Geometry-based stiffness parameters for predicting approach of limit points in finite element studies

Several parameters for evaluating the decrease in structural stiffness in nonlinear finite element problems are defined here. Two types of parameters were considered: those that measure the overall softening and those that measure only a selected type of response, such as ovalization or bending. These parameters were used for detecting the approach of limit points in cylinder buckling problems under combined bending and external pressure. This is necessary for determining when the Newton—Raphson scheme should be replaced by displacement control to prevent numerical instability. The two types of parameters used in conjunction provide not only a reliable means for sensing the approach of limit points but also a determination of buckling modes.