P. Duysinx | Université de Liège (original) (raw)
Papers by P. Duysinx
Composite structures design for strength and stiffness
Integrated Design and Manufacturing in Mechanical Engineering, 2002
Structural and Multidisciplinary Optimization, 2013
The so-called bi-value coding parameterization (BCP) method is developed for the simultaneous opt... more The so-called bi-value coding parameterization (BCP) method is developed for the simultaneous optimization of layout design and discrete fiber orientations of laminated structures related to the compliance minimization and natural frequency maximization. Both kinds of problems are transformed into a discrete material selection problem that is then solved as a continuous topology optimization problem with multiphase materials. A new form of the volume constraint is introduced in accordance with the BCP to control the material usage and material removal in the corresponding problem formulation. The BCP scheme assigning the integer value of +1 or-1 to each design variable for the unique "coding" is efficiently used to interpolate discrete fiber orientations and to identify the presence and removal of materials. Meanwhile, a general setup strategy is proposed by assigning "uniform" weight values in BCP to ensure the feasibility of the initial starting point. Numerical tests illustrate that the BCP is efficient in dealing with both kinds of design problems including the volume constraint.
International Journal for Numerical Methods in Engineering, 2012
The discrete optimal orientation design of the composite laminate can be treated as a material se... more The discrete optimal orientation design of the composite laminate can be treated as a material selection problem dealt with by continuous topology optimization method. In this work, a new bi-value coding parameterization (BCP) scheme is proposed to this aim. The idea of the BCP scheme is to "code" each material phase using integer values of +1 and-1. Each available material phase has one unique "code" consisting of +1 and/or-1 assigned to design variables. Theoretical and numerical comparisons between the proposed BCP scheme and existing schemes show that the BCP has the advantage of an evident reduction of the number of design variables in logarithmic form. This is very beneficial when the number of candidate materials becomes important. Numerical tests with up to 36 candidate material orientations are illustrated for the first time to indicate the reliability and efficiency of the proposed scheme in solving this kind of problem. It proves that the BCP is an interesting and potential scheme to achieve the optimal orientations for large-scale design problems.
International Journal for Numerical Methods in Engineering, 2016
The equivalent static load (ESL) method is a powerful approach to solve dynamic response structur... more The equivalent static load (ESL) method is a powerful approach to solve dynamic response structural optimization problems. The method transforms the dynamic response optimization into a static response optimization under multiple load cases. The ESL cases are defined based on the transient analysis response whereupon all the standard techniques of static response optimization can be used. In the last decade, the ESL method has been applied to perform the structural optimization of flexible components of mechanical systems modeled as multibody systems (MBS). The ESL evaluation strongly depends on the adopted formulation to describe the MBS and has been initially derived based on a floating frame of reference formulation. In this paper, we propose a method to derive the ESL adapted to a nonlinear finite element approach based on a Lie group formalism for two main reasons. Firstly, the finite element approach is completely general to analyze complex MBS and is suitable to perform more advanced optimization problems like topology optimization. Secondly, the selected Lie group formalism leads to a formulation of the equations of motion in the local frame, which turns out to be a strong practical advantage for the ESL evaluation. Examples are provided to validate the proposed method.
Mechanism and Machine Theory, 2016
The paper presents how to optimize the flexible components in a flexible multibody system undergo... more The paper presents how to optimize the flexible components in a flexible multibody system undergoing both large overall motion and large deformation by using the Absolute Nodal Coordinate Formulation (ANCF) and the equivalent static load (ESL) method. Before the structural optimization, the flexible multibody system is modeled via ANCF first so as to describe the coupled overall motion and large deformation accurately. During the structural optimization, the elastic deformation of the flexible component to be optimized is split from the overall motion of the flexible component, and then the equivalent static loads are determined by using the ESL method such that the structural optimization of nonlinear dynamic response can be transformed into a static one. In addition, the nonlinear interior point method is adopted to solve the corresponding structural optimization problem of nonlinear static response. The paper gives three numerical examples to validate the above optimization procedure. The final example of optimizing the arms in a rigid-flexible grasping robot shows that the proposed optimization procedure enables one to deal with realistic engineering systems.
Structural and Multidisciplinary Optimization, 2013
The paper presents a stress-based approach that copes with the optimal design of truss-like elast... more The paper presents a stress-based approach that copes with the optimal design of truss-like elastic structures in case of unilateral behavior of material or ground supports. The conventional volume-constrained minimization of compliance is coupled with a set of local stress constraints that are enforced, all over the domain or along prescribed boundaries, to control the arising of members with tension-only or compression-only strength. A Drucker-Prager failure criterion is formulated to provide a smooth approximation of the no-tension or no-compression conditions governing the stress field. A selection strategy is implemented to handle efficiently the multi-constrained formulation that is solved through mathematical programming. Benchmark examples are investigated to discuss the features of the achieved optimal designs, as compared with problems involving material and ground supports with equal behavior in tension and compression. Numerical simulations show that a limited set of constraints is needed in the first iterations to steer the solution of the energy-driven optimization towards designs accounting for the prescribed assumption of unilateral strength.
