Forecast buckling and wrinkling analysis of Föppl von-Kármàn plates in functionally graded materials using Hermite-type approaches

This work presents a numerical analysis of buckling and wrinkling phenomena in thin Functionally Graded (FG) isotropic and FG sandwich plates using the Föppl von-Kàrmàn theory. Three numerical approaches based on the use of the Asymptotic Numerical Method (ANM) with Hermite-type approximations under either strong or weak formulations are introduced. These approaches include the recently suggested Collocation Hermite-type Weighted Least Squares method (CHtWLS) coupled with ANM, the Finite Element Method (FEM) with ANM, and the Hermite-type Element Free Galerkin method (HEFG) with ANM. They are applied to study the influence of boundary conditions, plate geometry, and material distribution in FG sandwich plates on the stationary bifurcation behavior. The presented approaches employ path-following techniques to accurately and efficiently predict critical load factors and wrinkling shape modes. The use of different numerical methods adds versatility and robustness to the analysis, making the proposed CHtWLS with ANM particularly efficient and straightforward for nonlinear problems with Hermitian boundary conditions and a low degree of freedom, unlike FEM and HEFG with ANM, which are used under a weak form without the need for special treatment techniques. The buckling phenomenon is investigated in this study on square and rectangular plates using a biaxial compressive load, while the wrinkling phenomenon is investigated using a uniaxial tensile and compressive loads. The numerical findings underscore the significance of the FG power-law index as a crucial parameter influencing buckling behavior and critical loads under various boundary conditions. Notably, the study unveils an unusual wrinkling phenomenon under simply-supported boundaries, revealing a nonlinear bifurcation diagram featuring multiple critical points and folding behaviors in both square and rectangular plates.