This paper presents an analytical approach to investigate the nonlinear buckling and post-buckling of thin annular spherical shells made of functionally graded materials (FGM) and subjected to mechanical load and resting on Winkler-Pasternak type elastic foundations. | Volume 36 Number 4 4 2014 Vietnam Journal of Mechanics, VAST, Vol. 36, No. 4 (2014), pp. 291 – 306 NONLINEAR POST-BUCKLING OF THIN FGM ANNULAR SPHERICAL SHELLS UNDER MECHANICAL LOADS AND RESTING ON ELASTIC FOUNDATIONS Vu Thi Thuy Anh, Dao Huy Bich, Nguyen Dinh Duc∗ Vietnam National University, Hanoi, Viet Nam ∗ E-mail: ducnd@ Received July 27, 2014 Abstract. This paper presents an analytical approach to investigate the nonlinear buckling and post-buckling of thin annular spherical shells made of functionally graded materials (FGM) and subjected to mechanical load and resting on Winkler-Pasternak type elastic foundations. Material properties are graded in the thickness direction according to a simple power law distribution in terms of the volume fractions of constituents. Equilibrium and compatibility equations for annular spherical shells are derived by using the classical thin shell theory in terms of the shell deflection and the stress function. Approximate analytical solutions are assumed to satisfy simply supported boundary conditions and Galerkin method is applied to obtain closed-form of load-deflection paths. An analysis is carried out to show the effects of material and geometrical properties and combination of loads on the stability of the annular spherical shells. Keywords: Nonlinear buckling, post-buckling, FGM annular spherical shells, mechanical loads, elastic foundations. 1. INTRODUCTION Considerable researches have focused on the thermo-elastic, dynamic and buckling analyses of functionally graded plates and shells in recent years. This is mainly due to the increased use of functionally graded materials (FGMs) as the components of structures in the advanced engineering. FGMs consisting of metal and ceramic constituents have received increasingly attention in structural applications. Smooth and continuous change in material properties enable FGMs to avoid interface problems and unexpected thermal stress concentrations. By high .
