scholarly journals Connecting Microstructures for Multiscale Topology Optimization With Connectivity Index Constraints

2018 ◽  
Vol 140 (11) ◽  
Author(s):  
Zongliang Du ◽  
Xiao-Yi Zhou ◽  
Renato Picelli ◽  
H. Alicia Kim
Keyword(s):  
Topology Optimization ◽  
Connectivity Index ◽  
Homogenization Theory ◽  
Advanced Manufacturing ◽  
Numerical Investigations ◽  
Repeated Unit ◽  
Unit Cells ◽  
Architected Material ◽  
Topological Connectivity ◽  
Additional Constraints

With the rapid developments of advanced manufacturing and its ability to manufacture microscale features, architected materials are receiving ever increasing attention in many physics fields. Such a design problem can be treated in topology optimization as architected material with repeated unit cells using the homogenization theory with the periodic boundary condition. When multiple architected materials with spatial variations in a structure are considered, a challenge arises in topological solutions, which may not be connected between adjacent material architecture. This paper introduces a new measure, connectivity index (CI), to quantify the topological connectivity, and adds it as a constraint in multiscale topology optimization to achieve connected architected materials. Numerical investigations reveal that the additional constraints lead to microstructural topologies, which are well connected and do not substantially compromise their optimalities.

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.

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.

scholarly journals An Integrated Geometric-Graph-Theoretic Approach to Representing Origami Structures and Their Corresponding Truss Frameworks

2019 ◽  
Vol 141 (9) ◽  
Author(s):  
Yao Chen ◽  
Pooya Sareh ◽  
Jiayi Yan ◽  
Arash S. Fallah ◽  
Jian Feng
Keyword(s):  
Mechanical Analysis ◽  
Geometric Graph ◽  
Theoretic Approach ◽  
Graph Products ◽  
Science And Engineering ◽  
Graph Theoretic ◽  
Graph Theoretic Approach ◽  
Repeated Unit ◽  
Unit Cells ◽  
Scientists And Engineers

Origami has provided various interesting applications in science and engineering. Appropriate representations and evaluation on crease patterns play an important role in developing an innovative origami structure with desired characteristics. However, this is generally a challenge encountered by scientists and engineers who introduce origami into various fields. As most practical origami structures contain repeated unit cells, graph products provide a suitable choice for the formation of crease patterns. Here, we will employ undirected and directed graph products as a tool for the representation of crease patterns and their corresponding truss frameworks of origami structures. Given that an origami crease pattern can be considered to be a set of directionless crease lines that satisfy the foldability condition, we demonstrate that the pattern can be exactly expressed by a specific graph product of independent graphs. It turns out that this integrated geometric-graph-theoretic method can be effectively implemented in the formation of different crease patterns and provide suitable numbering of nodes and elements. Furthermore, the presented method is useful for constructing the involved matrices and models of origami structures and thus enhances configuration processing for geometric, kinematic, or mechanical analysis on origami structures.

Quasicrystal-related mosaics with periodic lattices interlaid with aperiodic tiles

2020 ◽  
Vol 76 (2) ◽  
pp. 137-144
Author(s):  
Zhanbing He ◽  
Yihan Shen ◽  
Haikun Ma ◽  
Junliang Sun ◽  
Xiuliang Ma ◽  
...  
Keyword(s):  
Solid State ◽  
Long Range ◽  
Orientational Order ◽  
Translational Symmetry ◽  
Repeated Unit ◽  
Unit Cells ◽  
Potential Applications ◽  
New Type ◽  
Structural Blocks

Quasicrystals, which have long-range orientational order without translational symmetry, are incompatible with the theory of conventional crystals, which are characterized by periodic lattices and uniformly repeated unit cells. Reported here is a novel quasicrystal-related solid state observed in two Al–Cr–Fe–Si alloys, which can be described as a mosaic of aperiodically distributed unit tiles in translationally periodic structural blocks. This new type of material possesses the opposing features of both conventional crystals and quasicrystals, which might trigger wide interest in theory, experiments and the potential applications of this type of material.

Topology Optimization of Periodic Structures With Substructuring

2019 ◽  
Vol 141 (7) ◽  
Author(s):  
Junjian Fu ◽  
Liang Xia ◽  
Liang Gao ◽  
Mi Xiao ◽  
Hao Li
Keyword(s):  
Topology Optimization ◽  
Linear System ◽  
Periodic Structures ◽  
Computational Cost ◽  
Optimization Method ◽  
Displacement Fields ◽  
Element Analysis ◽  
Level Set Function ◽  
Static Condensation ◽  
Unit Cells

Topology optimization of macroperiodic structures is traditionally realized by imposing periodic constraints on the global structure, which needs to solve a fully linear system. Therefore, it usually requires a huge computational cost and massive storage requirements with the mesh refinement. This paper presents an efficient topology optimization method for periodic structures with substructuring such that a condensed linear system is to be solved. The macrostructure is identically partitioned into a number of scale-related substructures represented by the zero contour of a level set function (LSF). Only a representative substructure is optimized for the global periodic structures. To accelerate the finite element analysis (FEA) procedure of the periodic structures, static condensation is adopted for repeated common substructures. The macrostructure with reduced number of degree of freedoms (DOFs) is obtained by assembling all the condensed substructures together. Solving a fully linear system is divided into solving a condensed linear system and parallel recovery of substructural displacement fields. The design efficiency is therefore significantly improved. With this proposed method, people can design scale-related periodic structures with a sufficiently large number of unit cells. The structural performance at a specified scale can also be calculated without any approximations. What’s more, perfect connectivity between different optimized unit cells is guaranteed. Topology optimization of periodic, layerwise periodic, and graded layerwise periodic structures are investigated to verify the efficiency and effectiveness of the presented method.

