A NEW METHOD FOR TOPOLOGY OPTIMIZATION OF THREE-DIMENSIONAL CONTINUUM STRUCTURES BASED ON BIONICS

Wolff’s law in biomechanics states that the microstructure of bone adapts gradually to the environment as a result of remodeling process. A new method for topology optimization of three-dimensional (3D) continuum structure based on Wolff’s law is proposed. The continuum structure is optimized as a piece of bone which obeys Wolff’s law, and the process of locating the optimum topology of structure is assumed to be equivalent to the “bone” remodeling process. Secondly, a second order positive definite fabric tensor is introduced to express the material anisotropy. If the fabric tensor is proportional to the second order identity tensor, the material is isotropic. Thirdly, an interval of reference strain is adopted and the remodeling rule can be established. During the growing process, at any material point, if the absolute value of its principal strain is out of the interval, then the increment of the corresponding eigenvalue of fabric tensor, i.e. the growth speed is non-zero; but if all the absolute values locate in the interval, the growth speeds are equal to zero and the material point is in a state of remodeling equilibrium. Finally, the global optimum of structure requires all material points being in the state of remodeling equilibrium under the loading conditions. Degenerated method, in which all fabric tensors of all the material points are restricted to be proportional to the second order identity tensor, is proposed to solve the topology optimization problem of the 3D continuum structures. Numerical results are given to demonstrate the validity and capability of the theories and algorithm developed.