An Efficient and High-Resolution Topology Optimization Method Based on Convolutional Neural Networks

Topology optimization is a pioneering design method that can provide various candidates with high mechanical properties. However, the high-resolution for the optimum structures is highly desired, normally in turn leading to computationally intractable puzzle, especially for the famous Solid Isotropic Material with Penalization (SIMP) method. In this paper, an efficient and high-resolution topology optimization method is proposed based on the Super-Resolution Convolutional Neural Network (SRCNN) technique in the framework of SIMP. The SRCNN includes four processes, i.e. refining, path extraction & representation, non-linear mapping, and reconstruction. The high computational efficiency is achieved by a pooling strategy, which can balance the number of finite element analysis (FEA) and the output mesh in optimization process. To further reduce the high computational cost of 3D topology optimization problems, a combined treatment method using 2D SRCNN is built as another speeding-up strategy. A number of typical examples justify that the high-resolution topology optimization method adopting SRCNN has excellent applicability and high efficiency for 2D and 3D problems with arbitrary boundary conditions, any design domain shape, and varied load.

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Efficient, high-resolution topology optimization method based on convolutional neural networks

Frontiers of Mechanical Engineering ◽

10.1007/s11465-020-0614-2 ◽

2021 ◽

Author(s):

Liang Xue ◽

Jie Liu ◽

Guilin Wen ◽

Hongxin Wang

Keyword(s):

Topology Optimization ◽

High Resolution ◽

High Efficiency ◽

Optimization Problems ◽

Combined Treatment ◽

Computational Cost ◽

Treatment Method ◽

Optimization Method ◽

Arbitrary Boundary ◽

Topology Optimization Method

AbstractTopology optimization is a pioneer design method that can provide various candidates with high mechanical properties. However, high resolution is desired for optimum structures, but it normally leads to a computationally intractable puzzle, especially for the solid isotropic material with penalization (SIMP) method. In this study, an efficient, high-resolution topology optimization method is developed based on the superresolution convolutional neural network (SRCNN) technique in the framework of SIMP. SRCNN involves four processes, namely, refinement, path extraction and representation, nonlinear mapping, and image reconstruction. High computational efficiency is achieved with a pooling strategy that can balance the number of finite element analyses and the output mesh in the optimization process. A combined treatment method that uses 2D SRCNN is built as another speed-up strategy to reduce the high computational cost and memory requirements for 3D topology optimization problems. Typical examples show that the high-resolution topology optimization method using SRCNN demonstrates excellent applicability and high efficiency when used for 2D and 3D problems with arbitrary boundary conditions, any design domain shape, and varied load.

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Non-Probabilistic Based Topology Optimization Under External Load Uncertainty With Eigenvalue-Superposition of Convex Models

Volume 3A: 39th Design Automation Conference ◽

10.1115/detc2013-13317 ◽

2013 ◽

Cited By ~ 1

Author(s):

Xike Zhao ◽

Hae Chang Gea ◽

Wei Song

Keyword(s):

Topology Optimization ◽

External Load ◽

Optimization Problems ◽

Optimization Methods ◽

Optimization Method ◽

Convex Model ◽

Structure Response ◽

Gradient Based ◽

Bounded Convex ◽

Topology Optimization Method

In this paper the Eigenvalue-Superposition of Convex Models (ESCM) based topology optimization method for solving topology optimization problems under external load uncertainties is presented. The load uncertainties are formulated using the non-probabilistic based unknown-but-bounded convex model. The sensitivities are derived and the problem is solved using gradient based algorithm. The proposed ESCM based method yields the material distribution which would optimize the worst structure response under the uncertain loads. Comparing to the deterministic based topology optimization formulation the ESCM based method provided more reasonable solutions when load uncertainties were involved. The simplicity, efficiency and versatility of the proposed ESCM based topology optimization method can be considered as a supplement to the sophisticated reliability based topology optimization methods.

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A topology optimization method of robot lightweight design based on the finite element model of assembly and its applications

Science Progress ◽

10.1177/0036850420936482 ◽

2020 ◽

Vol 103 (3) ◽

pp. 003685042093648

Author(s):

Liansen Sha ◽

Andi Lin ◽

Xinqiao Zhao ◽

Shaolong Kuang

Keyword(s):

Finite Element Analysis ◽

Finite Element ◽

Topology Optimization ◽

Lightweight Design ◽

Element Model ◽

Optimization Method ◽

Maximum Displacement ◽

Element Analysis ◽

Upper Limb Exoskeleton ◽

Topology Optimization Method

Topology optimization is a widely used lightweight design method for structural design of the collaborative robot. In this article, a topology optimization method for the robot lightweight design is proposed based on finite element analysis of the assembly so as to get the minimized weight and to avoid the stress analysis distortion phenomenon that compared the conventional topology optimization method by adding equivalent confining forces at the analyzed part’s boundary. For this method, the stress and deformation of the robot’s parts are calculated based on the finite element analysis of the assembly model. Then, the structure of the parts is redesigned with the goal of minimized mass and the constraint of maximum displacement of the robot’s end by topology optimization. The proposed method has the advantages of a better lightweight effect compared with the conventional one, which is demonstrated by a simple two-linkage robot lightweight design. Finally, the method is applied on a 5 degree of freedom upper-limb exoskeleton robot for lightweight design. Results show that there is a 10.4% reduction of the mass compared with the conventional method.

