A new bionics method for topology optimization of continuum structures

Wolff's law in biomechanics states that bone microstructure and local stiffness tend to align with the stress principal directions to adapt to its mechanical environment. In this paper, a new method for topology optimization of continuum structure based on Wolff's law is presented. Four major ideas of the present approach can be summarized. Firstly, it considers the structure to be optimized as a piece of "bone" which obeys Wolff's law. The process of finding the optimum topology of structure is equivalent to the "bone" remodeling process. Secondly, a second rank positive and definite fabric tensor is introduced to express the porosity and anisotropy of a material point in structure. Thirdly, an interval of reference strain is adopted and the update rule of material properties can be established as: During the process of structural optimization, if any one of the absolute values of the principal strains is out of the interval, then the fabric tensor at the material point will be changed. In contrast to this, if all of the absolute values locate in the interval, then the fabric tensor keeps constant and the material point is in equilibrium state. If all the material points are in the equilibrium state, then the global optimal topology of the structure is achieved. The optimal structural topology is shown by the distribution of the effective volume fractions of the material points in admissible design domain expressed by the invariants of fabric tensors. Both of 2D and 3D numerical results are supplied to show the validity and capability of the theories and the algorithm developed.