Buckling analysis of elastic thin shells with stepwise variable thickness under static thermomechanical effects
DOI:
https://doi.org/10.32347/2410-2547.2025.115.94-106Keywords:
thin shell, geometrically nonlinear deformation, buckling, thermomechanical loading, bifurcation, universal 3D finite element, finite element moment schemeAbstract
The results of a comprehensive analysis of elastic shell behavior under static thermomechanical loads are presented. The study focuses on geometrically nonlinear deformation, buckling, and natural vibrations of shells. Special attention is given to the identification of bifurcation points in the pre-buckling domain of shell deformation.The proposed comprehensive method is implemented as a two-stage algorithm. At each step of the thermomechanical loading, it combines the solution of the geometrically nonlinear static problem for the shell with a modal analysis at the same step. This approach allows the determination of critical states according to both the static criterion (maximum point of the load–deflection curve) and the dynamic criterion (load at which the lowest natural frequency of the shell becomes zero). The method is based on the geometrically nonlinear theory of thermoelasticity, the moment scheme of finite elements, and a universal three-dimensional finite element. We apply the methodology of introducing small non-symmetric perturbations into the initial geometry of the midsurface of the shell to determine bifurcation points iin the pre-buckling domain. This approach enables tracing new solution branches corresponding to adjacent forms of buckling. The presented numerical examples confirm the accuracy, universality, and effectiveness of the proposed method.
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