Parameterized level set method for structural topology optimization based on the Cosserat elasticity

Abstract

When describing the mechanical behavior of some engineering materials, such as composites, grains, biological materials and cellular solids, the Cosserat continuum theory has more powerful capabilities compared with the classical Cauchy elasticity since an additional local rotation of point and its counterpart (couple stress) are considered in the Cosserat elasticity to represent the material microscale effects. In this paper, a parameterized level set topology optimization method is developed based on the Cosserat elasticity for the minimum compliance problem of the Cosserat solids. The influence of material characteristic length and Cosserat shear modulus on the optimized structure is investigated in detail. It can be found that the microstructural constants in the Cosserat elasticity have a significant impact on the optimized topology configurations. In addition, the minimum feature size and the geometric complexity of the optimized structure can be controlled implicitly by adjusting the parameters of the characteristic length and Cosserat shear modulus easily. Furthermore, the optimized structure obtained by the developed Cosserat elasticity based parameterized level set method will degenerate to the result by using the classical Cauchy elasticity based parameterized level set method when the Cosserat shear modulus approaches zero. A parameterized level set topology optimization method is developed based on the Cosserat elasticity for the optimization of minimum compliance of the structures with micropolar materials. The influence of characteristic length and Cosserat shear modulus of the micropolar material on the optimized structure has been investigated in detail. It can be found that the minimum feature size and the geometric complexity of the optimized structure can be controlled implicitly by adjusting the parameters of the characteristic length and Cosserat shear modulus easily.