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Topology Optimization of Periodic Structures With Substructuring

Journal of Mechanical Design ◽

10.1115/1.4042616 ◽

2019 ◽

Vol 141 (7) ◽

Cited By ~ 8

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.

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Displacement and Stress Constrained Topology Optimization

Volume 2A: 33rd Computers and Information in Engineering Conference ◽

10.1115/detc2013-13521 ◽

2013 ◽

Author(s):

Meisam Takalloozadeh ◽

Krishnan Suresh

Keyword(s):

Finite Element Analysis ◽

Finite Element ◽

Topology Optimization ◽

Level Set ◽

Numerical Experiments ◽

Optimization Method ◽

Stress Constraints ◽

Element Analysis ◽

The Finite Element Analysis ◽

Topology Optimization Method

The objective of this paper is to demonstrate a topology optimization method subject to displacement and stress constraints. The method does not rely on pseudo-densities; instead it exploits the concept of topological level-set where ‘partial’ elements are avoided. Consequently: (1) the stresses are well-defined at all points within the evolving topology, and (2) the finite-element analysis is robust and efficient. Further, in the proposed method, a series of topologies of decreasing volume fractions are generated in a single optimization run. The method is illustrated through numerical experiments in 2D.

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Finite element analysis of the dental implant using a topology optimization method

Medical Engineering & Physics ◽

10.1016/j.medengphy.2012.06.004 ◽

2012 ◽

Vol 34 (7) ◽

pp. 999-1008 ◽

Cited By ~ 33

Author(s):

Chih-Ling Chang ◽

Chen-Sheng Chen ◽

Chang-Hung Huang ◽

Ming-Lun Hsu

Keyword(s):

Finite Element Analysis ◽

Finite Element ◽

Topology Optimization ◽

Dental Implant ◽

Optimization Method ◽

Element Analysis ◽

Topology Optimization Method

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Topology Optimization on the Cloud: A Confluence of Technologies

Volume 1A: 35th Computers and Information in Engineering Conference ◽

10.1115/detc2015-46137 ◽

2015 ◽

Cited By ~ 2

Author(s):

Krishnan Suresh

Keyword(s):

Topology Optimization ◽

Computational Cost ◽

Optimization Method ◽

Element Analysis ◽

Structural Problems ◽

Free Service ◽

3D Geometry ◽

Many Core ◽

3D Topology ◽

Multiple Clients

Topology optimization is a systematic method of generating designs to meet specific engineering requirements. It is exploited today in several industries including aircraft, automobile, and machinery, and it strongly complements the emerging field of additive manufacturing. Yet, the wide-spread use of topology optimization has been deterred due to high computational cost and significant software/hardware investment. In this paper, we propose a cloud based topology optimization (CTO) framework to overcome these challenges, thereby promoting the wider use of topology optimization. CTO requires a confluence of several methods and technologies, each of which is discussed in this paper. First and foremost, CTO requires a fast 3D topology optimization method that can respond rapidly to multiple clients. Here, PareTO, a topological sensitivity based method is used as the backbone of the framework. PareTO relies on limited-memory finite element analysis with a deflated linear solver that is designed to exploit multi-core and many-core architectures. At the client-end, the framework relies on JavaScript based WebGL and ThreeJS technologies to display 3D geometry and formulate structural problems within a browser. Finally, Ajax, php and HTML5 technologies are exploited to achieve asynchronous and robust user experience. An implementation of this framework is available at www.cloudtopopt.com; to use this free service, JavaScript must be enabled within the browser.

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A New Bionic Topology Optimization Method Based Model of Bone Adaptation

Applied Mechanics and Materials ◽

10.4028/www.scientific.net/amm.433-435.2254 ◽

2013 ◽

Vol 433-435 ◽

pp. 2254-2259

Author(s):

Kaysar Rahman ◽

Nurmamat Helil ◽

Rahmatjan Imin ◽

Mamtimin Geni

Keyword(s):

Topology Optimization ◽

Reaction Diffusion ◽

Optimization Method ◽

Bone Adaptation ◽

Reaction Diffusion Equations ◽

Structural Topology ◽

Element Analysis ◽

Optimum Topology ◽

Instability Control ◽

Topology Optimization Method

A new bionic topology optimization method by combining reaction-diffusion equations describing bone adaptation process with finite element analysis is presented in this study. The major idea of the present approach is to consider the structure to be optimized as a piece of bone that obeys bone adaptation and the process of finding the optimum topology of a structure is equivalent to the bone remodeling process. Two widely used numerical examples demonstrate that the proposed approach greatly improves numerical efficiency compared with the othert well known methods for structural topology optimization in open literature. The results show that the optimal designs from the present bionic topology optimization method without use mathematical programming and numerical instability control techniques. The proposed method results in a better and faster convergence.

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