References of "Structural and Multidisciplinary Optimization"
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See detailSimultaneous design of structural layout and discrete fiber orientation using bi-value coding parameterization and volume constraint
TONG, Gao; ZHANG, Weihong; Duysinx, Pierre ULg

in Structural and Multidisciplinary Optimization (2013), 48(6), 1075-1088

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 ... [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 set-up 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. [less ▲]

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See detailDiscussion on the optimization problem formulation of flexible components in multibody systems
Tromme, Emmanuel ULg; Bruls, Olivier ULg; Emonds-Alt, Jonathan et al

in Structural and Multidisciplinary Optimization (2013), 48(6), 1189-1206

This paper is dedicated to the structural optimization of flexible components in mechanical systems modeled as multibody systems. While most of the structural optimization developments have been conducted ... [more ▼]

This paper is dedicated to the structural optimization of flexible components in mechanical systems modeled as multibody systems. While most of the structural optimization developments have been conducted under (quasi-)static loadings or vibration design criteria, the proposed approach aims at considering as precisely as possible the effects of dynamic loading under service conditions. Solving this problem is quite challenging and naive implementations may lead to inaccurate and unstable results. To elaborate a robust and reliable approach, the optimization problem formulation is investigated because it turns out that it is a critical point. Different optimization algorithms are also tested. To explain the efficiency of the various solution approaches, the complex nature of the design space is analyzed. Numerical applications considering the optimization of a two-arm robot subject to a trajectory tracking constraint and the optimization of a slider-crank mechanism with a cyclic dynamic loading are presented to illustrate the different concepts. [less ▲]

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See detailA stress-based approach to the optimal design of structures with unilateral behavior of material or supports
Bruggi, Matteo; Duysinx, Pierre ULg

in Structural and Multidisciplinary Optimization (2013), 48

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 ... [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. [less ▲]

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See detailTopology optimization for minimum weight with compliance and stress constraints
Bruggi, Matteo; Duysinx, Pierre ULg

in Structural and Multidisciplinary Optimization (2012), 46(3), 269-384

The paper deals with a formulation for the topology optimization of elastic structures that aims at minimizing the structural weight subject to compliance and local stress constraints. The global ... [more ▼]

The paper deals with a formulation for the topology optimization of elastic structures that aims at minimizing the structural weight subject to compliance and local stress constraints. The global constraint provides the expected stiffness to the optimal design while a selected set of local enforcements require feasibility with respect to the assigned strength of material. The Drucker–Prager failure criterion is implemented to handle materials with either equal or unequal behavior in tension and compression. A suitable relaxation of the equivalent stress measure is implemented to overcome the difficulties related to the singularity problem. Numerical examples are presented to discuss the features of the achieved optimal designs along with performances of the adopted procedure. Comparisons with pure compliance–based or pure stress–based strategies are also provided to point out differences arising in the optimal design with respect to conventional approaches, depending on the assumed material behavior. [less ▲]

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See detailStress concentration minimization of 2D filets using X-FEM and level set description
Van Miegroet, Laurent ULg; Duysinx, Pierre ULg

in Structural and Multidisciplinary Optimization (2007), 33(4-5), 425-438

This paper presents and applies a novel shape optimization approach based on the level set description of the geometry and the extended finite element method (X-FEM). The method benefits from the fixed ... [more ▼]

This paper presents and applies a novel shape optimization approach based on the level set description of the geometry and the extended finite element method (X-FEM). The method benefits from the fixed mesh work using X-FEM and from the curves smoothness of the level set description. Design variables are shape parameters of basic geometric features that are described with a level set representation. The number of design variables of this formulation remains small, whereas global (i.e. compliance) and local constraints (i.e. stresses) can be considered. To illustrate the capability of the method to handle stress constraints, numerical applications revisit the minimization of stress concentration in a 2D filet in tension, which has been previously studied in Pedersen (2003). Our results illustrate the great interest of using X-FEM and level set description together. A special attention is also paid to stress computation and accuracy with the X-FEM. [less ▲]

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See detailAn augmented Lagrangian optimization method for inflatable structures analysis problems
Bruyneel, Michaël ULg; Jetteur, Pierre ULg; Granville, D. et al

in Structural and Multidisciplinary Optimization (2006), 32(5), 383-395

This paper describes the development of an augmented Lagrangian optimization method for the numerical simulation of the inflation process in the design of inflatable space structures. Although the Newton ... [more ▼]

