Jacobi–Ritz Method for Buckling of Unitized Curvilinearly Stiffened Functionally Graded Plates

This study presents an efficient way for buckling analysis of functionally graded material panels with curvilinear stiffeners. Both the plate and stiffeners are modeled using the first-order shear deformation theory. Functionally graded material (FGM) properties vary continuously in the thickness direction using the power law. Compared to Finite Element Method (FEM), the Ritz method is beneficial while applying the skin-stiffener compatibility conditions, as the stiffeners can be placed arbitrarily and do not have to share nodes with the base structure finite element model. Such an approach would be efficient during shape optimization studies, as remeshing of the structure would not be required for changes in geometry. Orthogonal Jacobi polynomials as trial functions make the Ritz analysis robust, as they do not suffer matrix ill-conditioning-induced numerical issues when higher-order polynomials are required to accurately obtain the complex buckling mode shapes for curvilinearly stiffened panels. Stiffener displacements are approximated independently using one-dimensional trial functions, and compatibility is explicitly satisfied at the integration points along the stiffener path, which saves the computational cost by reducing the integration order. Accuracy of the proposed method is verified using several literature examples and commercial FEM software. Parametric studies on buckling response of the studied model with variation in the FGM power law index are conducted.