Data-Driven Multiscale Topology Optimization Using Multi-Response Latent Variable Gaussian Process

2020 ◽  
Author(s):  
Liwei Wang ◽  
Siyu Tao ◽  
Ping Zhu ◽  
Wei Chen
Keyword(s):  
Topology Optimization ◽  
Gaussian Process ◽  
Latent Variable ◽  
Distance Measure ◽  
Material Design ◽  
Cell Types ◽  
Unit Cell ◽  
Data Driven ◽  
Single Class ◽  
Unit Cells

Abstract The data-driven approach is emerging as a promising method for the topological design of the multiscale structure with greater efficiency. However, existing data-driven methods mostly focus on a single class of unit cells without considering multiple classes to accommodate spatially varying desired properties. The key challenge is the lack of inherent ordering or “distance” measure between different classes of unit cells in meeting a range of properties. To overcome this hurdle, we extend the newly developed latent-variable Gaussian process (LVGP) to creating multi-response LVGP (MRLVGP) for the unit cell libraries of metamaterials, taking both qualitative unit cell concepts and quantitative unit cell design variables as mixed-variable inputs. The MRLVGP embeds the mixed variables into a continuous design space based on their collective effect on the responses, providing substantial insights into the interplay between different geometrical classes and unit cell materials. With this model, we can easily obtain a continuous and differentiable transition between different unit cell concepts that can render gradient information for multiscale topology optimization. While the proposed approach has a broader impact on the concurrent topological and material design of engineered systems, we demonstrate its benefits through multiscale topology optimization with aperiodic unit cells. Design examples reveal that considering multiple unit cell types can lead to improved performance due to the consistent load-transferred paths for micro- and macrostructures.

scholarly journals Data-Driven Topology Optimization With Multiclass Microstructures Using Latent Variable Gaussian Process

2020 ◽  
Vol 143 (3) ◽  
Author(s):  
Liwei Wang ◽  
Siyu Tao ◽  
Ping Zhu ◽  
Wei Chen
Keyword(s):  
Topology Optimization ◽  
Gaussian Process ◽  
Latent Variable ◽  
Load Transfer ◽  
Distance Measure ◽  
Data Driven ◽  
Collective Effects ◽  
Single Class ◽  
Design Variables ◽  
Data Driven Approach

Abstract The data-driven approach is emerging as a promising method for the topological design of multiscale structures with greater efficiency. However, existing data-driven methods mostly focus on a single class of microstructures without considering multiple classes to accommodate spatially varying desired properties. The key challenge is the lack of an inherent ordering or “distance” measure between different classes of microstructures in meeting a range of properties. To overcome this hurdle, we extend the newly developed latent-variable Gaussian process (LVGP) models to create multi-response LVGP (MR-LVGP) models for the microstructure libraries of metamaterials, taking both qualitative microstructure concepts and quantitative microstructure design variables as mixed-variable inputs. The MR-LVGP model embeds the mixed variables into a continuous design space based on their collective effects on the responses, providing substantial insights into the interplay between different geometrical classes and material parameters of microstructures. With this model, we can easily obtain a continuous and differentiable transition between different microstructure concepts that can render gradient information for multiscale topology optimization. We demonstrate its benefits through multiscale topology optimization with aperiodic microstructures. Design examples reveal that considering multiclass microstructures can lead to improved performance due to the consistent load-transfer paths for micro- and macro-structures.

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.

scholarly journals MEMS mirrors using sub-wavelength High- Contrast-Gratings with asymmetric unit cells

2016 ◽  
Vol 19 (2) ◽  
pp. 52
Author(s):  
Milan Maksimović
Keyword(s):  
Spectral Response ◽  
Practical Interest ◽  
Optimization Procedure ◽  
Material Design ◽  
Unit Cell ◽  
High Contrast ◽  
Asymmetric Unit ◽  
Unit Cells ◽  
Thin Elements ◽  
Sub Wavelength

High-contrast gratings (HCG) are ultra-thin elements operating in sub-wavelength regime with the period of the grating smaller than the wavelength and with the high-index grating material fully surrounded by low-index material. Design of MEMS mirrors made from HCG with specific reflectivity response is of great practical interest in integrated optoelectronics. We theoretically investigate design of the spectral response for HCGs with the complex unit cells. We show that the spectral response can be tailored via the unit cell perturbations and with the asymmetric unit cell perturbations may introduce completely new spectral response. Our results can serve as guidance for the design of the complex HCGs and help with the choice of the efficient initial grating topology prior to global optimization procedure.