This paper concerns the modeling and the integrated numerical simulation of flexible mechanisms s... more This paper concerns the modeling and the integrated numerical simulation of flexible mechanisms subject to the action of a digital control system. A general method is proposed, based on the formalism of flexible multibody systems (MBS) using the Finite Element Method (FEM). Nonlinear e ects in the mechanical structure or in the control system can be taken into account. The numerical simulation tool is applied to design an active control system in a hot-dip galvanizing line, which aims at reducing the vibrations of the steel strip
Since the fundamental work by Bendsoe and Kikuchi [3], topology optimization has been based on co... more Since the fundamental work by Bendsoe and Kikuchi [3], topology optimization has been based on compliance type formulations [4] while the number of works considering stress constraints are rather limited [6]. More recently the generalized shape optimization approach using level set methods (see for instance [1,2]) 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 Ref. [8] truss topology optimization can lead to different results when there ...
Recently mechanical engineering has extended from a component to a system oriented approach. The ... more Recently mechanical engineering has extended from a component to a system oriented approach. The structural analysis of components is now completed by the whole mechanical system simulation using multibody system analysis. This evolution aims at capturing better the real loading conditions account-ing for the component interaction and couplings in the system. Structural optimization is continuing along the same tracks. Recent works in structural optimization have tried to optimize components with respect to loadings conditions defined through dynamic loading coming from multibody system dynamic analysis [1, 2, 3] Generally, optimization techniques consider that the structural component is isolated from the rest of the mechanism and use simplified quasi-static load cases to mimic the complex loadings in service. In contrast, we have shown in previous works devoted to topology optimization [3] that an optimization directly based on the dynamic response of the flexible multibody system...
We consider topology optimization of elastic continuum structures including a bound on the perime... more We consider topology optimization of elastic continuum structures including a bound on the perimeter of the structures domain Such a bound is known to ensure existence of solutions and it stabilizes the behavior of numerical nite element FE solutions However the straightforward way of calculating the perimeter is rotationally meshdependent In this paper we present new perimeter formulae with weaker rotational dependence ie perimeters that are almost isotropic An overview of some theoretical results as well as numerical tests are given
We consider topology optimization of elastic continuum structures including a bound on the perime... more We consider topology optimization of elastic continuum structures including a bound on the perimeter of the structure's domain. Such a bound is known to ensure existence of solutions and it stabilizes the behavior of numerical finite element (FE) solutions. However, the straightforward way of calculating the perimeter is rotationally mesh-dependent. In this paper we present new perimeter formulae with weaker rotational dependence, i.e. perimeters that are "almost isotropic". An overview of some theoretical results as well as numerical tests are given. 2. Keywords Topology Optimization, Finite Elements, Perimeter Constraints 3. Problem Formulation The considered optimization problem is concerned with designing shapes, holes and connectivities of a structure contained in a given open domain\Omega ae R d to achieve maximum stiffness with respect to given boundary conditions. Each point x 2\Omega is assigned a displacement u(x) and an amount of material ae(x). For fixed a...
The Proceedings of the International Conference on Motion and Vibration Control
Proceedings of the Fifteenth International Conference on Civil, Structural and Environmental Engineering Computing, 2015
The aim of this article is to present the background, improvements and variants of the particle s... more The aim of this article is to present the background, improvements and variants of the particle swarm optimization algorithm (PSO) based on the movement of a bird flock, as an alternative method of optimization for composite structures. The strong point of this algorithm is its simplicity and adaptability to all kind of problems and fields. The first part of this article consists in a compilation of different papers that deal with problems encountered while applying PSO and their solutions. The article discusses about the way to deal with large design spaces, about the convergence problem and local vs. global minima. In the second part of the article, the PSO algorithm is compared to the classical genetic algorithms used for optimization in the software BOSS Quattro. Other kinds of problems that can appear are the constrained ones. In order to solve them, a study of the Augmented Lagrange Multiplier Method is considered. In this case, the PSO is used to optimize the Augmented Lagrangian function giving satisfactory results for common problems. As future prospects, the study of different ways to improve the algorithm is considered. For example, the way to update the particles has been studied: choosing to update the worse particle, the best one or a percentage of the best/worst population. Future studies could include the way the particles are chosen. As last results, industrial applications will be tested in different software.
Most of the available formulations for topology optimization are conceived to cope with linear el... more Most of the available formulations for topology optimization are conceived to cope with linear elastic structures exhibiting the same behavior in tension and compression for both material and ground constraints.
