Shape Optimization of Metal Welded Bellows Seal Based on the Turing Reaction-Diffusion Model Coupled with FEM

Mathematical Problems in Engineering

Geni

Mamut³

et al. 2014

Bone adaptive repair theory considers that the external load is the direct source of bone remodeling; bone achieves its maintenance by remodeling some microscopic damages due to external load during the process. This paper firstly observes CT data from the whole self-repairing process in bone defects in rabbit femur. Experimental result shows that during self-repairing process there exists an interaction relationship between spongy bone and enamel bone volume changes of bone defect, that is when volume of spongy bone increases, enamel bone decreases, and when volume of spongy bone decreases, enamel bone increases. Secondly according to this feature a bone remodeling model based on cross-type reaction-diffusion system influenced by mechanical stress is proposed. Finally, this model coupled with finite element method by using the element adding and removing process is used to simulate the self-repairing process and engineering optimization problems by considering the idea of bionic topology optimization.

Section: Bone Remodeling Model Based On Cross-type Reaction-diffusionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Experimental Observation of the Skeletal Adaptive Repair Mechanism and Bionic Topology Optimization Method

Mathematical Problems in Engineering

Geni

Mamut³

et al. 2014

“…Tezuka et all [3] constructed a bone remodeling model based on Turing system with linear kinetic reaction term and named this model as "iBone". Mamtimin Geni et al Generalized "iBone" model and applied this model bone formation and resoption under different boundary conditions and shape optimization of Metal Welded Bellows Seal problems [4,5].…”

Section: Introductionmentioning

confidence: 99%

A New Heuristic Topology Optimization Method Based on Bone Remodeling Model

Samsak

Halik

et al. 2014

AMR

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.

“…Then they constructed a bone remodeling model based on Turing system and named this model as "iBone" [3,4]. Mamtimin Geni et al Generalized "iBone" model and applied this model bone formation and resoption under different boundary conditions and shape optimization of Metal Welded Bellows Seal problems [5,6].…”

Section: Introductionmentioning

confidence: 99%

Structural Topology Optimization Method Based on Bone Remodeling

Helil²,

Imin³

et al. 2013

AMM

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.