Stress-Constrained Design of Functionally Graded Lattice Structures With Spline-Based Dimensionality Reduction

Zhang, Jenmy Zimi; Sharpe, Conner; Seepersad, Carolyn Conner

doi:10.1115/detc2019-97905

Cited by 5 publications

(6 citation statements)

References 35 publications

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“…Note that the value and location of the maximum stress depend on the applied strain field, making that the stress of each element of the unit cells needs to be evaluated. In this article, we adopt the worst-case analysis method to predict the maximum microscopic von Mises stress 37,38 instead of calculating all the microscopic stresses in the optimization. To employ this method, we rewrite Equation ( 6) as:…”

Section: Prediction Of the Maximum Microscopic Stress By Worst-case A...mentioning

confidence: 99%

“…Substituting Equation (38) into Equation (37), the sensitivity of the constraint function can be written as:…”

Section: Sensitivity Analysismentioning

confidence: 99%

“…Note that the value and location of the maximum stress depend on the applied strain field, making that the stress of each element of the unit cells needs to be evaluated. In this article, we adopt the worst‐case analysis method to predict the maximum microscopic von Mises stress 37,38 instead of calculating all the microscopic stresses in the optimization. To employ this method, we rewrite Equation (6) as:

\begin{aligned} {bold-italicσ}_{m n}^{mi} & = H ((), boldx) {boldD}^{normalB} ((), boldI prefix- boldb ((), boldx) {bold-italicχ}_{n}) {((), {boldD}_{}^{normalH})}^{prefix- 1} {\overset{bold-italicσ}{true}}_{m}^{ma} \\ = H ((), boldx) {boldD}^{normalB} ((), boldI prefix- boldb ((), boldx) {bold-italicχ}_{n}) {((), {boldD}_{}^{normalB})}^{prefix- 1} {bold-italicσ}_{normalB m}^{ma} \\ = {boldC}_{n} ((), boldx) {bold-italicσ}_{normalB m}^{ma} \end{aligned},

where

{\overset{bold-italic‾}{σ}}_{m}^{ma} = D_{}^{H} ε_{m}^{ma}

represents the homogenized stress,

σ_{B m}^{ma} = D_{}^{B} ε_{m}^{ma}

is the stress of the

m

th macroscopic element with the solid material,

…”

Section: Generation Of Connectable Graded Microstructures and Their R...mentioning

confidence: 99%

“…36 Based on the worst-case analysis, 37 Zhang et al used the surrogate modeling technique to design the functionally graded lattice structure considering the strength performance. 38 Thillaithevan et al utilized the response surface model to design structures with graded lattice microstructures. 39 Yu et al handled the shell-lattice infill structural design under the von Mises stress-based and Tsai-Hill yield criteria-based constraints by using the level set method.…”

Section: Introductionmentioning

confidence: 99%

“…Qiu et al proposed a topology optimization approach for the structure with solid material and lattice material under the stress constraint 36 . Based on the worst‐case analysis, 37 Zhang et al used the surrogate modeling technique to design the functionally graded lattice structure considering the strength performance 38 . Thillaithevan et al utilized the response surface model to design structures with graded lattice microstructures 39 .…”

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: Prediction Of the Maximum Microscopic Stress By Worst-case A...mentioning

confidence: 99%

“…Substituting Equation (38) into Equation (37), the sensitivity of the constraint function can be written as:…”

Section: Sensitivity Analysismentioning

confidence: 99%

“…Note that the value and location of the maximum stress depend on the applied strain field, making that the stress of each element of the unit cells needs to be evaluated. In this article, we adopt the worst‐case analysis method to predict the maximum microscopic von Mises stress 37,38 instead of calculating all the microscopic stresses in the optimization. To employ this method, we rewrite Equation (6) as: