Thermal buckling solutions of generic metallic and laminated structures: Total and updated Lagrangian formulations via refined beam elements

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.

Automated summary

The thermal buckling behavior of metallic and laminated beams/plates is investigated using a linearized stability analysis. Different types of stability equations are derived by selecting different reference frames and using arbitrary expansion of generalized variables. The validity of these models is confirmed through validation with commercial software and the effect of strain distribution on plate-like structures is evaluated.