Topology optimization of compliant mechanisms with distributed compliance (hinge-free compliant mechanisms) by using stiffness and adaptive volume constraints instead of stress constraints

Many approaches have been developed for the synthesis of compliant mechanisms via topology optimization. Most of these approaches produce mechanisms with lumped compliance if not extended appropriately, such as with stress constraints. With mechanisms with lumped compliance, the deformation is concentrated in regions of small dimensions (referred to as ''de facto hinges'' or ''one-node connected hinges'') causing notch overstresses. Some extensions to these approaches overcome this by forcing mechanisms with distributed compliance (also referred to as ''hinge-free compliant mechanisms''). However, the currently known extensions have a number of drawbacks. Stress constraints, for example, make the optimization formulation highly nonlinear and non-convex. In this paper, a new extension is presented that permits the synthesis of mechanisms with distributed compliance by combining a constraint for the allowed structural stiffness with an adaptive volume constraint. The presented optimization approach can be easily solved using linear optimization. The basis for the extension presented in this paper is the modal synthesis approach, which permits the synthesis of transverse-load-insensitive compliant mechanisms. The methodology developed is tested on suitable design examples.