Studies on linear thermoelastic buckling and free vibration analysis of geometrically perfect hemispherical shells with cut-out

Abstract

Abstract Thermoelastic buckling and free vibration analysis of geometrically perfect isotropic hemispherical shells subjected to axisymmetric temperature variation are presented. First order shear deformation theory is used to analyze the moderately thick elastic hemispherical shells. The variations of various field variables are assumed in the circumferential direction and the finite element matrices used in the numerical studies are based on the semi-analytical method. The formulation is validated for thermal buckling strains available in the literature. Thermal buckling temperatures are evaluated for deep shells having a cut-out at the apex. Parameters considered in the study include hemispherical shells with a/h ratios of 100 and 500 and each with cut-out angle at apex equal to 7°, 30° and 45°. Boundary conditions considered are clamped–clamped and clamped–free. A study on the distribution of the stress resultants due to thermal loading is examined in order to relate their influence on the buckling temperature of the shells with respect to above-stated geometric parameters. The effect of temperature on the free vibration natural frequency of the hemispherical shell is also analyzed.