Finite Element Analysis of the Deformation of a Rubber Diaphragm

Several rubber diaphragms, of the same type used inside an hydraulic accumulator, failed a short time after they were mounted. While there is nothing special with these failures the cost, in some cases can be high. A closer look, at the damaged diaphragms reveal an interesting nonsymmetric radial deformation accompanied in some cases by cracks. Most of the analyses regarding the failures of rubber diaphragms offer explanations only from a chemical or material science point of view.

We propose in this thesis a new perspective from a mechanical-structural engineering view. Therefore the main goal of the thesis is to investigate the deformation of a diaphragm and based on this analysis to propose an explanation for formation of the cracks. It is shown that the analysis of the diaphragm problem leads to a pseudo-nonconservative system and involves a buckling, a post buckling (dynamic snap-through), an eversion, and a load response analysis. The problem is approached numerically using the nite element method. The character of pseudo-nonconservativeness of the system requires, in this case, an update of the tangent stiffness matrix with a certain stiffness correction. This new correction is proposed also. The result is valid not only for this particular problem but for the entire class of problems to which the diaphragm belongs. This correction is implemented in an existing nite element program (NIKE3D) and used to analyze the diaphragm deformation. The results indicate that under the typical load condition for a diaphragm a certain deformation pattern occurs, and this can lead to the formation of cracks. This deformation matches extremely well with the actual deformed shape of a typical failed diaphragm. It is shown that the deformation pattern depends on the structural properties of the diaphragm rather than on the magnitude of the applied load. The nonsymmetry in the diaphragm deformation and the difference in the crack development is explained also.