Structural Topology Optimization Method Based on Bone Remodeling

Bone is a dynamic living tissue that undergoes continuous adaptation of its mass and structure in response to mechanical and biological environment demands. In this paper, we firstly propose a mathematical model based on cross-type reaction diffusion equations of bone adaptation during a remodeling cycle due to mechanical stimulus. The model captures qualitatively very well the bone adaptation and cell interactions during the bone remodeling. Secondly assuming the bone structure to be a self-optimizing biological material which maximizes its own structural stiffness, bone remodeling model coupled with finite element method by using the add and remove element a new topology optimization of continuum structure is presented. Two Numerical examples demonstrate that the proposed approach greatly improves numerical efficiency, compared with the others well known methods for structural topology optimization in open literatures.

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Structural Topology Optimization Using Turing Model

Advanced Materials Research ◽

10.4028/www.scientific.net/amr.889-890.595 ◽

2014 ◽

Vol 889-890 ◽

pp. 595-599

Author(s):

Kaysar Rahman ◽

Azhar Halik ◽

Kahar Samsak ◽

Nurmamat Helil

Keyword(s):

Topology Optimization ◽

Bone Remodeling ◽

Reaction Diffusion ◽

Optimization Method ◽

Reaction Diffusion Equations ◽

Structural Topology Optimization ◽

Structural Topology ◽

Hypothetical Model ◽

Continuum Structures ◽

Material Formation

In this paper firstly a new hypothetical model of bone remodeling based on bone bioactivity mechanism and Turing reaction-diffusion equations is presented. Secondly this model of bone remodeling is translated to material formation and resorption process of continuum structures, a new heuristic structural topology optimization is presented. Finally short cantilever beam problem, one of the widely used examples in structural topology optimization are carried out by using present method to confirm the validity of the proposed topology optimization method.

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Analogy of Strain Energy Density Based Bone-Remodeling Algorithm and Structural Topology Optimization

Journal of Biomechanical Engineering ◽

10.1115/1.3005202 ◽

2008 ◽

Vol 131 (1) ◽

Cited By ~ 23

Author(s):

In Gwun Jang ◽

Il Yong Kim ◽

Byung Man Kwak

Keyword(s):

Topology Optimization ◽

Energy Density ◽

Bone Remodeling ◽

Strain Energy Density ◽

Strain Energy ◽

Optimization Method ◽

Bone Adaptation ◽

Structural Topology Optimization ◽

Structural Topology ◽

Topology Optimization Method

In bone-remodeling studies, it is believed that the morphology of bone is affected by its internal mechanical loads. From the 1970s, high computing power enabled quantitative studies in the simulation of bone remodeling or bone adaptation. Among them, Huiskes et al. (1987, “Adaptive Bone Remodeling Theory Applied to Prosthetic Design Analysis,” J. Biomech. Eng., 20, pp. 1135–1150) proposed a strain energy density based approach to bone remodeling and used the apparent density for the characterization of internal bone morphology. The fundamental idea was that bone density would increase when strain (or strain energy density) is higher than a certain value and bone resorption would occur when the strain (or strain energy density) quantities are lower than the threshold. Several advanced algorithms were developed based on these studies in an attempt to more accurately simulate physiological bone-remodeling processes. As another approach, topology optimization originally devised in structural optimization has been also used in the computational simulation of the bone-remodeling process. The topology optimization method systematically and iteratively distributes material in a design domain, determining an optimal structure that minimizes an objective function. In this paper, we compared two seemingly different approaches in different fields—the strain energy density based bone-remodeling algorithm (biomechanical approach) and the compliance based structural topology optimization method (mechanical approach)—in terms of mathematical formulations, numerical difficulties, and behavior of their numerical solutions. Two numerical case studies were conducted to demonstrate their similarity and difference, and then the solution convergences were discussed quantitatively.

