abstract The paper presents a theoretical framework for the shape sensitivity analysis of systems governed by partial differential equations. The proposed approach, based on geometrical concepts borrowed from differential geometry, shows that sensitivity of a performance function (i.e. any function of the solution of the problem) with respect to a given design variable can be represented mathematically as a Lie derivative, i.e. the derivative of that performance function along a flow representing the continuous shape modification of the geometrical model induced by the variation of the considered design variable. Theoretical formulae to express sensitivity analytically are demonstrated in detail in the paper, and applied to a nonlinear magnetostatic and a linear elastic problem, following both the direct and the adjoint approaches. Following the analytical approach, one linear system of which only the right-hand side needs be evaluated (the system matrix being known already) has to be solved for each of the design variables in the direct approach, or for each performance functions in the adjoint approach. A substantial gain in computation time is obtained this way compared to a finite difference evaluation of sensitivity, which requires solving a second nonlinear system for each design variable. This is the main motivation of the analytical approach. There is some freedom in the definition of the auxiliary flow that represents the shape modification. We present a method that makes benefit of this freedom to express sensitivity locally as a volume integral over a single layer of finite elements connected to both sides of the surfaces undergoing shape modification. All sensitivity calculations are checked with a finite difference in order to validate the analytic approach. Convergence is analyzed in 2D and 3D, with first and second order finite elements. [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 detailDesign of microstructures using stress-based topology optimization
Collet, Maxime ULiege; Bruggi, Matteo; Noël, Lise ULiege et al

Conference (2016, August 22)

This paper aims at designing microstructures using stress-based topology optimization. Most of the developments so far have been made for compliance design in various field of applications as reflected in ... [more ▼]

This paper aims at designing microstructures using stress-based topology optimization. Most of the developments so far have been made for compliance design in various field of applications as reflected in the literature. The emergence of the new additive manufacturing techniques allows to consider porous material, such as lattice structures for instance, which ca be used for the design of structural components subject to various solicitations. Those components must account for the stress level to prevent failure everywhere in the microstructures and by extension the whole structure itself. This work proposes to design such microstructures using topology optimization with limitation on the stress level within the microstructures before printing the result. The homogenization technique is used to determine the equivalent material properties. The issues and perspectives are also discussed. [less ▲]

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See detailTopology optimization for minimum weight with compliance and simpli ed nominal stress constraints for fatigue resistance
Collet, Maxime ULiege; Bruggi, Matteo; Duysinx, Pierre ULiege

in Structural and Multidisciplinary Optimization (2016)

This work investigates a simpli ed approach to cope with the optimization of preliminary design of structures under local fatigue constraints along with a global enforcement on the overall compliance. The ... [more ▼]

This work investigates a simpli ed approach to cope with the optimization of preliminary design of structures under local fatigue constraints along with a global enforcement on the overall compliance. The problem aims at the minimization of the weight of linear elastic structures under given loads and boundary conditions. The expected sti ness of the optimal structure is provided by the global constraint, whereas a set of local stress-based constraints ask for a structure to be fatigue resistant. A modi ed Goodman fatigue strength comparison is implemented through the same formalism to address pressure-dépendent failure in materials as in Drucker-Prager strength criterion. As a simplification, the Sines approach is used to de ne the equivalent mean and alternating stresses to address the fatigue resistance for an infinite life time. Sines computation is based on the equivalent mean and alternate stress depending on the invariants of the stress tensor and itsdeviatoric part, respectively. The so-called singularity phenomenon is overcome by the implementation of a suitable qp-relaxation of the equivalent stress measures. Numerical examples are presented to illustrate the features of the achieved optimal layouts and of the proposed algorithm. [less ▲]

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See detailShape optimization of microstructural designs subject to local stress constraints within an XFEM-level set framework
Noël, Lise ULiege; Duysinx, Pierre ULiege

in Structural and Multidisciplinary Optimization (2016)

The present paper investigates the tailoring of bimaterial microstructures minimizing their local stress field exploiting shape optimization. The problem formulation relies on the extended finite element ... [more ▼]

