scholarly journals Topology optimization of periodically arranged components using shared design domains

2021 ◽  
Vol 65 (1) ◽  
Author(s):  
Jasper Rieser ◽  
Markus Zimmermann
Keyword(s):  
Topology Optimization ◽  
Design Problem ◽  
Periodic Structures ◽  
Computational Cost ◽  
Structural Complexity ◽  
Connected Components ◽  
Periodic Pattern ◽  
Building Structures ◽  
Constraint Aggregation ◽  
Component Design

AbstractBuilding structures from identical components organized in a periodic pattern is a common design strategy to reduce design effort, structural complexity and cost. However, any periodic pattern will impose certain design restrictions often leading to lower structural efficiency and heavier weight. Much research is available for periodic structures with connected components. This paper addresses minimal compliance design for periodic arrangements of unconnected components. The design problem discussed here is relevant for many applications where a tightly nested, space-saving arrangement of identical components is required. We formulate an optimal design problem for a component being part of a periodic arrangement. The orientation and position of the component relatively to its neighbours are prescribed. The component design is computed by topology optimization on a design domain possibly shared by several neighbouring components. Additional constraints prevent components from overlapping. Constraint aggregation is employed to reduce the computational cost of many local constraints. The effectiveness of the method is demonstrated by a series of 2D and 3D examples with an ever-smaller distance between the components. Moreover, problem-specific ranges with only little to no increase in compliance are reported.

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.

Improved Melting and Solidification in Thermal Energy Storage Through Topology Optimization of Highly Conductive Fins

2017 ◽  
Author(s):  
Alberto Pizzolato ◽  
Adriano Sciacovelli ◽  
Vittorio Verda
Keyword(s):  
Topology Optimization ◽  
Energy Storage ◽  
Phase Change ◽  
Thermal Energy ◽  
Thermal Energy Storage ◽  
Phase Change Materials ◽  
Optimization Method ◽  
Periodic Pattern ◽  
Melting Time ◽  
Bottom Part

Thermal energy storage units based on phase change materials (PCMs) need a fine design of highly conductive fins to improve the average heat transfer rate. In this paper, we seek the optimal distribution of a highly conductive material embedded in a PCM through a density-based topology optimization method. The phase change problem is solved through an enthalpy-porosity model, which accounts for natural convection in the fluid. Results show fundamental differences in the optimized layout between the solidification and the melting case. Fins optimized for solidification show a quasi-periodic pattern along the angular direction. On the other hand, fins optimized for melting elongate mostly in the bottom part of the unit leaving only two short baffles at the top. In both cases, the optimized structures show non-intuitive details which could not be obtained neglecting fluid flow. These additional features reduce the solidification and melting time by 11 % and 27 % respectively compared to a structure optimized for diffusion.

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 A Parameter Study of Localization

1996 ◽  
Vol 3 (1) ◽  
pp. 1-10 ◽  
Author(s):  
Sandor Stephen Mester ◽  
Haym Benaroya
Keyword(s):  
Periodic Structures ◽  
Numerical Study ◽  
Vibration Characteristics ◽  
Periodic Pattern ◽  
Parameter Study ◽  
Structural Damping ◽  
One Dimensional

Extensive work has been done on the vibration characteristics of perfectly periodic structures. Disorder in the periodic pattern has been found to lead to localization in one-dimensional periodic structures. It is important to understand localization because it causes energy to be concentrated near the disorder and may cause an overestimation of structural damping. A numerical study is conducted to obtain a better understanding of localization. It is found that any mode, even the first, can localize due to the presence of small imperfections.

(Generalized) Bloch mode synthesis for the fast dispersion curve calculation of 3D periodic metamaterials

2021 ◽  
Vol 263 (4) ◽  
pp. 2102-2113
Author(s):  
Vanessa Cool ◽  
Lucas Van Belle ◽  
Claus Claeys ◽  
Elke Deckers ◽  
Wim Desmet
Keyword(s):  
Dispersion Curve ◽  
Periodic Structures ◽  
Cell Model ◽  
Stop Band ◽  
Computational Cost ◽  
Order Reduction ◽  
Element Model ◽  
Unit Cell ◽  
Reduction Techniques ◽  
Bloch Mode

