Abstract:

In order to avoid the degradation of mechanism performance due to the inherent uncertainties in the production process, a reliability-based topology optimization method for the compliant mechanisms with geometrical nonlinearity is presented. In the investigation, an increment equilibrium formula is established and the structural response with geometrical nonlinearity is calculated based on the Total-Lagrange method and an incremental scheme combined with Newton-Raphson iterations. Then, by taking into consideration the randomness of the loads and the geometry description, a mathematical model is set up for the muhiobjective optimization of the compliant mechanism. In this model, the minimum average compliance and the maximum geometric advantage are taken as the objective functions to meet the requirements for the stiffness and the flexibility; the first-order reliability method is adopted to calculate the probabilistic constraint of the reliability index; the adjoint method is used to analyze the sensitivity of the objective functions; the solid isotropic material with penalization approacb is used to optimize the topology ; and the moving asymptote method is employed to solve the optimization problem. Finally, a compliant micro-gripper is used to perform a case study. The results indicate that the proposed method is correct and effective because it helps to obtain mechanisms with higher reliability than those obtained by the deterministic topology optimization.

Key words: compliant mechanism, gripper, geometrical nonlinearity, topology optimization, reliability