  To solve large-scale or high-resolution topology optimization problem, a
novel algorithm is developed based on modified bi-directional evolutionary
structure optimization (BESO) and extended finite element method (XFEM). Within
XFEM, a set of enriched nodes are defined to divide the finite element into
several uniform sub-regions, i.e. sub-triangles and sub-tetrahedrons. The
material grid and shape functions are defined on each sub-region to improve the
computational accuracy, whereas the equilibrium equation is established on the
level of coarse finite elements to increase the computational efficiency. We
set all the standard FE nodes and the enriched nodes as the design variables,
and a modified material interpolation model is introduced to calculate the
material properties for sub-regions. An enrichment function originating from
modeling voids scheme is adopted to character the discontinuity between solid
material to void material. To efficiently use the gradient-based algorithm,
BESO, sensitivity analysis is performed with the aid of adjoint method. Typical
numerical examples, involving millions of design variables, are carried to
verify the effectiveness of the proposed method.