The present paper investigates the tailoring of bimaterial microstructures minimizing their local stress field exploiting shape optimization. The problem formulation relies on the extended finite element method (XFEM) combined with a level set representation of the geometry, to deal with complex microstructures and handle large shape modifications while working on fixed meshes. The homogenization theory, allowing extracting the behavior of periodic materials built from the repetition of a representative volume element (RVE), is applied to impose macroscopic strain fields and periodic boundary conditions to the RVE. Classical numerical homogenization techniques are adapted to the selected XFEM-level set framework. Following previous works on analytical sensitivity analysis [31], the scope of the developed approach is extended to tackle the problem of stress objective or constraint functions. Finally, the method is illustrated by revisiting 2D classical shape optimization examples: finding the optimal shapes of single or multiple inclusions in a microstructure while minimizing its local stress field. [less ▲]

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See detailWeakly and fully coupled methods for structural optimization of flexible mechanisms
Tromme, Emmanuel ULiege; Bruls, Olivier ULiege; Duysinx, Pierre ULiege

in Multibody System Dynamics (2016), 38(4), 391-417

The paper concerns a detailed comparison between two optimization methods that are used to perform the structural optimization of flexible components within a multibody system (MBS) simulation. The ... [more ▼]

The paper concerns a detailed comparison between two optimization methods that are used to perform the structural optimization of flexible components within a multibody system (MBS) simulation. The dynamic analysis of flexible MBS is based on a nonlinear finite element formulation. The first method is a weakly coupled method, which reformulates the dynamic response optimization problem in a two-level approach. First, a rigid or flexible MBS simulation is performed, and second, each component is optimized independently using a quasi-static approach in which a series of equivalent static load (ESL) cases obtained from the MBS simulation are applied to the respective components. The second method, the fully coupled method, performs the dynamic response optimization using the time response obtained directly from the flexible MBS simulation. Here, an original procedure is proposed to evaluate the ESL from a nonlinear finite element simulation, contrasting with the floating reference frame formulation exploited in the standard ESL method. Several numerical examples are provided to support our position. It is shown that the fully coupled method is more general and accommodates all types of constraints at the price of a more complex optimization process. [less ▲]

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See detailAnalytical sensitivity analysis using the extended finite element method in shape optimization of bimaterial structures
Noël, Lise ULiege; Van Miegroet, Laurent; Duysinx, Pierre ULiege

in International Journal for Numerical Methods in Engineering (2016)

The present work investigates the shape optimization of bimaterial structures. The problem is formulated using a level set description of the geometry and the extended finite element method (XFEM) to ... [more ▼]

The present work investigates the shape optimization of bimaterial structures. The problem is formulated using a level set description of the geometry and the extended finite element method (XFEM) to enable an easy treatment of complex geometries. A key issue comes from the sensitivity analysis of the structural responses with respect to the design parameters ruling the boundaries. Even if the approach does not imply any mesh modification, the study shows that shape modifications lead to difficulties when the perturbation of the level sets modifies the set of extended finite elements. To circumvent the problem, an analytical sensitivity analysis of the structural system is developed. Differences between the sensitivity analysis using FEM or XFEM are put in evidence. To conduct the sensitivity analysis, an efficient approach to evaluate the so-called velocity field is developed within the XFEM domain. The proposed approach determines a continuous velocity field in a boundary layer around the zero level set using a local finite element approximation. The analytical sensitivity analysis is validated against the finite differences and a semi- analytical approach. Finally our shape optimization tool for bimaterial structures is illustrated by revisiting the classical problem of the shape of soft and stiff inclusions in plates. [less ▲]

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See detailSimplified fatigue resistance in mechanical engineering using topology optimization
Collet, Maxime ULiege; Bruggi, Matteo; Bauduin, Simon ULiege et al

Conference (2015, July 09)

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See detailDeterministic Manufacturing constraints for Optimal Distribution in the Case of Additive Manufacturing
Bauduin, Simon ULiege; Collet, Maxime ULiege; Duysinx, Pierre ULiege et al

Conference (2015, July 09)

An overview of the difficulties of coupling additive manufacturing to topology optimization with various solution founded and implemented.

