Structural Topology Optimization Method Based on Bone Remodeling

Abstract

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.

ECMS 2021 Proceedings edited by Khalid Al-Begain, Mauro Iacono, Lelio Campanile, Andrzej Bargiela

“…With the use of second-order elements, the checkerboard problem is not revealed. (Bendsoe 2003), (Rahman et al 2013) The results in Figure 7 shows that bigger initial density means a bigger apparent mass. At first glance, it is evident, but it can be seen that the difference between the apparent masses becomes a constant value as the number of the calculation steps is increasing.…”