An adaptive refinement approach for topology optimization based on separated density field description

This paper presents an adaptive density point refinement approach for continuum topology optimization on the basis of an analysis-mesh separated material density field description based on nodal design variables. The Shepard interpolants are used to construct a strictly range-restricted density field over the design domain with the density design variables defined on a density point grid. Since the density points are defined independent of the finite element mesh, it is easy to refine the density point grid without remeshing the finite element model. A refinement criterion is given to identify the gray transitional regions to be adaptively refined in the subsequent optimization iterations. With such a refinement scheme, the topology optimization can start from a relatively coarse density point grid but still yields a desired higher resolution of the structural boundaries in the final design. Because refinements are only performed when and where necessary, this method is able to improve the boundary description quality of the optimal result with much less design variables as compared with the case of global refinement, and therefore can greatly reduce the computational burden involved in the sensitivity analysis and optimization process. Moreover, the percentage of transitional regions in the final solutions can also be reduced. Compared with using a uniformly globally-dense density point arrangement, this approach can achieve similar optimal designs but with much less computational cost. Numerical examples are given to demonstrate the effectiveness and efficiency of the present approach.