Thermal buckling solutions of generic metallic and laminated structures: Total and updated Lagrangian formulations via refined beam elements
Yang Yan, A. Pagani, Erasmo Carrera
Abstract
The thermal buckling behavior of metallic and laminated beams/plates is investigated using a linearized stability analysis. By selecting different reference frames, two distinct types of 3 D stability equations can be generated using total and updated Lagrangian formulations (TLF and ULF). Various beam theory kinematics can be obtained within the framework of 1 D Carrera Unified Formulation (CUF) by employing an arbitrary expansion of the generalized variables. More precisely, an improved hierarchical Legendre expansion (IHLE) is used to formulate the Layer-Wise (LW) model in a robust manner. Additionally, using a finite element approximation in conjunction with CUF-IHLE, the obtained stability equations are discretized into a set of algebraic equations. The critical temperatures predicted by TLF- and ULF-based CUF-IHLE models are compared using numerical examples of beams and plates with varying boundary conditions, lamination schemes, and thickness-to-width ratios. Both models are validated for correctness using the commercial software ABAQUS. Besides, the effect of strain distribution during the pre-buckling stage is evaluated in the plate-like structure using one- and two-step analyses.