Stress-Constrained Topology Optimization for Lattice Materials

Pasini, Damiano; Moussa, A.; Rahimizadeh, Amirmohammad

doi:10.1007/978-3-662-55771-6_249

Cited by 4 publications

(11 citation statements)

References 34 publications

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“…The theory of homogenization is related to the development of partial differential equations with non-constant coefficients [147]. Asymptotic homogenization assumes that each field quantity depends on two scale lengths, namely the microscopic (local) and macroscopic (global) levels [95]. For elastic materials, the displacements, strains, stiffness and stresses are assumed to vary smoothly at the global level while behave periodically at the local level [147].…”

Section: Homogenization Methods For Elastic Materialsmentioning

confidence: 99%

“…In addition to homogenized elasticity matrices, homogenization can calculate the relative yield stress of a periodic medium. This was performed for two dimensional lattice materials by Pasini et al [95]. The effective or relative stress tensor of an elastic medium is given as:…”

Section: Relative Yield Strengthmentioning

confidence: 99%

“…Aggregate clustering results in new structural responses equal to the number of desired clusters. This technique has been implemented for stress based constraints in topology optimization and successfully used by Holmberg et al [184] and Pasini et al [95]. When the number of clusters is equal to one, the response is equal to the global approximation first explained in section 7.5.2.…”

Section: E42 Clustering Strategiesmentioning

confidence: 99%

“…Consistently sized unit cells are important to correctly reflect the properties of the lattice topologies. This is even more of a concern for topology optimizations of lattice structures that rely on asymptotic homogenization [95]. The relative properties from the homogenization rely on perfectly repeated unit cell properties.…”

Section: G5 Local Stiffness Matrix Sensitivitiesmentioning

confidence: 99%

“…The relative stress properties can therefore be implemented into the stress response for the lattice optimizations. This strategy had been implemented with great success by Pasini et al who homogenized properties of two dimensional lattice structures to derive properties of relative modulus, Poisson ratio, shear modulus and yield stress[95]. Pasisni et alincluded the microscopic stress measurements in the evaluation of the stresses to scale the problem accordingly[95].…”

mentioning

confidence: 99%

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Numerical and Experimental Optimization for Specific Fatigue Life Maximization of Additively Manufactured Ti-6Al-4V Aerospace Components

Trudel¹

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Section: Homogenization Methods For Elastic Materialsmentioning

confidence: 99%

Section: Relative Yield Strengthmentioning

confidence: 99%

Section: E42 Clustering Strategiesmentioning

confidence: 99%

Section: G5 Local Stiffness Matrix Sensitivitiesmentioning

confidence: 99%

mentioning

confidence: 99%

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Numerical and Experimental Optimization for Specific Fatigue Life Maximization of Additively Manufactured Ti-6Al-4V Aerospace Components

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Stress‐constrained concurrent topology optimization of two‐scale hierarchical structures

Zhao

Wang

2021

Numerical Meth Engineering

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This article develops a concurrent topology optimization approach for designing two-scale hierarchical structures under stress constraints without specifying the topology of the unit cell as a priori. Compared with traditional stress-constrained topology optimization, the number of stress constraints involved in concurrent topology optimization is much larger and the sensitivity analysis for stress constraints is computationally more expensive. To address these challenges, a novel hierarchical aggregation strategy is proposed to handle the large number of stress constraints and an adjoint method is developed for efficient sensitivity analysis. Several numerical examples are presented to demonstrate the effectiveness of the proposed method. It is also found that the structures obtained by traditional topology optimization usually perform better than the two-scale structures obtained by concurrent topology optimization when only concentrated loads are considered, while the latter may exhibit better performance in the case that distributed loads are involved.

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Stress‐constrained multiscale topology optimization with connectable graded microstructures using the worst‐case analysis

Zhao

Wang

2022

Numerical Meth Engineering

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This article proposes a stress-constrained multiscale topology optimization approach with connectable graded microstructures. The proposed method includes two stages. In the first stage, the shape interpolation method is first employed to generate a series of connectable unit cells. Then the effective elasticity tensors are calculated by the numerical homogenization and XFEM. Besides, the worst-case analysis and stress correction factor are employed to predict the maximum microscopic stress of the unit cells under arbitrary loading conditions. Furthermore, reduced-order models for the stress correction factor and effective elasticity tensor are built to efficiently predict the mechanical properties of the unit cell with any specified volume fraction. In the second stage, stress-constrained topology optimization is employed to find the distribution of microstructures by using established reduced-order models. Except for applying approaches commonly used in the traditional stress-constrained topology optimization, the moving Heaviside function is also proposed to include the void material into optimization. Finally, a threshold projection scheme is performed to realize the design of multiscale structures. Two numerical examples are presented to validate the proposed method. In addition, because the worst-case analysis overestimates the structural stress, an evolutionary discrete optimization is employed to further explore the potential of the multiscale structures.

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Stress-Constrained Topology Optimization for Lattice Materials

Cited by 4 publications

References 34 publications

Numerical and Experimental Optimization for Specific Fatigue Life Maximization of Additively Manufactured Ti-6Al-4V Aerospace Components

Numerical and Experimental Optimization for Specific Fatigue Life Maximization of Additively Manufactured Ti-6Al-4V Aerospace Components

Stress‐constrained concurrent topology optimization of two‐scale hierarchical structures

Stress‐constrained multiscale topology optimization with connectable graded microstructures using the worst‐case analysis

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