ICM method for topology optimization of multimaterial continuum structure with displacement constraint

Ye, Hongling; Dai, Zong-Jie; Wang, Weiwei; Sui, Yunkang

doi:10.1007/s10409-018-0827-3

Cited by 28 publications

(6 citation statements)

References 31 publications

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“…It has higher overall and local performance. To give full play to the performance advantages of multi-material structures, MMTO is used to obtain structures with optimal performance that meet the design requirements [29]. The development of additive manufacturing also enables the MMTO.…”

Section: Multi-materials Interpolation Modelmentioning

confidence: 99%

Probabilistic-Ellipsoid Hybrid Reliability Multi-Material Topology Optimization Method Based on Stress Constraint

Mao,

Zhao,

Zhang

2024

CMES

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This paper proposes a multi-material topology optimization method based on the hybrid reliability of the probability-ellipsoid model with stress constraint for the stochastic uncertainty and epistemic uncertainty of mechanical loads in optimization design. The probabilistic model is combined with the ellipsoidal model to describe the uncertainty of mechanical loads. The topology optimization formula is combined with the ordered solid isotropic material with penalization (ordered-SIMP) multi-material interpolation model. The stresses of all elements are integrated into a global stress measurement that approximates the maximum stress using the normalized p-norm function. Furthermore, the sequential optimization and reliability assessment (SORA) is applied to transform the original uncertainty optimization problem into an equivalent deterministic topology optimization (DTO) problem. Stochastic response surface and sparse grid technique are combined with SORA to get accurate information on the most probable failure point (MPP). In each cycle, the equivalent topology optimization formula is updated according to the MPP information obtained in the previous cycle. The adjoint variable method is used for deriving the sensitivity of the stress constraint and the moving asymptote method (MMA) is used to update design variables. Finally, the validity and feasibility of the method are verified by the numerical example of L-shape beam design, T-shape structure design, steering knuckle, and 3D T-shaped beam.

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Section: Multi-materials Interpolation Modelmentioning

confidence: 99%

Probabilistic-Ellipsoid Hybrid Reliability Multi-Material Topology Optimization Method Based on Stress Constraint

Mao,

Zhao,

Zhang

2024

CMES

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“…To determine which kind of microstructure is suitable for every element, multiple kinds of topological variables relating to every element are introduced to seek out the optimized macroscopic topology and rational layout of various lattice microstructures. The volume

and stiffness matrix

of the i -th element in a three-phase domain (two different constituent materials and one void phase) can be identified using various filter functions [ 56 ] as follows:

where

and

are the first and second kinds of topological variables with regard to the i -th element, respectively;

and

respectively represent the intrinsic volumes of the first and second kinds of microstructure elements;

and

indicate the intrinsic stiffness matrices of the first and second kinds of microstructure elements, respectively;

and

are the first and second volume filter functions, respectively; and

and

are the first and second stiffness matrix filter functions, respectively. Based on Equations (3) and (4), it can be apparently seen that the first kind

confirms the macroscale structure (with or without material), while the second kind

recognizes the designated material for every retained element.…”

Section: Parallel Topology Optimization Formulations For Hlcmsmentioning

confidence: 99%

Topology Optimization for Hybrid Lattice Compliant Mechanisms with Multiple Microstructures

Wei

Wang

et al. 2022

Materials

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Hybrid lattice compliant mechanisms (HLCMs) composed of multiple microstructures have attracted widespread interest due to their superior compliant performance compared to the traditional solid compliant mechanisms. A novel optimization scheme for HLCMs is presented using the independent continuous mapping (ICM) method. Firstly, the effective properties of multiple orthogonal and anisotropic lattice microstructures are obtained by taking advantage of homogenization theory, which are used to bridge the relationship between the macrostructure layout and microstructure recognition. Then, a new parallel topology optimization model for optimizing HLCMs is built via a generalized multi-material, recognizing interpolation scheme with filter functions. In addition, the characterization relationship between independent continuous variables and performance of different elements is established. Sensitivity analysis and linear programming are utilized to solve the optimal model. Lastly, numerical examples with a displacement inverter mechanism and compliant gripper mechanism demonstrate the effectiveness of the proposed method for designing HLCMs with various lattice microstructures. Anisotropic lattice microstructures (ALMs) significantly facilitate the efficient use of constitutive properties of materials. Hence, HLCMs consisting of various ALMs achieve superior compliant performance than counterparts comprising different orthogonal lattice microstructures (OLMs). The presented method offers a reference to optimize HLCMs, as well as promotes the theoretical development and application of the ICM method.

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“…Topology optimization may greatly enhance the performances of materials and structures for many engineering applications. It has been exhaustively studied, and various topology optimization methods have been developed over the past few decades, e.g., the solid isotropic material with penalization (SIMP) method [17], evolutionary structural optimization (ESO) method [18], bi-directional evolutionary structural optimization (BESO) method [19,20], moving morphable component (MMC) method [21], feature-drive method [22,23], level set method [24,25], independent continuous mapping (ICM) method [26], and feasible domain adjustment topology optimization method [27].…”

Section: Optimization Of Cellular Materials and Sandwich Structuresmentioning

confidence: 99%

DMA2022 Dynamic resistance and energy absorption of sandwich beam with based on micro-topology optimization with maximum shear modulus

et al. 2022

Preprint

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Based on the mechanical characteristics of the core layer, which withstands the shear stress and deformation of a sandwich beam, a topology optimization framework based on the bi-directional evolutionary structural optimization method is proposed to optimize the core layer composed of a periodic base cell with extreme shear stiffness. The effects of the volume fraction, filter radius, and initial periodic base cell (PBC) aspect ratio on the micro-topology of the core and the dynamic response process, core compression, and energy absorption capacity of the sandwich beams under blast impact loading were analyzed by the finite element method. The results demonstrated that the over-pressure action stage was coupled with the core compression stage. Under the same loading and mass per unit area, the sandwich beam with a 20% volume fraction core layer had the best blast resistance. The filter radius has a slight effect on the shear stiffness and blast resistances of the sandwich beams, but increasing the filter radius could slightly improve the bending stiffness. Upon changing the initial PBC aspect ratio, there are three methods for PBC evolution: the first is to change the angle between the adjacent bars, the second is to further form holes in the bars, and the third is to combine the first two methods. However, not all three methods can improve the energy absorption capacity of the structure. Changing the aspect ratio of the PBC arbitrarily may lead to worse results. More detailed studies are necessary if further optimization is to be achieved.

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ICM method for topology optimization of multimaterial continuum structure with displacement constraint

Cited by 28 publications

References 31 publications

Probabilistic-Ellipsoid Hybrid Reliability Multi-Material Topology Optimization Method Based on Stress Constraint

Probabilistic-Ellipsoid Hybrid Reliability Multi-Material Topology Optimization Method Based on Stress Constraint

Topology Optimization for Hybrid Lattice Compliant Mechanisms with Multiple Microstructures

DMA2022 Dynamic resistance and energy absorption of sandwich beam with based on micro-topology optimization with maximum shear modulus

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