Rapid Modeling and Design Optimization of Multi-Topology Lattice Structure Based on Unit-Cell Library

2020 ◽  
Vol 142 (9) ◽  
Author(s):  
Yuan Liu ◽  
Shurong Zhuo ◽  
Yining Xiao ◽  
Guolei Zheng ◽  
Guoying Dong ◽  
...  
Keyword(s):  
Topology Optimization ◽  
Lattice Structure ◽  
Structure Design ◽  
Parametric Modeling ◽  
Unit Cell ◽  
Element Analysis ◽  
Structure Generation ◽  
Cell Library ◽  
Unit Cells ◽  
Property Space

Abstract Lightweight lattice structure generation and topology optimization (TO) are common design methodologies. In order to further improve potential structural stiffness of lattice structures, a method combining the multi-topology lattice structure design based on unit-cell library with topology optimization is proposed to optimize the parts. First, a parametric modeling method to rapidly generate a large number of different types of lattice cells is presented. Then, the unit-cell library and its property space are constructed by calculating the effective mechanical properties via a computational homogenization methodology. Third, the template of compromise Decision Support Problem (cDSP) is applied to generate the optimization formulation. The selective filling function of unit cells and geometric parameter computation algorithm are subsequently given to obtain the optimum lightweight lattice structure with uniformly varying densities across the design space. Lastly, for validation purposes, the effectiveness and robustness of the optimized results are analyzed through finite element analysis (FEA) simulation.

Gaussian Process Emulation for Big Data in Data-Driven Metamaterials Design

2019 ◽  
Author(s):  
Ramin Bostanabad ◽  
Yu-Chin Chan ◽  
Liwei Wang ◽  
Ping Zhu ◽  
Wei Chen
Keyword(s):  
Big Data ◽  
Gaussian Process ◽  
Engineering Design ◽  
Training Data ◽  
Data Driven ◽  
Training Dataset ◽  
Massive Datasets ◽  
Unit Cells ◽  
Gaussian Process Emulation ◽  
Novel Method

Abstract Our main contribution is to introduce a novel method for Gaussian process (GP) modeling of massive datasets. The key idea is to build an ensemble of independent GPs that use the same hyperparameters but distribute the entire training dataset among themselves. This is motivated by our observation that estimates of the GP hyperparameters change negligibly as the size of the training data exceeds a certain level, which can be found in a systematic way. For inference, the predictions from all GPs in the ensemble are pooled to efficiently exploit the entire training dataset for prediction. We name our modeling approach globally approximate Gaussian process (GAGP), which, unlike most largescale supervised learners such as neural networks and trees, is easy to fit and can interpret the model behavior. These features make it particularly useful in engineering design with big data. We use analytical examples to demonstrate that GAGP achieves very high predictive power that matches or exceeds that of state-of-the-art machine learning methods. We illustrate the application of GAGP in engineering design with a problem on data-driven metamaterials design where it is used to link reduced-dimension geometrical descriptors of unit cells and their properties. Searching for new unit cell designs with desired properties is then accomplished by employing GAGP in inverse optimization.