Metamaterials, i.e. artificial structures with unconventional properties, have shown to be highly potential lightweight and compact solutions for the attenuation of noise and vibrations in targeted frequency ranges, called stop bands. In order to analyze the performance of these metamaterials, their stop band behavior is typically predicted by means of dispersion curves, which describe the wave propagation in the corresponding infinite periodic structure. The input for these calculations is usually a finite element model of the corresponding unit cell. Most common in literature are 2D plane metamaterials, which often consist of a plate host structure with periodically added masses or resonators. In recent literature, however, full 3D metamaterials are encountered which are periodic in all three directions and which enable complete, omnidirectional stop bands. Although these 3D metamaterials have favorable vibro-acoustic characteristics, the computational cost to analyze them quickly increases with unit cell model size. Model order reduction techniques are important enablers to overcome this problem. In this work, the Bloch Mode Synthesis (BMS) and generalized BMS (GBMS) reduction techniques are extended from 2D to 3D periodic structures. Through several verifications, it is demonstrated that dispersion curve calculation times can be strongly reduced, while accurate stop band predictions are maintained.

Using Bayesian Optimization With Knowledge Transfer for High Computational Cost Design: A Case Study in Photovoltaics

2019 ◽  
Author(s):  
Mine Kaya ◽  
Shima Hajimirza
Keyword(s):  
Solar Cells ◽  
Design Problem ◽  
Cost Optimization ◽  
Computational Cost ◽  
Design Procedure ◽  
Bayesian Optimization ◽  
Optimization Framework ◽  
Previous Design ◽  
High Computational Cost

Abstract Engineering design is usually an iterative procedure where many different configurations are tested to yield a desirable end performance. When the design objective can only be measured by costly operations such as experiments or cumbersome computer simulations, a thorough design procedure can be limited. The design problem in these cases is a high cost optimization problem. Meta model-based approaches (e.g. Bayesian optimization) and transfer optimization are methods that can be used to facilitate more efficient designs. Transfer optimization is a technique that enables using previous design knowledge instead of starting from scratch in a new task. In this work, we study a transfer optimization framework based on Bayesian optimization using Gaussian Processes. The similarity among the tasks is determined via a similarity metric. The framework is applied to a particular design problem of thin film solar cells. Planar multilayer solar cells with different sets of materials are optimized to obtain the best opto-electrical efficiency. Solar cells with amorphous silicon and organic absorber layers are studied and the results are presented.

Dimension reduction and surrogate based topology optimization of periodic structures

2019 ◽  
Vol 229 ◽  
pp. 111385 ◽  
Author(s):  
Min Li ◽  
Zhibao Cheng ◽  
Gaofeng Jia ◽  
Zhifei Shi
Keyword(s):  
Topology Optimization ◽  
Dimension Reduction ◽  
Periodic Structures

Application of Regional Strain Energy in Topology Optimization With Inertia Relief Analysis

2013 ◽  
Author(s):  
Wei Song ◽  
Hae Chang Gea ◽  
Ren-Jye Yang ◽  
Ching-Hung Chuang
Keyword(s):  
Finite Element ◽  
Topology Optimization ◽  
Strain Energy ◽  
Computational Cost ◽  
Structure Design ◽  
Protective Structure ◽  
Element Analysis ◽  
Regional Strain ◽  
Unbalanced Loads ◽  
Energy Formulation

In finite element analysis, inertia relief solves the response of an unconstrained structure subject to constant or slowly varying external loads with static analysis computational cost. It is very attractive to utilize it in topology optimization to design structures under unbalanced loads, such as in impact and drop phenomena. In this paper, regional strain energy formulation and inertia relief is integrated into topology optimization to design protective structure under unbalanced loads. For background, the equations of inertia relief are introduced and a commonly used solving method is revisited. Then the regional strain energy formulation for topology optimization with inertia relief is proposed and its sensitivity is derived from the adjoint method. Based on the solving method, the sensitivity is evaluated term by term to simplify the results. The simplified sensitivity can be calculated easily using the output of commercial finite element packages. Finally, the effectiveness of this formulation is shown in the first example and the proposed regional strain energy formulation for topology optimization with inertia relief are presented and discussed in the protective structure design examples.

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