The gradient projection method for structural topology optimization including density-dependent force

This paper proposes a modified gradient projection method (GPM) that can solve the structural topology optimization problem including density-dependent force efficiently. The particular difficulty of the considered problem is the non-monotonicity of the objective function and consequently the optimization problem is not definitely constrained. Transformation of variables technique is used to eliminate the constraints of the design variables, and thus the volume is the only possible constraint. The negative gradient of the objective function is adopted as the most promising search direction when the point is inside the feasible domain, while the projected negative gradient is used instead on condition that the point is on the hypersurface of the constraint. A rational step size is given via a self-adjustment mechanism that ensures the step size is a good compromising between efficiency and reliability. Furthermore, some image processing techniques are employed to improve the layouts. Numerical examples with different prescribed volume fractions and different load ratios are tested respectively to illustrate the characteristics of the topology optimization with density-dependent load.