This paper describes the development of an augmented Lagrangian optimization method for the numerical simulation of the inflation process in the design of inflatable space structures. Although the Newton-Raphson scheme was proven to be efficient for solving many nonlinear problems, it can lead to lack of convergence when it is applied to the simulation of the inflation process. As a result, it is recommended to use an optimization algorithm to find the minimum energy configuration that satisfies the equilibrium equations characterizing the final shape of the inflated structure subject to an internal pressure. On top of that, given that some degrees of freedom may be linked, the optimum may be constrained, and specific optimization methods for constrained problems must be considered. The paper presents the formulation and the augmented Lagrangian method (ALM) developed in SAMCEF Mecano for inflatable structures analysis problems. The related quasi-unconstrained optimization problem is solved with a nonlinear conjugate gradient method. The Wolfe conditions are used in conjunction with a cubic interpolation for the line search. Equality constraints are considered and can be easily treated by the ALM formulation. Numerical applications present simulations of unconstrained and constrained inflation processes (i.e., where the motion of some nodes is ruled by a rigid body element restriction and/or problems including contact conditions). [less ▲]

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See detailNote on singular optima in laminate design problems
Bruyneel, Michael; Duysinx, Pierre ULg

in Structural and Multidisciplinary Optimization (2006), 31(2), 156-159

This paper studies the design of laminates subject to restrictions on the ply strength. The minimum weight design is considered. It is shown that this formulation includes singular optima, which are ... [more ▼]

This paper studies the design of laminates subject to restrictions on the ply strength. The minimum weight design is considered. It is shown that this formulation includes singular optima, which are similar to the ones observed in topology optimization including local stress constraints. In laminate design, these singular optima are linked to the removal of 'zero thickness' plies from the stacking sequence. It is shown how the fiber orientation variables can circumvent the singularity by relaxing the strength constraints related to such vanishing plies. This demonstrates the key role of fiber orientations in the optimization of laminates and the need for their efficient treatment as design variables. [less ▲]

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See detailNote on topology optimization of continuum structures including self-weight
Bruyneel, Michael; Duysinx, Pierre ULg

in Structural and Multidisciplinary Optimization (2005), 29(4), 245-256

This paper proposes to investigate topology optimization with density-dependent body forces and especially self-weight loading. Surprisingly the solution of such problems cannot be based on a direct ... [more ▼]

This paper proposes to investigate topology optimization with density-dependent body forces and especially self-weight loading. Surprisingly the solution of such problems cannot be based on a direct extension of the solution procedure used for minimum-compliance topology optimization with fixed external loads. At first the particular difficulties arising in the considered topology problems are pointed out: non-monotonous behaviour of the compliance, possible unconstrained character of the optimum and the parasitic effect for low densities when using the power model (SIMP). To get rid of the last problem requires the modification of the power law model for low densities. The other problems require that the solution procedure and the selection of appropriate structural approximations be revisited. Numerical applications compare the efficiency of different approximation schemes of the MMA family. It is shown that important improvements are achieved when the solution is carried out using the gradient-based method of moving asymptotes (GBMMA) approximations. Criteria for selecting the approximations are suggested. In addition, the applications also provide the opportunity to illustrate the strong influence of the ratio between the applied loads and the structural weight on the optimal structural topology. [less ▲]

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See detailA family of MMA approximations for structural optimization
Bruyneel, Michaël ULg; Duysinx, Pierre ULg; Fleury, Claude ULg

in Structural and Multidisciplinary Optimization (2002), 24(4), 263-276

This paper proposes a new first-order approximation scheme used for solving structural optimization problems. It is based on approximations of the MMA family (MMA and GCMMA), but it utilizes the gradients ... [more ▼]

This paper proposes a new first-order approximation scheme used for solving structural optimization problems. It is based on approximations of the MMA family (MMA and GCMMA), but it utilizes the gradients and/or the function values at two successive design points to improve the quality of the approximation. In addition, this scheme can consider simultaneously monotonous and nonmonotonous structural behaviour. According to the characteristics of the treated problem, one of the approximations or a mix of them is automatically selected. Based on this approach, the accuracy of the approximated subproblems is improved and the solution process can be sped up. Numerical results compare the effectiveness of the method with previously derived approximations of the MMA family for shape optimization of trusses and for composite design problems. The benefit of using mixed approximations is also discussed. [less ▲]

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See detailFirst and second order convex approximation strategies in structural optimization
Fleury, Claude ULg

in Structural and Multidisciplinary Optimization (1989), 1(1), 3-10

In this paper, various methods based on convex approximation schemes are discussed, that have demonstrated strong potential for efficient solution of structural optimization problems. First, the convex ... [more ▼]

In this paper, various methods based on convex approximation schemes are discussed, that have demonstrated strong potential for efficient solution of structural optimization problems. First, the convex linearization method (CONLIN) is briefly described, as well as one of its recent generalizations, the method of moving asymptotes (MMA). Both CONLIN and MMA can be interpreted as first order convex approximation methods, that attempt to estimate the curvature of the problem functions on the basis of semi-empirical rules. Attention is next directed toward methods that use diagonal second derivatives in order to provide a sound basis for building up high quality explicit approximations of the behaviour constraints. In particular, it is shown how second order information can be effectively used without demanding a prohibitive computational cost. Various first and second order approaches are compared by applying them to simple problems that have a closed form solution. [less ▲]

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