In this paper, we present a method for preventing numerical instabilities such as checkerboards, mesh-dependence and local minima occurring in topology optimization in which SLP method is used as optimizer. The method presented here is that a function based on the concept of gravity (we named "gravity control function") is added to the objective function with a weight. The distribution of density of the topology is concentrated by maximizing this function, and as a result, checkerboards and intermediate densities are eliminated. Some techniques are introduced in the optimization procedure for preventing the local minima. The homogenization design method is used to obtain the optimum topology. The validity of the present method is demonstrated by numerical examples of the short cantilever beam and the MBB beam.
