Elastic Buckling of a Circular Disk due to Internal Membrane Forces

Residual internal stresses often remain in materials after thermal-mechanical processes. Considerable deformation, such as elastic buckling, may result from such stresses. Some cases of circular-plate buckling due to internal membrane forces are analyzed in this work. The internal membrane-force field is introduced with a nonuniform radial temperature distribution in the disk. Detailed analysis is performed and critical buckling criteria are tabulated for some specific sets of parameters. Although the membrane force in the plate is axially symmetric, symmetry breaking is found at buckling. When the temperature is higher at the disk center, the first buckling mode is domeshaped, which maintains the polar symmetry. The mode of buckling, however, changes to a saddle shape when the radial temperature distribution is reversed.