A topology optimization method based on element independent nodal density

A methodology for topology optimization based on element independent nodal density (EIND) is developed. Nodal densities are implemented as the design variables and interpolated onto element space to determine the density of any point with Shepard interpolation function. The influence of the diameter of interpolation is discussed which shows good robustness. The new approach is demonstrated on the minimum volume problem subjected to a displacement constraint. The rational approximation for material properties (RAMP) method and a dual programming optimization algorithm are used to penalize the intermediate density point to achieve nearly 0-1 solutions. Solutions are shown to meet stability, mesh dependence or non-checkerboard patterns of topology optimization without additional constraints. Finally, the computational efficiency is greatly improved by multithread parallel computing with OpenMP.