Stress-based topology optimization of compliant mechanisms design using geometrical and material nonlinearities

In this work, a density-based method is applied for synthesizing compliant mechanisms using topology optimization. This kind of mechanisms uses the elastic strain as the basis for kinematic actuation and it is widely used in precision mechanical devices, in biomedical engineering, and recently in MicroElectroMechanical Systems (MEMS). Geometrical and material (compressible hyperelasticity) nonlinearities are taken into account to obtain mechanisms near real-world applications. A strength criterion for the optimization problem is applied, to design compliant mechanisms that fulfill the desired kinematic tasks while complying with a stress threshold. The addition of a stress constraint to the formulation also aims to alleviate the appearance of hinges in the optimized design. Employing benchmark examples, we investigate the influence of a nonlinear formulation with a stress constraint in the final designs. It is shown that material nonlinearity plays an important role for stress constraint problems. The use of a projection scheme helps to obtain optimized topologies with a high level of discreteness. The Method of Moving Asymptotes (MMA) is applied for design variables updating and the required derivatives are calculated analytically by the adjoint method.