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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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A NEW ELEMENT-BASED METHOD FOR SOLVING STRUCTURAL TOPOLOGY OPTIMIZATION PROBLEMS WITH NON-UNIFORM MESHES

Proceedings of International Structural Engineering and Construction ◽

10.14455/isec.2021.8(1).str-19 ◽

2021 ◽

Vol 8 (1) ◽

Author(s):

Kuang-Wu Chou ◽

Chang-Wei Huang

Keyword(s):

Topology Optimization ◽

Optimization Problems ◽

Optimization Method ◽

Optimal Topology ◽

Evolutionary Stage ◽

Structural Topology Optimization ◽

Volume Constraint ◽

Structural Topology ◽

Exchange Method ◽

Python Scripting

This study proposes a new element-based method to solve structural topology optimization problems with non-uniform meshes. The objective function is to minimize the compliance of a structure, subject to a volume constraint. For a structure of a fixed volume, the method is intended to find a topology that could almost conform to the compliance minimum. The method is refined from the evolutionary switching method, whose policy of exchanging elements is improved by replacing some empirical decisions with ones according to optimization theories. The method has the evolutionary stage and the element exchange stage to conduct topology optimization. The evolutionary stage uses the evolutionary structural optimization method to remove inefficient elements until the volume constraint is satisfied. The element exchange stage performs a procedure refined from the element exchange method. Notably, the procedures of both stages are refined to conduct non-uniform finite element meshes. The proposed method was implemented to use the Abaqus Python scripting interface to call the services of Abaqus such as running analysis and retrieving the output database of an analysis. Numerical examples demonstrate that the proposed optimization method could determine the optimal topology of a structure that is subject to a volume constraint and whose mesh is non-uniform.

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A CAD-oriented structural topology optimization method

Computers & Structures ◽

10.1016/j.compstruc.2020.106324 ◽

2020 ◽

Vol 239 ◽

pp. 106324 ◽

Cited By ~ 1

Author(s):

Lipeng Jiu ◽

Weihong Zhang ◽

Liang Meng ◽

Ying Zhou ◽

Liang Chen

Keyword(s):

Topology Optimization ◽

Optimization Method ◽

Structural Topology Optimization ◽

Structural Topology ◽

Topology Optimization Method

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A Feature-Based Structural Topology Optimization Method

Solid Mechanics and Its Applications - IUTAM Symposium on Topological Design Optimization of Structures, Machines and Materials ◽

10.1007/1-4020-4752-5_48 ◽

2006 ◽

pp. 505-514 ◽

Cited By ~ 10

Author(s):

Gengdong Cheng ◽

Yulin Mei ◽

Xiaoming Wang

Keyword(s):

Topology Optimization ◽

Optimization Method ◽

Structural Topology Optimization ◽

Structural Topology ◽

Feature Based ◽

Topology Optimization Method

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Topology Optimization of Bracing Systems for Multistory Steel Frames under Earthquake Loads

Advanced Materials Research ◽

10.4028/www.scientific.net/amr.255-260.2388 ◽

2011 ◽

Vol 255-260 ◽

pp. 2388-2393 ◽

Cited By ~ 2

Author(s):

Ji Zhuo Huang ◽

Zhan Wang

Keyword(s):

Topology Optimization ◽

Weighted Average ◽

Optimization Method ◽

Layout Design ◽

Computational Effort ◽

Steel Frame ◽

Structural Topology Optimization ◽

Structural Topology ◽

Earthquake Loads ◽

Element Removal

Application of continuum structural topology optimization methods to the layout design of bracing systems for multistory steel frame buildings under earthquake loads is explored in this work. A weighted average strain energy sensitivity of element is formulated to be served as the element removal criterion in the optimization process, and then an ESO-based continuum structural topology optimization method for the layout design of multistory steel frame bracing systems subjected to earthquake-induced ground motions is presented. In each iterative design, an approximate reanalysis technique named CA method is adopted to reduce the computational effort. Finally, a design example is given to demonstrate the effectiveness of the presented optimization method for the optimal layout design of steel frame bracing systems under earthquake loads.

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