Large deformation analysis of functionally graded revolutionary shallow thin shells with bi-modular effect: Snap-through buckling under different boundary constraints

Functionally graded materials (FGMs) enable structures to achieve a smooth transition between different material properties, providing an optimized combination of functions to meet the diversity of engineering needs. However, the presence of bi-modular effect in FGMs is often neglected due to the complexity in the analysis. In this paper, the curvature correction equivalent method based on the von K ' arm ' an theory will be applied to the theoretical study for the large deformation problem and the resulting snap-through buckling of functionally graded revolutionary shallow thin shells with bi-modular effect under different boundary constraints. Furthermore, a bi-modular FGMs user material subroutine (UMAT) is developed for the first time to simulate the real material model, thus validating the theoretical solution. The results show that except for the bi-modular effect of materials, boundary constraints of shells also have important influences on the relationship of load vs. central deflection and snap-through buckling. The research of boundary constraints brings new conclusions to snapthrough buckling: the rotation constraint and radial constraint at the shell edge have opposite effects on snapthrough buckling. This work will contribute to the analysis of the snap-through buckling of functionally graded revolutionary shallow thin shells with an obvious bi-modular effect and under various boundary constraints.