A New Heuristic Topology Optimization Method Based on Bone Remodeling Model

2014 ◽  
Vol 889-890 ◽  
pp. 622-627
Author(s):  
Kaysar Rahman ◽  
Kahar Samsak ◽  
Azhar Halik ◽  
Nurmamat Helil
Keyword(s):  
Topology Optimization ◽  
Bone Remodeling ◽  
Optimization Method ◽  
Mechanical Efficiency ◽  
Bone Adaptation ◽  
Optimization Approach ◽  
Optimum Structure ◽  
Numerical Examples ◽  
Mechanical Theorem ◽  
Topology Optimization Method

The law of bone remodeling asserts that the internal trabecular bone adapts to external loadings, reorienting with the principal stress trajectories to maximize mechanical efficiency creating a naturally optimum structure. In this paper a new heuristic topology optimization method based on ordinary differential equations describing bone remodeling process is presented. The basis for numerical algorithm formulation was the phenomenon of bone adaptation to mechanical stimulation. The resulting optimization system allows fulling mechanical theorem for the stiffest design by use of presented heuristic topology optimization approach. Two widely used numerical examples are shown to confirm the validity and utility of the proposed topology optimization method.

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

2008 ◽  
Vol 131 (1) ◽  
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.

Bridging Topological Results and Thin-Walled Frame Structures Considering Manufacturability

2021 ◽  
Vol 143 (9) ◽  
Author(s):  
Jiantao Bai ◽  
Yanfang Zhao ◽  
Guangwei Meng ◽  
Wenjie Zuo
Keyword(s):  
Topology Optimization ◽  
Cross Section ◽  
Structural Complexity ◽  
Optimization Method ◽  
Frame Structure ◽  
Frame Structures ◽  
Manufacturing Constraints ◽  
Numerical Examples ◽  
Thin Walled ◽  
Topology Optimization Method

Abstract Topology optimization has been intensively studied and extensively applied in engineering design. However, the optimized results often take the form of a solid frame structure; hence, it is difficult to apply the topological results in the design of a thin-walled frame structure. Therefore, this paper proposes a novel bridging method to transform the topological results into a lightweight thin-walled frame structure while satisfying the stiffness and manufacturing requirements. First, the optimized topological results are obtained using the classical topology optimization method, which is smoothed to reduce structural complexity. Then, the initial thin-walled frame structure is created by referring to the smoothed topological results, in which the thin-walled cross section is designed according to the mechanical properties and manufacturing requirements. Furthermore, the size and shape of the thin-walled frame structure is optimized to minimize mass with the stiffness and manufacturing constraints. Finally, numerical examples demonstrate that the proposed method can reasonably design an optimized thin-walled frame structure from the topological results.

Structural Topology Optimization Method Based on Bone Remodeling

2013 ◽  
Vol 423-426 ◽  
pp. 1813-1818
Author(s):  
Kaysar Rahman ◽  
Nurmamat Helil ◽  
Rahmatjan Imin ◽  
Mamtimin Geni
Keyword(s):  
Topology Optimization ◽  
Bone Remodeling ◽  
Bone Structure ◽  
Reaction Diffusion ◽  
Optimization Method ◽  
Mechanical Stimulus ◽  
Bone Adaptation ◽  
Reaction Diffusion Equations ◽  
Structural Topology Optimization ◽  
Structural Topology

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.

A New Bionic Topology Optimization Method Based Model of Bone Adaptation

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.

scholarly journals Topology Optimization of Hard-Coating Thin Plate for Maximizing Modal Loss Factors

Coatings ◽  
2021 ◽  
Vol 11 (7) ◽  
pp. 774
Author(s):  
Haitao Luo ◽  
Rong Chen ◽  
Siwei Guo ◽  
Jia Fu
Keyword(s):  
Topology Optimization ◽  
Objective Function ◽  
Composite Plates ◽  
Optimization Method ◽  
Hard Coating ◽  
Design Variables ◽  
Coating Composite ◽  
Damping Materials ◽  
Topology Optimization Method ◽  
Loss Factors

At present, hard coating structures are widely studied as a new passive damping method. Generally, the hard coating material is completely covered on the surface of the thin-walled structure, but the local coverage cannot only achieve better vibration reduction effect, but also save the material and processing costs. In this paper, a topology optimization method for hard coated composite plates is proposed to maximize the modal loss factors. The finite element dynamic model of hard coating composite plate is established. The topology optimization model is established with the energy ratio of hard coating layer to base layer as the objective function and the amount of damping material as the constraint condition. The sensitivity expression of the objective function to the design variables is derived, and the iteration of the design variables is realized by the Method of Moving Asymptote (MMA). Several numerical examples are provided to demonstrate that this method can obtain the optimal layout of damping materials for hard coating composite plates. The results show that the damping materials are mainly distributed in the area where the stored modal strain energy is large, which is consistent with the traditional design method. Finally, based on the numerical results, the experimental study of local hard coating composites plate is carried out. The results show that the topology optimization method can significantly reduce the frequency response amplitude while reducing the amount of damping materials, which shows the feasibility and effectiveness of the method.

Structural Topology Optimization Using Frame Elements Based on the Complementary Strain Energy Concept for Eigen-Frequency Maximization

2005 ◽  
Author(s):  
Akihiro Takezawa ◽  
Shinji Nishiwaki ◽  
Kazuhiro Izui ◽  
Masataka Yoshimura
Keyword(s):  
Topology Optimization ◽  
Cross Sections ◽  
Strain Energy ◽  
Optimization Procedure ◽  
Optimization Method ◽  
Structural Topology ◽  
Energy Concept ◽  
Conceptual Design Phase ◽  
Complementary Strain ◽  
Topology Optimization Method

This paper discuses a new topology optimization method using frame elements for the design of mechanical structures at the conceptual design phase. The optimal configurations are determined by maximizing multiple eigen-frequencies in order to obtain the most stable structures for dynamic problems. The optimization problem is formulated using frame elements having ellipsoidal cross-sections, as the simplest case. Construction of the optimization procedure is based on CONLIN and the complementary strain energy concept. Finally, several examples are presented to confirm that the proposed method is useful for the topology optimization method discussed here.

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