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See detailStress constrained topology optimization for additive manufacturing: Specific character and solution aspects
Duysinx, Pierre ULiege

Conference (2015, July 07)

Since the fundamental work by Bendsøe and Kikuchi (1988), topology optimization has been based on compliance type formulations (Bendsoe & Sigmund, 2003) while the number of works considering stress ... [more ▼]

Since the fundamental work by Bendsøe and Kikuchi (1988), topology optimization has been based on compliance type formulations (Bendsoe & Sigmund, 2003) while the number of works considering stress constraints are rather limited (Duysinx & Bendsoe, 1998). More recently the generalized shape optimization approach using level set methods (see for instance Allaire, Jouve, Troader, 2004, Belytchko, Xiao, Parimi, 2003) has followed the tracks of topology optimization and has mainly been focusing on compliance minimization problems. The ‘compliance type’ formulation has produced quite interesting results in many problems because controlling the energy and the displacements under the loads is generally favourable for deflection control and because, for one load case, the compliance minimization leads to a fully stressed design nearly everywhere in the structure. However there are theoretical results that clearly show that the strongest and the stiffest structural layout can be quite different. As demonstrated in Rozvany & Birker (1994) truss topology optimization can lead to different results when there are several load cases, different stress limits in tension and compression, or when there are several materials involved. Therefore, the first goal of the paper points out the importance of considering stress constraints as soon as the preliminary design phase, that is, to include stress constraints in the topology optimization problem. Revisiting some contributions of the authors, this paper aims at illustrating the key role of stress constraints in the framework of topology optimization of continuum structures. The recent developments are able to treat: • Integrated stress criteria (i.e. global) relaxed stress constraints that aggregate the stress constraints in each finite element in order to be able to circumvent the large scale character of the local stress constraints. • Stress criteria that are able to tackle non equal stress limits in tension and compression. The usual von Mises criterion is unable to predict real-life designs when the structure is made of materials with unequal stress limits like concrete or composite materials. These different behaviours in tension and compression result in quite specific designs. Numerical applications make possible to point out the different nature of structural lay out for maximum strength and maximum stiffness. This one is clearly demonstrated in two kinds of particular situations: once several load cases are considered and when unequal stress limits in tension and compression are involved. The second contribution of the paper deals with the solution aspects of large scale constrained optimization problems. Because of the huge number of design variables, dual methods combined with local convex approximations such as CONLIN (Fleury, 1989) or MMA (Svanberg, 1987) are well indicated to solve classical topology optimization methods. However stress constrained problems introduce also a so large number of active constraints that one comes to a rather delicate situation. We show that the optimizer effort increases mostly as the cube of the number of constraints. In order to circumvent the problem, the idea developed in the paper is to combine first or second order approximations (Bruyneel, Duysinx, Fleury, 2002) with zero order approximations of stress constraints, especially for the subset of restrictions that are likely not to be active or not to change too fast. At first the paper presents the way to derive zero-order approximations of -relaxed stress constraints (that is necessary to cope with the singularity phenomenon of stress constraints in topology optimization). Then the proposed hybrid approach mixing approximation of different orders is benchmarked on numerical applications illustrating the reduction of computation time for solving optimization problems without sacrifying to the robustness and efficiency. Numerical applications will investigate topology optimized benchmark examples combined with additive manufacturing fabrication to illustrate the developments. [less ▲]

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See detailStructural optimization of multibody system components described using level set techniques
Tromme, Emmanuel ULiege; Tortorelli, Daniel; Bruls, Olivier ULiege et al

in Structural and Multidisciplinary Optimization (2015)

The structural optimization of the components in multibody systems is performed using a fully coupled optimization method. The design’s predicted response is obtained from a flexible multibody system ... [more ▼]

