scholarly journals Bézier extraction based isogeometric approach to multi‐objective topology optimization of periodic microstructures

2021 ◽  
Author(s):  
Chungang Zhuang ◽  
Zhenhua Xiong ◽  
Han Ding
Keyword(s):  
Topology Optimization ◽  
Multi Objective ◽  
Periodic Microstructures ◽  
Bézier Extraction

scholarly journals NODAL COSINE SINE MATERIAL INTERPOLATION IN MULTI OBJECTIVE TOPOLOGY OPTIMIZATION WITH THE GLOBAL CRITERIA METHOD FOR LINEAR ELASTO STATIC, HEAT TRANSFER, POTENTIAL FLOW AND BINARY CROSS ENTROPY SHARPENING

2021 ◽  
Vol 1 ◽  
pp. 2247-2256
Author(s):  
Martin Denk ◽  
Klemens Rother ◽  
Mario Zinßer ◽  
Christoph Petroll ◽  
Kristin Paetzold
Keyword(s):  
Heat Transfer ◽  
Topology Optimization ◽  
Potential Flow ◽  
Cross Entropy ◽  
Objective Criterion ◽  
Multi Objective ◽  
Material Interpolation ◽  
Continuous Material ◽  
Mean Compliance ◽  
Transfer Potential

AbstractTopology optimization is typically used for suitable design suggestions for objectives like mean compliance, mean temperature, or model analysis. Some modern modeling technics in topology optimization require a nodal based material interpolation. Therefore this article is referred to a continuous material interpolation in topology optimization. To cover a smooth and differentiable density field, we address trigonometric shape functions which are infinitely differentiable. Furthermore, we extend a so-known global criteria method with a sharpening function based on binary cross-entropy, so that sharper solutions results. The proposed material interpolation is applied to different applications such as heat transfer, elasto static, and potential flow. Furthermore, these different objectives are together optimized using a multi-objective criterion.

An Evolutionary Multi-Objective Optimization Approach to the Topology Optimization of Auxetic Structures

2002 ◽  
Author(s):  
Ashraf O. Nassef
Keyword(s):  
Topology Optimization ◽  
Elastic Modulus ◽  
Finite Elements ◽  
Multiobjective Optimization ◽  
Poisson Ratio ◽  
Optimization Approach ◽  
Multi Objective Optimization ◽  
Finite Elements Analysis ◽  
Multi Objective ◽  
Auxetic Structures

Auxetic structures are ones, which exhibit an in-plane negative Poisson ratio behavior. Such structures can be obtained by specially designed honeycombs or by specially designed composites. The design of such honeycombs and composites has been tackled using a combination of optimization and finite elements analysis. Since, there is a tradeoff between the Poisson ratio of such structures and their elastic modulus, it might not be possible to attain a desired value for both properties simultaneously. The presented work approaches the problem using evolutionary multiobjective optimization to produce several designs rather than one. The algorithm provides the designs that lie on the tradeoff frontier between both properties.

Multiscale Topology Optimization With Gaussian Process Regression Models

2021 ◽  
Author(s):  
Joel C. Najmon ◽  
Homero Valladares ◽  
Andres Tovar
Keyword(s):  
Topology Optimization ◽  
Gaussian Process ◽  
Regression Models ◽  
Computational Cost ◽  
Gaussian Process Regression ◽  
Analytical Sensitivity ◽  
Inverse Homogenization ◽  
Discrete Location ◽  
Unit Cells ◽  
Periodic Microstructures

