Parameter analysis in Wolff's law based approach of continuum structural topology optimization

Wolff's law indicates that bone is endowed with the ability to adapt its internal structure to the load environment and trabecular bone distributes along the trajectories of the principal stresses, which motivates to propose for continuum structural topology optimization. The structure is cosidered as a piece of bone obeying Wolff's law and the process of finding the optimum structural topology is simulated as the bone remodeling/growth, where a second rank positive and definite fabric tensor as the design variable of a material point is introduced to express the geometry and elasticity of the material point in design domain. An interval of reference strain corresponding to the dead zone in biomechanics, is presented to determine the update rule of the eigenvalues of fabric tensors. And, the physical significations of the parameters, i.e. the initial design variables, increments of the design variable and the interval of reference strain, as well their effects on the convergence behaviour of the optimization algorithm are discussed. Some useful conclusions for setting the parameters are presented to improve the convergence behaviour.