Keywords: numerical analysis, buckling and post buckling, thermal environment, functionally graded beam, thin-walled cross-section, porous material.

A numerical model to predict the thermal buckling analysis of thin-walled porous functionally graded (FG) beams is presented in this work. A geometric nonlinear algorithm that uses a 1D numerical model with a spatial beam finite element is employed. The Green-Lagrange deformation tensor defines small deformations. The Euler-Bernoulli theory for bending and the Vlasov theory for torsion are used to create the finite element model. Nonlinear analysis uses the UL (updated Lagrangian) incremental formulation with the principle of virtual works. The cross-sectional displacement field accounts for warping torsion and large rotations. Material properties are assumed to vary continuously through the wall thickness based on power-law distribution. The proposed beam model analyses buckling in cases of uniform, linear, and nonlinear temperature distribution through the thickness of the cross-sectional walls. The analysis also considers the temperature dependence of the mechanical properties of the material. Numerical results investigate critical buckling temperatures and post-buckling responses for different thin-walled sections with various configurations. These configurations include boundary conditions, geometry, FG skin-core-skin ratios, and power-law index. The numerical algorithm's accuracy and reliability are compared with established software packages' 2D finite element models. The comparison shows excellent agreement with the results obtained with shell models.

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