A binary discrete topology optimization method

The inaccurate evaluation of the element sensitivities can result in the numerical non-stability of the discrete topology optimization algorithm, especially, when material is added to elements, the element sensitivity is highly overestimated, which yields the so called chess pattern results. To overcome the problem, a new sensitivity estimation formula is constructed based on the perturbation analysis of the elastic equilibrium increment equation, which can provide a good estimate of the change of the objective function whether the material is removed from or added to elements. Our research shows the new sensitivity estimation formula can increase estimation accuracy by about 25 times, compared with the conventional one. As a consequence, a simple discrete topology optimization method is established, and the optimization process characterizes itself by the ability to remove material from any element or to add material to any element in each iterative step.