Topology Optimization Using a Hybrid Cellular Automaton Method With Local Control Rules

2006 ◽  
Vol 128 (6) ◽  
pp. 1205-1216 ◽  
Author(s):  
Andrés Tovar ◽  
Neal M. Patel ◽  
Glen L. Niebur ◽  
Mihir Sen ◽  
John E. Renaud
Keyword(s):  
Topology Optimization ◽  
Cellular Automaton ◽  
Optimization Problems ◽  
Control Loop ◽  
Structural Adaptation ◽  
Computationally Efficient ◽  
Element Analysis ◽  
Control Rules ◽  
Numerical Instabilities ◽  
Cellular Automaton Method

The hybrid cellular automaton (HCA) algorithm is a methodology developed to simulate the process of structural adaptation in bones. This methodology incorporates a distributed control loop within a structure in which ideally localized sensor cells activate local processes of the formation and resorption of material. With a proper control strategy, this process drives the overall structure to an optimal configuration. The controllers developed in this investigation include two-position, proportional, integral and derivative strategies. The HCA algorithm combines elements of the cellular automaton (CA) paradigm with finite element analysis (FEA). This methodology has proved to be computationally efficient to solve topology optimization problems. The resulting optimal structures are free of numerical instabilities such as the checkerboarding effect. This investigation presents the main features of the HCA algorithm and the influence of different parameters applied during the iterative optimization process.

The Convergence and Algorithm Factors Analysis of Topology Optimization for Crashworthiness Based on Hybrid Cellular Automata

2012 ◽  
Author(s):  
LianShui Guo ◽  
Jun Huang ◽  
Xuan Zhou ◽  
Andres Tovar
Keyword(s):  
Topology Optimization ◽  
Cellular Automata ◽  
Structural Adaptation ◽  
Element Analysis ◽  
Hybrid Cellular Automata ◽  
Complex Interactions ◽  
Control Rules ◽  
Factors Analysis ◽  
Cantilevered Beam ◽  
Crashworthiness Design

Structural design for crashworthiness is a challenging area of research due to large plastic deformations and complex interactions among diverse components of the vehicle. A notable idea in topology optimization is the hybrid cellular automaton (HCA) method capable of topology synthesis for crashworthiness design. The HCA algorithm was inspired by the structural adaptation of bones to their ever changing mechanical environment. This methodology has been shown to be an effective topology synthesis tool. The objective of this investigation is to examine the convergence and algorithm factors analysis of topology optimization for crashworthiness based on hybrid cellular automata paradigm. The orthogonal test is also proposed to study the effects of the algorithm factors on the dependent variables of the structure with new optimized topology. To demonstrate the convergence properties influenced by factors of the HCA algorithm in dynamic problems, the HCA framework is developed to a methodology for crashworthiness, which combines transient, non-linear finite-element analysis and local control rules acting on cells, and some simple cantilevered beam examples are utilized.

Research on Techniques of Structural Topology Optimization Using Cellular Automaton

2011 ◽  
Vol 308-310 ◽  
pp. 987-993
Author(s):  
Yi Xian Du ◽  
Wei Wang ◽  
Qi Hua Tian ◽  
Jin Run Hu
Keyword(s):  
Topology Optimization ◽  
Cellular Automaton ◽  
Optimization Design ◽  
Mechanical Response ◽  
Optimization Problems ◽  
Structural Topology Optimization ◽  
Structural Topology ◽  
Computationally Efficient ◽  
Local Rule ◽  
Loaded Structure

By integrating cellular automaton (CA) theory into topology optimization of continuum, the local rule is defined for sensitivity analysis and updating of the design variable, according to the analysis of the structural mechanical response. Topology optimization design of loaded structure is conducted using minimal compliance as the optimization objective. The optimal distribution of material in the design domain is finally obtained. Comparing to other algorithms, the local rule has proved to be computationally efficient to solve structural topology optimization problems. The resulting optimal structures are free of numerical instabilities such as the checkerboard patterns and mesh dependency.

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

2019 ◽  
Author(s):  
Liang Xue ◽  
Jie Liu ◽  
Guilin Wen ◽  
Hongxin Wang
Keyword(s):  
Topology Optimization ◽  
High Resolution ◽  
High Efficiency ◽  
Optimization Problems ◽  
Combined Treatment ◽  
Computational Cost ◽  
Optimization Method ◽  
Element Analysis ◽  
Arbitrary Boundary ◽  
Topology Optimization Method

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.

scholarly journals Topology Optimization of Elastoplastic Behavior Conditions by Selectively Suppressing Plastic Work

Mathematics ◽  
2020 ◽  
Vol 8 (11) ◽  
pp. 2062
Author(s):  
Eun-Ho Lee ◽  
Tae-Hyun Kim
Keyword(s):  
Plastic Deformation ◽  
Topology Optimization ◽  
Elastic Deformation ◽  
Deformation Zone ◽  
Strain Energy ◽  
Optimization Problems ◽  
Elastic Stiffness ◽  
Plastic Work ◽  
Plastic Deformation Zone ◽  
Element Analysis

This work conducted topology optimization with an implicit analysis of elastoplastic constitutive equation in order to design supporting structures for unexpected heavy loading conditions. In this topology optimization model, plastic work was extracted from strain energy and selectively employed in the objective function according to deformation mode. While strain energy was minimized in elastic deformation areas, in elastoplastic deformation areas, the plastic work was minimized for the purpose of suppressing plastic deformation. This method can focus on suppressing plastic strain in the plastic deformation zone with maintaining elastic stiffness in the elastic deformation zone. These formulations were implemented into MATLAB and applied to three optimization problems. The elastoplastic optimization results were compared to pure elastic design results. The comparison showed that structures designed with accounting for plastic deformation had a reinforced area where plastic deformation occurs. Finally, a finite element analysis was conducted to compare the mechanical performances of structures with respect to the design method.

