Imperfection Analysis of a Bistable Shell

Bistable compliant flexures serve as mechanical memory and threshold devices for switches and sensors. One class of bistable compliant flexures is the annular, spherical shell, termed a bistable snap disc. These structures offer flexibility for mechanical memory and threshold devices because large changes in buckling loads can be achieved without significantly modifying the geometry. The sensitivity of these bistable snap discs to imperfections, however, prevents them from withstanding pre-buckling loads predicted by idealized models. A method to incorporate geometric imperfections into an existing finite element mesh of the idealized geometry using a set of orthonormal polynomials, specifically the annular Zernike polynomials, is proposed in this paper. A sensitivity analysis of five terms from the Zernike polynomial expansion is performed with a geometrically nonlinear finite element model to identify their effect on buckling, snap-through, and quasi-static stability. The effects of the perturbations are established by identifying key points on a force-deflection curve and potential energy curve. Results show that the geometric perturbations may account for the discrepancy in buckling between the idealized model and experiments. Error between the experiments and the model with geometric perturbations persist because the actual imperfections of the discs used in the experiments have not yet been characterized, and the finite element model does not account for non-homogeneous material properties and residual stresses.