The structural optimization of the components in multibody systems is performed using a fully coupled optimization method. The design’s predicted response is obtained from a flexible multibody system simulation under various service conditions. In this way, the resulting optimization process enhances most existing studies which are limited to weakly coupled (quasi-) static or frequency domain loading conditions. A level set description of the component geometry is used to formulate a generalized shape optimization problem which is solved via efficient gradient-based optimization methods. Gradients of cost and constraint functions are obtained from a sensitivity analysis which is revisited in order to facilitate its implementation and retain its computational efficiency. The optimizations of a slider-crank mechanism and a 2-dof robot are provided to exemplify the procedure. [less ▲]

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See detailA level set approach for the structural optimization of flexible mechanisms
Tromme, Emmanuel ULiege; Tortorelli, Daniel; Bruls, Olivier ULiege et al

Conference (2015, June 08)

With the evolution of virtual prototyping, mechanical systems are commonly analyzed using a multibody system (MBS) approach to study the behavior of the entire system and notably the dynamic interactions ... [more ▼]

With the evolution of virtual prototyping, mechanical systems are commonly analyzed using a multibody system (MBS) approach to study the behavior of the entire system and notably the dynamic interactions between the components. Modern structural optimization of mechanical systems considers the dynamic loading exerted on the individual flexible components. The consideration is an essential feature and can be implemented in two ways. Firstly, one can consider a strong coupling wherein the component’s optimization is performed using the time dependent loading conditions coming directly from the MBS simulation. Secondly, one can consider a weak coupling wherein the component’s optimization is performed using a series of static load cases that do not fully account for the interactions between the components of the MBS. Rather this approach performs a MBS simulation to evaluate the loads for the initial design and then optimizes the component assuming the loads do not change. The process of evaluating the loads and then performing the optimization is repeated until suitable convergence criteria is satisfied, assuming convergence is possible. The present paper focuses on the strong coupling method wherein the flexible MBS dynamic analysis is based on a nonlinear finite element formalism [1]. A level set (LS) description of the component geometry is used to enable a generalized shape optimization. The LS approach combines the advantages of shape and topology optimizations. Moreover, since the component boundaries are defined by CAD features, the manufacturing process is facilitated as no post-processing step of a rasterized design is required. The design sensitivity analysis for MBS is revisited in order to facilitate its implementation. The optimization of a slider-crank mechanism and a 2-dof robot is provided to exemplify the procedure. [1] Géradin M., Cardona A. (2001) Flexible Multibody Dynamics: A Finite Element Approach. John Wiley & Sons, New York. [less ▲]

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See detailTopology optimization of mechanical and aerospace components subject to fatigue stress constraints
Duysinx, Pierre ULiege; Collet, Maxime ULiege; Bauduin, Simon ULiege et al

Conference (2015, June 08)

While topology optimization has been based mostly on compliance type formulations, industrial applications call for more elaborated formulations including several restrictions on the local displacements ... [more ▼]

While topology optimization has been based mostly on compliance type formulations, industrial applications call for more elaborated formulations including several restrictions on the local displacements and the stress constraints in some critical zones. Topology optimization with stress constraints was initially considered in Duysinx & Bendsoe (1998). Later the stress constraint formulation was further extended to consider non equal stress constraints limits Bruggi & Duysinx (2012) and to improve the solution efficiency using different strategies such as global stress constraint formulations (Duysinx & Sigmund, 1998, Le et al. 2010). In the present work, the authors are investigating the formulations of stress constraint topology optimization to support the redesign of structural components that have to be fabricated using additive manufacturing. In this perspective, design problem requirements include tackling fatigue constraints during stress constrained topology optimization. The work investigates different formulations of fatigue resistance which could be appropriate in a topology approach. At first the classical approach of mechanical engineering based on SN curves and Goodman or Soderberg lines. The treatment of these fatigue restrictions can take advantage of former work developed for unequal stress constraints by considering mean and alternating components of the stress state. In a second step our research is now focussing on more complex situations (3D stress states) which require resorting to more advanced criteria. Dang Van fatigue theory (Dang Van, Griveau, Message, 1989) has been selected but calls for a more elaborated procedure that is currently validated. Topology optimized structural layouts predicted using classical stress criteria, Goodman and Dang Van theories are compared. [less ▲]

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