A unified three-dimensional meshless analysis of vibration and thermal buckling of variable-thickness cylindrical shells

This paper presents a comprehensive analysis of free vibrations and thermal buckling of cylindrical shells with variable thickness, formulated based on three-dimensional elasticity theory and the variational principle. The governing equations are derived by considering geometric nonlinearities and uniform temperature distribution, then solved meshlessly using the Radial Point Interpolation Method (RPIM).The key innovation of this research lies in developing an accurate and integrated model that effectively simulates the complex effects of variable thickness on the dynamic behavior and thermal stability of shells under various boundary and thermal conditions. Numerical results demonstrate that thickness variations significantly influence natural frequencies and critical buckling loads, particularly under thermal loading and diverse boundary conditions, where the shell's behavior undergoes remarkable changes. A comparison with reference data confirms the accuracy and efficiency of the proposed model. This study provides valuable insights for the design and optimization of shell structures in thermal environments.