Topology optimization using moving morphable bars for versatile thickness control

Topology optimization for minimum and maximum thickness control, uniform thickness control, and multiple thickness control is provided by using moving morphable bars formed of rectangles with semicircular ends. By employing the center coordinates of the semicircular ends and the thickness of a moving bar as design variables, the bar can float around the design domain while its shape morphs according to the design sensitivities. The overlapping of moving bars is allowed, and the element density is determined by the approximation of the Heaviside function by measuring the shortest distance from the boundaries of the bars. The minimum thickness of the members of an optimized structure is controlled by simply setting the lower bound of the thickness variables for the moving bars. No constraints or filtering techniques are required for the minimum thickness control. The maximum thickness is controlled for each moving bar through its corresponding constraint, which prevents an over-sized member due to the overlapping of moving bars. By solving benchmark problems, the validity of the method proposed for versatile thickness control is shown. It is also shown that the proposed method alleviates numerical difficulties for hinges when it is applied for compliant mechanism problems.