Abstract Multiscale topology optimization (MSTO) is a numerical design approach to optimally distribute material within coupled design domains at multiple length scales. Due to the substantial computational cost of performing topology optimization at multiple scales, MSTO methods often feature subroutines such as homogenization of parameterized unit cells and inverse homogenization of periodic microstructures. Parameterized unit cells are of great practical use, but limit the design to a pre-selected cell shape. On the other hand, inverse homogenization provide a physical representation of an optimal periodic microstructure at every discrete location, but do not necessarily embody a manufacturable structure. To address these limitations, this paper introduces a Gaussian process regression model-assisted MSTO method that features the optimal distribution of material at the macroscale and topology optimization of a manufacturable microscale structure. In the proposed approach, a macroscale optimization problem is solved using a gradient-based optimizer The design variables are defined as the homogenized stiffness tensors of the microscale topologies. As such, analytical sensitivity is not possible so the sensitivity coefficients are approximated using finite differences after each microscale topology is optimized. The computational cost of optimizing each microstructure is dramatically reduced by using Gaussian process regression models to approximate the homogenized stiffness tensor. The capability of the proposed MSTO method is demonstrated with two three-dimensional numerical examples. The correlation of the Gaussian process regression models are presented along with the final multiscale topologies for the two examples: a cantilever beam and a 3-point bending beam.

Multi-Objective Topological Optimization of Support Frame for High-Speed and Heavy-Load Triangle Track Wheel Based on Analytic Hierarchy Process

2018 ◽  
Author(s):  
Fenghe Wu ◽  
Zhaohua Wang ◽  
Yinxu Sun ◽  
Yulin Yang ◽  
Yongxin Li ◽  
...  
Keyword(s):  
Topology Optimization ◽  
High Speed ◽  
Working Condition ◽  
Average Frequency ◽  
Frequency Method ◽  
Analytic Hierarchy ◽  
Heavy Load ◽  
Multi Objective ◽  
Support Frame ◽  
Hierarchy Process

The high-speed, heavy-load and changeable triangle track wheel is a motion device that can carry out interchange between the track wheel and tire in an ordinary vehicle. The topology optimization for the support frame can reduce weight and improve the maneuverability of the vehicle. However, it is difficult to consider simultaneously its weight, stiffness and modal in the process of the structure optimization. Thus, a topology optimization method for multi-objective and multi-working-condition is proposed based on the AHP (analytic hierarchy process) and average frequency method. Firstly, considering the static multi-stiffness target and dynamic vibration frequency target, using the compromise programming method and average frequency method, the objective function of the multi-objective and multi-working-condition topology optimization is established. Then, based on the optimization target, design criteria and indexes, the lightweight hierarchical structure model of the support frame consisting of three levels and eight weight factors is established. Values of 8 weight coefficients of the multi-objective topology optimization are determined through solving the weight factor judgment matrix. Finally, considering the multi-working-condition, taking the minimum objective function of the static and dynamic characteristics as target, and the volume ratio is 50% as boundary, the mathematical model of the topology optimization is established. Simulation results show that the stiffness and strength of the support frame are improved respectively by 74.3% and 1.3% while its weight is reduced by 16.3%. This method also provides a new way to the lightweight design for other large, heavy and multi-condition equipment.

Multi-Objective Topology Optimization for Bevel Gear and Geometrical Reconstruction

2013 ◽  
Vol 278-280 ◽  
pp. 139-142
Author(s):  
Xiang Bian ◽  
Zong De Fang ◽  
Kun Qin ◽  
Lifei Lian ◽  
Bao Yu Zhang
Keyword(s):  
Topology Optimization ◽  
Optimization Method ◽  
Tooth Root ◽  
Multi Objective Optimization ◽  
Direct Optimization ◽  
Multi Objective ◽  
Gear Modification ◽  
Parametric Cad ◽  
Straight Lines ◽  
Root Stress

Usually the gear modification is a main measure to reduce the vibration and noise of the gears, but in view of the complexity of the gear modification, topology optimization method was used to optimize the structure of the gear. The minimum volume was set as the direct optimization goal. To achieve the target of reducing contact stress, tooth root bending stress and improving flexibility, the upper bound of the stress and lower bound of the flexibility were set appropriately, thus realizing multi-objective optimization indirectly. A method for converting topology result into parametric CAD model which can be modified was presented, by fitting the topology result with simple straight lines and arcs, the model can be smoothed automatically, after further regulating, the geometry reconstruction was finished. After topology optimization, the resulting structure and properties of the gear are consistent with cavity gear. While reducing the weight of the gear, the noise can be reduced and its life would be extended through increasing flexibility and reducing tooth root stress.

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