Topology optimization for minimum mass design considering local failure constraints and contact boundary conditions

Fancello, Eduardo Alberto

doi:10.1007/s00158-006-0019-9

Cited by 71 publications

(40 citation statements)

References 18 publications

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“…[23][24][25][26][27][28][29][30][31][32][33][34][35][36] There are two main difficulties associated with stress constraints when the solid isotropic material with penalization (SIMP) approach is used for material parameterization. The first difficulty consists in the local nature of material failure constraints, which provides a major challenge due to the large number of stress constraints and their high nonlinearity.…”

Section: Introductionmentioning

confidence: 99%

“…One can use an augmented Lagrangian algorithm, which proved to be a mathematically consistent alternative with reasonable computational cost. [24][25][26]33,35 The other important issue that must be considered is the singularity phenomenon. There are 2 main techniques used to relax the design space: the qp approach 27 and the -relaxed approach.…”

Section: Introductionmentioning

confidence: 99%

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Topology optimization of continuum structures with stress constraints and uncertainties in loading

Silva

Beck

Cardoso

2017

Numerical Meth Engineering

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SummaryTopology optimization using stress constraints and considering uncertainties is a serious challenge, since a reliability problem has to be solved for each stress constraint, for each element in the mesh. In this paper, an alternative way of solving this problem is used, where uncertainty quantification is performed through the first-order perturbation approach, with proper validation by Monte Carlo simulation. Uncertainties are considered in the loading magnitude and direction. The minimum volume problem subjected to local stress constraints is formulated as a robust problem, where the stress constraints are written as a weighted average between their expected value and standard deviation. The augmented Lagrangian method is used for handling the large set of local stress constraints, whereas a gradient-based algorithm is used for handling the bounding constraints. It is shown that even in the presence of small uncertainties in loading direction, different topologies are obtained when compared to a deterministic approach. The effect of correlation between uncertainties in loading magnitude and direction on optimal topologies is also studied, where the main observed result is loss of symmetry in optimal topologies.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Topology optimization of continuum structures with stress constraints and uncertainties in loading

Silva

Beck

Cardoso

2017

Numerical Meth Engineering

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“…Petersson and Patriksson (1997) presented a pioneering work on the topology optimization of sheets in unilateral contact resorting to a sub-gradient method. A contact problem including Coulomb friction was tackled in Fancello (2006) through a penalization approach, while Mankame and Ananthasuresh (2004) extended investigations to the optimal design of compliant mechanisms introducing a regularized contact model. The very recent work in Strömberg and Klarbring (2010) addresses contact problems in the three-dimensional framework treating the Signorini's conditions by the augmented Lagrangian approach along with a smooth approximation technique.…”

Section: Introductionmentioning

confidence: 99%

A stress–based approach to the optimal design of structures with unilateral behavior of material or supports

Bruggi

Duysinx

2013

Struct Multidisc Optim

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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.

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“…A pioneering work on topology optimization of structures in unilateral contact is Petersson and Patriksson [7]. A more recent work is Fancello [8]. Another recent work is Mankame and Ananthasuresh [9], where compliant mechanisms were generated by including contact conditions.…”

Section: Introductionmentioning

confidence: 99%

Topology optimization of structures in unilateral contact

Strömberg

Klarbring

2009

Struct Multidisc Optim

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In this paper a general framework for topology optimization of structures in unilateral contact is developed. A linear elastic structure that is unilaterally constrained by rigid supports is considered. The supports are modeled by Signorini's contact conditions which in turn are treated by the augmented Lagrangian approach as well as by a smooth approximation. The latter approximation must not be confused with the well-known penalty approach. The state of the system, which is defined by the equilibrium equation and the two different contact formulations, is solved by a Newton method. The design parametrization is obtained by using the SIMP-model. The minimization of compliance for a limited value of volume is considered. The optimization problems are solved by SLP. This is done by using a nested approach where the state equations are linearized and sensitivities are calculated by the adjoint method. In order to avoid meshdependency the sensitivities are filtered by Sigmund's filter. The final LP-problem is solved by an interior point method that is 1 available in Matlab. The implementation is done for a general design domain in 2D as well as in 3D by using fully integrated isoparametric elements. The implementation seems to be very efficient and robust.

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Topology optimization for minimum mass design considering local failure constraints and contact boundary conditions

Cited by 71 publications

References 18 publications

Topology optimization of continuum structures with stress constraints and uncertainties in loading

Topology optimization of continuum structures with stress constraints and uncertainties in loading

A stress–based approach to the optimal design of structures with unilateral behavior of material or supports

Topology optimization of structures in unilateral contact

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