Composite structures design for strength and stiffness
Integrated Design and Manufacturing in Mechanical Engineering, 2002
Structural and Multidisciplinary Optimization, 2013
The so-called bi-value coding parameterization (BCP) method is developed for the simultaneous opt... more The so-called bi-value coding parameterization (BCP) method is developed for the simultaneous optimization of layout design and discrete fiber orientations of laminated structures related to the compliance minimization and natural frequency maximization. Both kinds of problems are transformed into a discrete material selection problem that is then solved as a continuous topology optimization problem with multiphase materials. A new form of the volume constraint is introduced in accordance with the BCP to control the material usage and material removal in the corresponding problem formulation. The BCP scheme assigning the integer value of +1 or-1 to each design variable for the unique "coding" is efficiently used to interpolate discrete fiber orientations and to identify the presence and removal of materials. Meanwhile, a general setup strategy is proposed by assigning "uniform" weight values in BCP to ensure the feasibility of the initial starting point. Numerical tests illustrate that the BCP is efficient in dealing with both kinds of design problems including the volume constraint.
International Journal for Numerical Methods in Engineering, 2012
The discrete optimal orientation design of the composite laminate can be treated as a material se... more The discrete optimal orientation design of the composite laminate can be treated as a material selection problem dealt with by continuous topology optimization method. In this work, a new bi-value coding parameterization (BCP) scheme is proposed to this aim. The idea of the BCP scheme is to "code" each material phase using integer values of +1 and-1. Each available material phase has one unique "code" consisting of +1 and/or-1 assigned to design variables. Theoretical and numerical comparisons between the proposed BCP scheme and existing schemes show that the BCP has the advantage of an evident reduction of the number of design variables in logarithmic form. This is very beneficial when the number of candidate materials becomes important. Numerical tests with up to 36 candidate material orientations are illustrated for the first time to indicate the reliability and efficiency of the proposed scheme in solving this kind of problem. It proves that the BCP is an interesting and potential scheme to achieve the optimal orientations for large-scale design problems.
International Journal for Numerical Methods in Engineering, 2016
The equivalent static load (ESL) method is a powerful approach to solve dynamic response structur... more The equivalent static load (ESL) method is a powerful approach to solve dynamic response structural optimization problems. The method transforms the dynamic response optimization into a static response optimization under multiple load cases. The ESL cases are defined based on the transient analysis response whereupon all the standard techniques of static response optimization can be used. In the last decade, the ESL method has been applied to perform the structural optimization of flexible components of mechanical systems modeled as multibody systems (MBS). The ESL evaluation strongly depends on the adopted formulation to describe the MBS and has been initially derived based on a floating frame of reference formulation. In this paper, we propose a method to derive the ESL adapted to a nonlinear finite element approach based on a Lie group formalism for two main reasons. Firstly, the finite element approach is completely general to analyze complex MBS and is suitable to perform more advanced optimization problems like topology optimization. Secondly, the selected Lie group formalism leads to a formulation of the equations of motion in the local frame, which turns out to be a strong practical advantage for the ESL evaluation. Examples are provided to validate the proposed method.
Mechanism and Machine Theory, 2016
The paper presents how to optimize the flexible components in a flexible multibody system undergo... more The paper presents how to optimize the flexible components in a flexible multibody system undergoing both large overall motion and large deformation by using the Absolute Nodal Coordinate Formulation (ANCF) and the equivalent static load (ESL) method. Before the structural optimization, the flexible multibody system is modeled via ANCF first so as to describe the coupled overall motion and large deformation accurately. During the structural optimization, the elastic deformation of the flexible component to be optimized is split from the overall motion of the flexible component, and then the equivalent static loads are determined by using the ESL method such that the structural optimization of nonlinear dynamic response can be transformed into a static one. In addition, the nonlinear interior point method is adopted to solve the corresponding structural optimization problem of nonlinear static response. The paper gives three numerical examples to validate the above optimization procedure. The final example of optimizing the arms in a rigid-flexible grasping robot shows that the proposed optimization procedure enables one to deal with realistic engineering systems.
Structural and Multidisciplinary Optimization, 2013
The paper presents a stress-based approach that copes with the optimal design of truss-like elast... more The paper presents a stress-based approach that copes with the optimal design of truss-like elastic structures in case of unilateral behavior of material or ground supports. The conventional volume-constrained minimization of compliance is coupled with a set of local stress constraints that are enforced, all over the domain or along prescribed boundaries, to control the arising of members with tension-only or compression-only strength. A Drucker-Prager failure criterion is formulated to provide a smooth approximation of the no-tension or no-compression conditions governing the stress field. A selection strategy is implemented to handle efficiently the multi-constrained formulation that is solved through mathematical programming. Benchmark examples are investigated to discuss the features of the achieved optimal designs, as compared with problems involving material and ground supports with equal behavior in tension and compression. Numerical simulations show that a limited set of constraints is needed in the first iterations to steer the solution of the energy-driven optimization towards designs accounting for the prescribed assumption of unilateral strength.
