Topology optimization for minimum weight with compliance and stress constraints

Bruggi, Matteo; Duysinx, Pierre

doi:10.1007/s00158-012-0759-7

Cited by 204 publications

(116 citation statements)

References 39 publications

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“…stresses. As investigated in [23], the formulation adopts the weight of the structure as objective function, including an energy-based constraint to control deformability and a selected set of constraints to control undesired stress peaks, if needed. Instead of using the displacement-based strain energy to evaluate the structural compliance, the stress-based complementary energy is herein considered.…”

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confidence: 99%

Topology optimization with mixed finite elements on regular grids

Bruggi

2016

Computer Methods in Applied Mechanics and Engineering

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Recently, new families of mixed finite elements have been proposed to address the analysis of linear elastic bodies on regular grids adopting a limited number of degrees of freedom per element. A twodimensional mixed discretization is implemented to formulate an alternative topology optimization problem where stresses play the role of main variables and both compressible and incompressible materials can be dealt with. The structural compliance is computed through the evaluation of the complementary energy, whereas the enforcement of stress constraints is straightforward. Numerical simulations investigate the features of the proposed approach: comparisons with a conventional displacement-based scheme are provided for compressible materials; stress-constrained solutions for structures made of incompressible media are introduced.

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confidence: 99%

Topology optimization with mixed finite elements on regular grids

Bruggi

2016

Computer Methods in Applied Mechanics and Engineering

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“…For a review of the recent developments in SIMP, the reader is referred to [17,18]. Research has also been conducted in using TO with material failure constraints [19] and stress constraints [20]. TO has been widely used in different domains such as fluid flow [21], heat transfer [22] and aerospace design [23,24].…”

Section: Literature Reviewmentioning

confidence: 99%

Extraction of Structural System Designs from Topologies via Morphological Analysis and Artificial Intelligence

Jootoo

Lattanzi

2018

Designs

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Structural system design is the process of giving form to a set of interconnected components subjected to loads and design constraints while navigating a complex design space. While safe designs are relatively easy to develop, optimal designs are not. Modern computational optimization approaches employ population based metaheuristic algorithms to overcome challenges with the system design optimization landscape. However, the choice of the initial population, or ground structure, can have an outsized impact on the resulting optimization. This paper presents a new method of generating such ground structures, using a combination of topology optimization (TO) and a novel system extraction algorithm. Since TO generates monolithic structures, rather than systems, its use for structural system design and optimization has been limited. In this paper, truss systems are extracted from topologies through morphological analysis and artificial intelligence techniques. This algorithm, and its assessment, constitutes the key contribution of this paper. The structural systems obtained are compared with ground truth solutions to evaluate the performance of the algorithms. The generated structures are also compared against benchmark designs from the literature. The results indicate that the presented truss generation algorithm produces structures comparable to those generated through metaheuristic optimization, while mitigating the need for assumptions about initial ground structures.

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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%

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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Topology optimization for minimum weight with compliance and stress constraints

Cited by 204 publications

References 39 publications

Topology optimization with mixed finite elements on regular grids

Topology optimization with mixed finite elements on regular grids

Extraction of Structural System Designs from Topologies via Morphological Analysis and Artificial Intelligence

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

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