Combining load-controlled and displacement-controlled algorithms to model thermal-mechanical snap-through instabilities in structures

This paper presents an analysis of thermal-mechanical snap-through instabilities in structures using a hybrid load-controlled/displacement-controlled algorithm. The derivation uses the finite element method with a combination of modified Newton-Raphson and arc-length methods, aimed at providing a robust and efficient means for modeling the buckling response of structures that exhibit instability in the presence of nonuniform time-varying temperature fields and temperature-dependent material response. Load control is used to model the system's response up to the point of instability, which is identified using the method of bisections. During the instability, the analysis switches to displacement control to capture the load-shedding behavior. Once a stable point is reached, the algorithm switches back to load control. The novelty lies in the ability of the hybrid algorithm to model instabilities that are caused by material degradation under nonuniform transient temperature fields, which is particularly important in the study of structural response under fire hazards. Numerical analyses are carried out using a two-dimensional (2D) fiber-based corotational beam element. Verifications at room temperature and at elevated temperature demonstrate that the proposed approach exhibits a high level of accuracy. A brief study of toggle frames subjected to various types of heating and loading conditions is presented to illustrate the kinds of behaviors that can be captured with the proposed modeling approach.