This paper concerns the modeling and the integrated numerical simulation of flexible mechanisms s... more This paper concerns the modeling and the integrated numerical simulation of flexible mechanisms subject to the action of a digital control system. A general method is proposed, based on the formalism of flexible multibody systems (MBS) using the Finite Element Method (FEM). Nonlinear e ects in the mechanical structure or in the control system can be taken into account. The numerical simulation tool is applied to design an active control system in a hot-dip galvanizing line, which aims at reducing the vibrations of the steel strip
Since the fundamental work by Bendsoe and Kikuchi [3], topology optimization has been based on co... more Since the fundamental work by Bendsoe and Kikuchi [3], topology optimization has been based on compliance type formulations [4] while the number of works considering stress constraints are rather limited [6]. More recently the generalized shape optimization approach using level set methods (see for instance [1,2]) 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 Ref. [8] truss topology optimization can lead to different results when there ...
Recently mechanical engineering has extended from a component to a system oriented approach. The ... more Recently mechanical engineering has extended from a component to a system oriented approach. The structural analysis of components is now completed by the whole mechanical system simulation using multibody system analysis. This evolution aims at capturing better the real loading conditions account-ing for the component interaction and couplings in the system. Structural optimization is continuing along the same tracks. Recent works in structural optimization have tried to optimize components with respect to loadings conditions defined through dynamic loading coming from multibody system dynamic analysis [1, 2, 3] Generally, optimization techniques consider that the structural component is isolated from the rest of the mechanism and use simplified quasi-static load cases to mimic the complex loadings in service. In contrast, we have shown in previous works devoted to topology optimization [3] that an optimization directly based on the dynamic response of the flexible multibody system...
We consider topology optimization of elastic continuum structures including a bound on the perime... more We consider topology optimization of elastic continuum structures including a bound on the perimeter of the structures domain Such a bound is known to ensure existence of solutions and it stabilizes the behavior of numerical nite element FE solutions However the straightforward way of calculating the perimeter is rotationally meshdependent In this paper we present new perimeter formulae with weaker rotational dependence ie perimeters that are almost isotropic An overview of some theoretical results as well as numerical tests are given
We consider topology optimization of elastic continuum structures including a bound on the perime... more We consider topology optimization of elastic continuum structures including a bound on the perimeter of the structure's domain. Such a bound is known to ensure existence of solutions and it stabilizes the behavior of numerical finite element (FE) solutions. However, the straightforward way of calculating the perimeter is rotationally mesh-dependent. In this paper we present new perimeter formulae with weaker rotational dependence, i.e. perimeters that are "almost isotropic". An overview of some theoretical results as well as numerical tests are given. 2. Keywords Topology Optimization, Finite Elements, Perimeter Constraints 3. Problem Formulation The considered optimization problem is concerned with designing shapes, holes and connectivities of a structure contained in a given open domain\Omega ae R d to achieve maximum stiffness with respect to given boundary conditions. Each point x 2\Omega is assigned a displacement u(x) and an amount of material ae(x). For fixed a...
The Proceedings of the International Conference on Motion and Vibration Control
Proceedings of the Fifteenth International Conference on Civil, Structural and Environmental Engineering Computing, 2015
The aim of this article is to present the background, improvements and variants of the particle s... more The aim of this article is to present the background, improvements and variants of the particle swarm optimization algorithm (PSO) based on the movement of a bird flock, as an alternative method of optimization for composite structures. The strong point of this algorithm is its simplicity and adaptability to all kind of problems and fields. The first part of this article consists in a compilation of different papers that deal with problems encountered while applying PSO and their solutions. The article discusses about the way to deal with large design spaces, about the convergence problem and local vs. global minima. In the second part of the article, the PSO algorithm is compared to the classical genetic algorithms used for optimization in the software BOSS Quattro. Other kinds of problems that can appear are the constrained ones. In order to solve them, a study of the Augmented Lagrange Multiplier Method is considered. In this case, the PSO is used to optimize the Augmented Lagrangian function giving satisfactory results for common problems. As future prospects, the study of different ways to improve the algorithm is considered. For example, the way to update the particles has been studied: choosing to update the worse particle, the best one or a percentage of the best/worst population. Future studies could include the way the particles are chosen. As last results, industrial applications will be tested in different software.
Most of the available formulations for topology optimization are conceived to cope with linear el... more Most of the available formulations for topology optimization are conceived to cope with linear elastic structures exhibiting the same behavior in tension and compression for both material and ground constraints.