Structure, Process, and Material Influences for 3D Printed Lattices Designed With Mixed Unit Cells

2020 ◽  
Author(s):  
Gabriel Briguiet ◽  
Paul F. Egan
Keyword(s):  
Elastic Modulus ◽  
Mechanical Testing ◽  
Mechanical Response ◽  
Cell Types ◽  
Unit Cell ◽  
Ultraviolet Curing ◽  
Mechanical Responses ◽  
Lattice Design ◽  
Unit Cells ◽  
3D Printed

Abstract Emerging 3D printing technologies are enabling the design and fabrication of novel architected structures with advantageous mechanical responses. Designing complex structures, such as lattices, with a targeted response is challenging because build materials, fabrication process, and topological design have unique influences on the structure’s mechanical response. Changing any factor may have unanticipated consequences, even for simpler lattice structures. Here, we conduct mechanical compression experiments to investigate varied lattice design, fabrication, and material combinations using stereolithography printing with a biocompatible polymer. Mechanical testing demonstrates that a higher ultraviolet curing time increases elastic modulus. Material testing demonstrated that anisotropy does not strongly influence lattice mechanics. Designs were altered by comparing homogenous lattices of single unit cell types and heterogeneous lattices that combine two types of unit cells. Unit cells for heterogeneous structures include a Cube design for a high elastic modulus and Cross design for improved shear response. Mechanical testing of three heterogeneous layouts demonstrated how unit cell organization influences mechanical outcomes, therefore enabling the tuning of an elastic modulus that surpasses the law of averages designed for application-dependent mechanical needs. These findings provide a foundation for linking design, process, and material for engineering 3D printed structures with preferred properties, while also facilitating new directions in design automation and optimization.

Meta-Material Design of the Shear Layer of a Non-Pneumatic Wheel Using Topology Optimization

2012 ◽  
Author(s):  
Christopher Czech ◽  
Paolo Guarneri ◽  
Georges Fadel
Keyword(s):  
Topology Optimization ◽  
Shear Layer ◽  
Material Properties ◽  
Relative Size ◽  
Material Design ◽  
Volume Averaging ◽  
Pneumatic Wheel ◽  
Elastomeric Materials ◽  
Unit Cells ◽  
Homogenization Methods

The meta-material design of the shear layer of a non-pneumatic wheel was completed using topology optimization. In order to reduce the hysteretic rolling loss, an elastic material is used and the shear layer microstructure is defined to achieve high compliance comparable to that offered by the elastomeric materials. To simulate the meta-material properties of the shear layer, the volume averaging analysis, instead of more popular homogenization methods, is used as the relative size of the shear layer places realistic manufacturing constraints on the size of unit cells used to generate the meta-material. In this design scenario the properties predicted by the homogenization methods are not accurate since the homogenization scaling assumptions are violated. A number of optimal designs are shown to have meta-material properties similar to those of the linear elastic properties of elastomers, making them good meta-material candidates for the shear layer of the non-pneumatic wheel.

Design of Adaptive Cores of Sandwich Structures Using a Compliant Unit Cell Approach and Topology Optimization

2010 ◽  
Vol 132 (8) ◽  
Author(s):  
Jiangzi Lin ◽  
Zhen Luo ◽  
Liyong Tong
Keyword(s):  
Topology Optimization ◽  
Large Scale ◽  
Sandwich Structures ◽  
Core Layer ◽  
Problem Formulation ◽  
Unit Cell ◽  
Cell Network ◽  
The Core ◽  
Unit Cells ◽  
Scaled Models

This paper presents a new method in designing the core layer of adaptive sandwich structures. The proposed design formulation treats the core layer as a compliant unit cell network while the unit cell network is synthesized by repeatedly linked identical compliant unit cells. Each unit cell is designed to possess shape adaptive functions independently and through the accumulation of the number of cells within the network, the global adaptive functions are accumulated also. Therefore, the network is capable of achieving large scale shape adaptations of complex profile with high fidelity. Topology optimization is used to design the compliant unit cell. Depending on the problem formulation, topology optimization can perform the simultaneous design of both the host material and the actuation material in the defined environment. This research includes a numerical case study to illustrate the technical aspects of this design philosophy. This is followed by the rapid prototyping of two scaled models and experimental validation.

Sign in / Sign up

Export Citation Format

Share Document