Nonlinear static and dynamic stability of functionally graded toroidal shell segments under axial compression: Fid-Bau Portal

Nonlinear static and dynamic stability of functionally graded toroidal shell segments under axial compression

Vuong, Pham Minh / Duc, Nguyen Dinh

Abstract This work presents an analytical approach to investigate nonlinear static and dynamic stability of toroidal shell segments resting on elastic foundation subjected to axial compression. The shells are made of functionally graded material (FGM) which created from metal and ceramic, and the volume fraction of constituents is supposed to gradually vary from one surface to another according to a power law function. Basic formulations are established based on Reddy's third-order shear deformation shell theory (TSDT) considering geometrical nonlinearity in von Kármán sense. Governing system of four-partial differential equations are converted into nonlinear differential equation using Galerkin method. Runge-Kutta method is used to solve nonlinear differential equation of motion and then nonlinear dynamic response of shell are examined. Budiansky-Roth criterion are used to obtain critical dynamic buckling load and then nonlinear dynamic stability of shells under axial compressive load linearly varying on time is analyzed. The influences of material and geometrical parameters, and elastic foundations on the static and dynamic stability of FGM toroidal sell segments are discussed in detail. The obtained results are validated by comparing with other results in the literature.

Highlights • Nonlinear static and dynamic stability. • The FGM toroidal shell segments resting on elastic foundation and subjected to axial compression. • Used analytical approach and Reddy's third-order shear deformation shell theory (TSDT) • Galerkin method and Runge-Kutta method is applied. • Used Budiansky-Roth criterion.