Multidomain Topology Optimization for Crashworthiness Based on Hybrid Cellular Automata

2011 ◽  
Vol 486 ◽  
pp. 250-253 ◽  
Author(s):  
Lian Shui Guo ◽  
Jun Huang ◽  
Andres Tavor ◽  
John E. Renaud
Keyword(s):  
Topology Optimization ◽  
Element Analysis ◽  
Design Problems ◽  
Practical Applications ◽  
Control Rules ◽  
Engineering Design Problems ◽  
Wide Range ◽  
Result Show ◽  
Update Rules ◽  
Structure Result

This research introduces a multidomain topology optimization algorithm for crashworthy structure undergoing large deformations. This technique makes use of the hybrid cellular automaton framework, which combines transient, non-linear finite-element analysis and local control rules acting on cells. The set of all cells defines the multidomains. Each subdomain has been defined by different material update rules according to specify constraint, and optimization iteration of each subdomain has been converged respectively during the optimal design process. The effectiveness of this technique is demonstrated through the design of a bumper-like structure. Result show that the new algorithm is suitable for practical applications. The case study presented demonstrates the potential significance of this work for a wide range of engineering design problems.

An Adaptive and Efficient Boundary Approach for Density-Based Topology Optimization

2019 ◽  
Author(s):  
Reza Behrou ◽  
Reza Lotfi ◽  
Josephine V. Carstensen ◽  
James K. Guest
Keyword(s):  
Finite Element Analysis ◽  
Finite Element ◽  
Topology Optimization ◽  
Finite Element Model ◽  
Element Model ◽  
Computational Domain ◽  
Element Analysis ◽  
The Finite Element Analysis ◽  
Numerical Instabilities ◽  
The Finite Element Model

Abstract This paper presents an adaptive nodal boundary condition scheme to systematically enhance the computational efficiency and circumvent numerical instabilities of the finite element analysis in density-based topology optimization problems. The approach revisits the idea originally proposed by Bruns and Tortorelli to eliminate the contribution of void elements from the finite element model and extends this idea to modern projection methods to stabilize the implementation, facilitate reintroduction of material, and consider additional physics. The computational domain is discretized on a fixed finite element mesh and a threshold density is used to determine if an element is sufficiently low relative density to be “removed” from the finite element analysis. By eliminating low-density elements from the design domain, the number of free Degrees-Of-Freedom (DOFs) is reduced, thereby reducing the solution cost of the finite element equations. Perhaps more importantly, it circumvents numerical instabilities such as element distortion when considering large deformations. Unlike traditional solids-only modeling approaches, a key feature of the projection-based scheme is that the design and finite element spaces are separate, allowing the design variable sensitivities in a region to remain active (and potentially non-zero) even if the corresponding analysis elements are removed from the finite element model. This ultimately means material reintroduction is systematic and driven by the design sensitivities. The Solid Isotropic Material with Penalization (SIMP) approach is used to interpolate material properties and the Heaviside Projection Method (HPM) is used to regularize the optimization problem and facilitate material reintroduction through the gradient-based optimizer. Several benchmark examples in areas of linear and nonlinear structural mechanics are presented to demonstrate the performance of the proposed approach. The resulting optimized designs are consistent with literature and results reveal the performance and efficiency of the developed method in reducing computational costs without numerical instabilities known to be due to modeling near-void elements.

A Modified Update Rule of Field Variable Using Hybrid Cellular Automata Method

2014 ◽  
Vol 543-547 ◽  
pp. 1995-1999
Author(s):  
Xiao Bo Xiang ◽  
Yi Xian Du ◽  
Qi Hua Tian ◽  
Jin Xue Wang
Keyword(s):  
Cellular Automaton ◽  
Field Variable ◽  
Element Analysis ◽  
State Information ◽  
Hybrid Cellular Automata ◽  
Continuum Structures ◽  
Mesh Dependency ◽  
The Finite Element Analysis ◽  
Numerical Instabilities ◽  
Update Rules

The hybrid cellular automaton (HCA) algorithm is a gradient-free methodology that combines both local update rules based on the cellular automaton (CA) paradigm and the finite element analysis (FEA). The local update rules could determine the distribution of the material based on the local state information collected from cellular automaton paradigm. This paper proposes a modified update rule of field variable to suppress the mesh dependency and gray-scale elements problems occurred in topology optimization of continuum structures. Two typical numerical examples are presented to prove the effectiveness and robustness of the proposed method in solving the numerical instabilities problem.

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