Stress-based and robust topology optimization for thermoelastic multi-material periodic microstructures

Alacoque, Lee; Watkins, Ryan; Tamijani, Ali Y.

doi:10.1016/j.cma.2021.113749

Cited by 58 publications

(20 citation statements)

References 50 publications

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“…Microstructures with high stiffness, robust strength, and unique thermal expansion properties were obtained in their works. 33 Recently, stress-constrained multiscale topology optimization has attracted much attention. Pasini et al studied stress-constrained topology optimization problems for lattice materials.…”

Section: Introductionmentioning

confidence: 99%

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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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Section: Introductionmentioning

confidence: 99%

“…Alacoque et al studied the robust topology optimization of the multi‐material microstructure under stress constraints and thermal load. Microstructures with high stiffness, robust strength, and unique thermal expansion properties were obtained in their works 33 …”

Section: Introductionmentioning

confidence: 99%

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

Zhao

Wang

2022

Numerical Meth Engineering

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“…41 The use of various AM techniques in conjunction with topology optimization has led to introducing the concept of architectured cellular structures for optimized properties under various operational conditions. 42,43 However, despite an accurate finish, the material properties of the additively manufactured cellular structures are affected by different printing parameters such as laser speed, thermal stresses, and build orientation. Such parameters must be considered for the optimal design of these components.…”

Section: Introductionmentioning

confidence: 99%

“…Using numerical homogenization instead of traditional relative density functions allows considering the effects of material anisotropies and furthermore computing macroscopic elastic properties for more complex patterns and cell topologies. 43,45 As for the fracture criterion, the MPS is formulated for anisotropic domains by considering the effect of T-stress (the first nonsingular term in continuum crack tip stress fields) as well as the stress intensity factors (SIFs). The proposed framework is examined against results obtained by the direct finite element analysis (FEA) (i.e., where the stress components are obtained directly from finite element [FE] results) and the effects of different cell topologies on the fracture behavior are discussed.…”

Section: Introductionmentioning

confidence: 99%

On brittle fracture of two‐dimensional lattices with material anisotropies

Mirsayar

2022

Fatigue Fract Eng Mat Struct

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For the first time, this paper proposes a multiscale computational approach to investigate mixed‐mode I/II fracture in two‐dimensional lattices containing material anisotropies which find their applications in additive manufacturing of cellular structures. The layer‐by‐layer fabrication of lattices produced by the additive manufacturing techniques causes material anisotropies corresponding to the build orientation. Such material anisotropies, together with the cell topology, affect the fracture behavior of lattice components under various mechanical loading. The effective macroscopic elastic properties of periodic lattices obtained via numerical homogenization are fed into a continuum‐based fracture criterion to obtain crack path and onset of fracture under mixed‐mode I/II conditions. Different cell topologies are considered, and the predictions are compared with the results obtained directly by the finite element analysis. The results of this work can pave the way toward further understanding, and eventually, optimizing fracture toughness of additively manufactured lattices against various loading profiles.

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“…The uncertainty-oriented approaches are divided into robust TO (RTO) [17] and reliability-based TO (RBTO) [18]. The RTO handles the uncertainties through constructing a comprehensive performance function in terms of their mean and standard deviation [19][20][21], while the RBTO brings the reliability theory, i.e., integrating the reliability index or failure probability, into the optimization framework [22,23]. Obviously, more precise layout may be achieved using the RBTO strategy because the structural performance is measured to control the uncertainty influence in every iteration.…”

Section: Introductionmentioning

confidence: 99%

A novel dynamic reliability-based topology optimization (DRBTO) framework for continuum structures via interval-process collocation and the first-passage theories

Wang

Liu

et al. 2021

Computer Methods in Applied Mechanics and Engineering

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Stress-based and robust topology optimization for thermoelastic multi-material periodic microstructures

Cited by 58 publications

References 50 publications

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

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

On brittle fracture of two‐dimensional lattices with material anisotropies

A novel dynamic reliability-based topology optimization (DRBTO) framework for continuum structures via interval-process collocation and the first-passage theories

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