The hybrid cellular automaton (HCA) algorithm is a gradient-free methodology that combines both local update rules based on the cellular automaton (CA) paradigm and the finite element analysis (FEA). The local update rules could determine the distribution of the material based on the local state information collected from cellular automaton paradigm. This paper proposes a modified update rule of field variable to suppress the mesh dependency and gray-scale elements problems occurred in topology optimization of continuum structures. Two typical numerical examples are presented to prove the effectiveness and robustness of the proposed method in solving the numerical instabilities problem.
