Predicting the Axisymmetric Manufacturing Deformations of Disk-Style Benders

The thermally-induced deformations of multilayer disk-style benders that are consolidated at elevated temperature to cure the adhesives bonding the layers together and then cooled to room temperature are studied. Only axisymmetric deformations are considered, and hence the disks cool to a dome-like shape due to the different thermal expansion properties of the layers. The paper derives the equations governing the deformation and, since the out-of-plane deformations are often many times the disk thickness, geometrically nonlinear effects are considered in the derivation. As a comparison case, the equations are linearized and solved in closed form. The geometrically nonlinear case is solved by using the shooting method and the Rayleigh-Ritz method. A number of simple bender designs are studied to examine the influence of geometric nonlinearities, disk geometry, and layer material properties on the deformations. It is concluded that geometric nonlinearities lead to flattening of the dome relative to the geometrically linear case, and the thermally-induced deformations are sensitive to layer material properties, layer thickness, and disk radius.