Topology optimization of multiscale structures considering local and global buckling response

Christensen, Christoffer Fyllgraf; Wang, Fengwen; Sigmund, Ole

doi:10.1016/j.cma.2023.115969

Cited by 27 publications

(7 citation statements)

References 44 publications

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“…We conclude from this, that the load factor could potentially be larger, i.e., better structures could be obtained, if we chose a lower ρ min . On the other hand, for very low ρ min , the problem would no longer be a sizing but rather a topology optimization problem, which would require special handling (see, e.g., Christensen et al (2022)).…”

Section: A) Pure Macroscopic Load Factor Optimizationmentioning

confidence: 99%

“…The work of Christensen et al (2022) is similar to ours, with some key differences: They assume isotropic buckling behavior of the microstructure, while our approach is applicable to arbitrary microstructures. They also fit a Willam-Warnke failure criterion to homogenized data, which introduces an approximation error of the local buckling factor.…”

Section: Introductionmentioning

confidence: 99%

“…In contrast, we build a worst-case model from homogenized data, which also comes with an approximation error; however, applying a full interpolation model in lieu of the worst case, it is possible to render this error negligible (see Remark 1 in Section 4.1). Moreover, Christensen et al (2022) employ a two term interpolation scheme to interpolate the buckling strength as a function of the relative porosity, whereas we use more accurate piecewise cubic interpolation. On the other hand, our approach is limited to sizing problems with a lower bound on the lattice density everywhere, while a major contribution of Christensen et al (2022) is the possibility to allow for void regions in the design while still being able to maintain the lower bound on the density of the lattice using an auxiliary design field.…”

Section: Introductionmentioning

confidence: 99%

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Two-Scale Optimization of Graded Lattice Structures respecting Buckling on Micro- and Macroscale

Hübner¹,

Wein²,

Stingl³

2023

Preprint

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Interest in components with detailed structures increased with the progress in advanced manufacturing techniques in recent years. Parts with graded lattice elements can provide interesting mechanical, thermal, and acoustic properties compared to parts where only coarse features are included. One of these improvements is better global buckling resistance of the component. However, thin features are prone to local buckling. Normally, analyses with high computational effort are conducted on high-resolution finite element meshes to optimize parts with good global and local stability. Until recently, works focused only on either global or local buckling behavior. We use two-scale optimization based on asymptotic homogenization of elastic properties and local buckling behavior to reduce the effort of full-scale analyses. For this, we present an approach for concurrent local and global buckling optimization of parameterized graded lattice structures. It is based on a worst-case model for the homogenized buckling load factor, which acts as a safeguard against pure local buckling. Cross-modes residing on both scales are not detected. We support our theory with numerical examples and validations on dehomogenized designs, which show the capabilities of our method, and discuss the advantages and limitations of the worst-case model.

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Section: A) Pure Macroscopic Load Factor Optimizationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Two-Scale Optimization of Graded Lattice Structures respecting Buckling on Micro- and Macroscale

Hübner¹,

Wein²,

Stingl³

2023

Preprint

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show abstract

“…Groen et al [22] simplified and improved the de-homogenization method [23], achieving the design of high-resolution multiscale structures through the projection method with orthotropic infill. Subsequently, the de-homogenization method has been extended to deal with optimization problems such as multiple loading cases [24], 3D topologies [25], buckling [26], and more. Moreover, Wang et al [27] extended the use of the sawtooth function to apply it to frequency response design.…”

Section: Introductionmentioning

confidence: 99%

Optimal design of non-uniform curved grid-stiffened shell with different stiffener patterns

Yu,

Xiaoang,

Yan

et al. 2023

Preprint

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This paper presents a non-uniform curved grid-stiffened shell design method aiming to enhance structural performance using various stiffener patterns, allowing simultaneous optimization of stiffener thickness and stiffener layout. Firstly, the grid-stiffened cell description function is defined using quadratic polynomial functions, comprising the orthogrid, the triangle grid, the rotated triangle grid and the Kagome grid. Then, the non-uniform stiffener layout description function is established using the sawtooth function, while a filter function is employed to ensure the smooth and continuous of the stiffeners. Moreover, the analytical sensitivity is thoroughly derived, and the optimization problem is formulated. Finally, the effectiveness of the proposed method is demonstrated through three representative numerical examples: the cantilever beam, the special-shaped plate and the S-shape shell. The study concludes that the proposed method can optimize arbitrary flat plates by embedding the design domain into the background grid. Additionally, the proposed method can be extended to perform stiffener design on complex surfaces using mesh projection technology. Optimization results indicate that the non-uniform curved grid-stiffened shell design exhibits superior structural performance compared to the uniform grid-stiffened shell design.

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“…From the computational viewpoint, combined microstructure and topology optimization problems have been recently investigated in a number of different settings. The reader is referred to [9,17,25,27,29,36] among others, as well as to the recent survey [38].…”

Section: Introductionmentioning

confidence: 99%

Topology Optimization for Incremental Elastoplasticity: A Phase-Field Approach

Almi¹,

Stefanelli²

2021

SIAM J. Control Optim.

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Progresses in additive manufacturing technologies allow the realization of finely graded microstructured materials with tunable mechanical properties. This paves the way to a wealth of innovative applications, calling for the combined design of the macroscopic mechanical piece and its underlying microstructure. In this context, we investigate a topology optimization problem for an elastic medium featuring a periodic microstructure. The optimization problem is variationally formulated as a bilevel minimization of phase-field type. By resorting to Γ -convergence techniques, we characterize the homogenized problem and investigate the corresponding sharp-interface limit. First-order optimality conditions are derived, both at the homogenized phase-field and at the sharp-interface level.

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Topology optimization of multiscale structures considering local and global buckling response

Cited by 27 publications

References 44 publications

Two-Scale Optimization of Graded Lattice Structures respecting Buckling on Micro- and Macroscale

Two-Scale Optimization of Graded Lattice Structures respecting Buckling on Micro- and Macroscale

Optimal design of non-uniform curved grid-stiffened shell with different stiffener patterns

Topology Optimization for Incremental Elastoplasticity: A Phase-Field Approach

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