Topology Optimization for Design of Origami-Based Active Mechanisms

2014 ◽  
Author(s):  
Kazuko Fuchi ◽  
Philip R. Buskohl ◽  
James J. Joo ◽  
Gregory W. Reich ◽  
Richard A. Vaia
Keyword(s):  
Topology Optimization ◽  
Mechanism Design ◽  
Design Method ◽  
Truss Structures ◽  
Systematic Design ◽  
Design Strategies ◽  
Foldable Structures ◽  
And Performance ◽  
2D And 3D ◽  
Additional Constraints

Origami structures morph between 2D and 3D conformations along predetermined fold lines that efficiently program the form of the structure and show potential for many engineering applications. However, the enormity of the design space and the complex relationship between origami-based geometries and engineering metrics place a severe limitation on design strategies based on intuition. The presented work proposes a systematic design method using topology optimization to distribute foldline properties within a reference crease pattern, adding or removing folds through optimization, for a mechanism design. Following the work of Schenk and Guest, foldable structures are modeled as pin-joint truss structures with additional constraints on fold, or dihedral, angles. The performance of a designed origami mechanism is evaluated in 3D by applying prescribed forces and finding displacements at set locations. The integration of the concept of origami in mechanism design thus allows for the description of designs in 2D and performance in 3D. Numerical examples indicate that origami mechanisms with desired deformations can be obtained using the proposed method. A constraint on the number of foldlines is used to simplify a design.

Optimal FRP Reinforcement of Masonry Walls under In- and Out-of-Plane Loads

2014 ◽  
Vol 624 ◽  
pp. 429-436 ◽  
Author(s):  
Matteo Bruggi ◽  
Gabriele Milani ◽  
Alberto Taliercio
Keyword(s):  
Topology Optimization ◽  
Strength Properties ◽  
Homogenization Theory ◽  
Masonry Walls ◽  
Optimization Approach ◽  
Optimal Layout ◽  
Transverse Loads ◽  
Out Of Plane ◽  
Frp Reinforcement ◽  
Frp Strips

The problem of finding the optimal layout of FRP strips to effectively retrofit masonry walls undergoing transverse loads is dealt with, taking the presence of permanent vertical loads into account. An innovative topology optimization approach is proposed to define the minimum amount of reinforcement that keeps the stress within a given strength domain throughout the wall. The macroscopic strength properties of masonry are defined by means of a simplified limit analysis approach based on homogenization theory. The capabilities of the proposed procedure are illustrated through applications on a windowed panel subjected to out-of-plane actions and vertical loads.

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 Designing photonic topological insulators with quantum-spin-Hall edge states using topology optimization

Nanophotonics ◽  
2019 ◽  
Vol 8 (8) ◽  
pp. 1363-1369 ◽  
Author(s):  
Rasmus E. Christiansen ◽  
Fengwen Wang ◽  
Ole Sigmund ◽  
Søren Stobbe
Keyword(s):  
Topology Optimization ◽  
Band Gap ◽  
Design Problem ◽  
Topological Insulators ◽  
Quantum Spin ◽  
Edge States ◽  
Unit Cells ◽  
Improved Performance ◽  
Inverse Design Problem ◽  
Quantum Spin Hall

AbstractDesigning photonic topological insulators (PTIs) is highly non-trivial because it requires inversion of band symmetries around the band gap, which was so far done using intuition combined with meticulous trial and error. Here we take a completely different approach: we consider the design of PTIs as an inverse design problem and use topology optimization to maximize the transmission through an edge mode past a sharp bend. Two design domains composed of two different but initially identical C6ν-symmetric unit cells define the geometrical design problem. Remarkably, the optimization results in a PTI reminiscent of the shrink-and-grow approach to quantum-spin-Hall PTIs but with notable differences in the crystal structure as well as qualitatively different band structures and with significantly improved performance as gauged by the band-gap sizes, which are at least 50% larger than in previous designs. Furthermore, we find a directional β-factor exceeding 99% and very low losses for sharp bends. Our approach allows the introduction of fabrication limitations by design and opens an avenue towards designing PTIs with hitherto-unexplored symmetry constraints.

Topology optimization for 3D microstructures of viscoelastic composite materials

2021 ◽  
Author(s):  
Jianglin Yang ◽  
Shiyang Zhang ◽  
Jian Li
Keyword(s):  
Composite Material ◽  
Topology Optimization ◽  
Viscoelastic Material ◽  
Effective Properties ◽  
Vibration Damping ◽  
Homogenization Theory ◽  
Viscoelastic Composite ◽  
Viscoelastic Composite Material ◽  
High Stiffness ◽  
Beso Method

Abstract Materials with high stiffness and good vibration damping properties are of great industrial interest. In this paper, a topology optimization algorithm based on the BESO method is applied to design viscoelastic composite material by adjusting its 3D microstructures. The viscoelastic composite material is assumed to be composed of a non-viscoelastic material with high stiffness and a viscoelastic material with good vibration damping. The 3D microstructures of the composite are uniformly represented by corresponding periodic unit cells (PUCs). The effective properties of the 3D PUC are extracted by the homogenization theory. The optimized properties of the composites and the optimal microscopic layout of the two materials phases under the conditions of maximum stiffness and maximum damping are given by several numerical examples.

Sign in / Sign up

Export Citation Format

Share Document