Exact solution for nonlinear static behaviors of functionally graded beams with porosities resting on elastic foundation using neutral surface concept

Abstract

In this paper, an exact solution for nonlinear static behaviors of functionally graded (FG) beams with porosities resting on the elastic foundation is presented. The FG material properties with porosities are assumed to vary along the thickness of the beam, and two types of porosity distributions are considered. Actually, the geometrical middle surface of the FG beam selected in computations is very popular in the literature. By contrast, in this study, the physical neutral surface of the beam is utilized. Based on the Timoshenko beam theory, von Kármán nonlinear assumption, together with neutral surface concept, the nonlinear governing equations of the FG beam resting on the elastic foundation are derived. By using the physical neutral surface, the nonlinear governing equations have simple forms and can be solved directly. The exact solution for the problem with all immovable and moveable boundary conditions is conducted in detail. Some numerical investigations to show the effects of boundary conditions, material properties, length-to-thickness ratio, elastic foundation coefficients and several types of applied load on nonlinear static bending behaviors of the beam are given.

On the stochastic natural frequency of graphene reinforced functionally graded porous panels with unconventional boundary conditions

“…[1][2][3][4][5][6][7][8][9][10] Such artificially engineered materials are called functionally graded porous materials (FGPMs) which of course possess light-weight, but they lose their stiffness/strength significantly. 11,12 The compensation for the reduction of stiffness/strength may be accomplished with reinforcement of carbonaceous nanofiller such as graphene nanoplatelets (GPLs) because of its high elastic modulus around 1 TPa. [13][14][15] Several studies have been accomplished to evaluate the behavior of FG-GPLs porous panels while performing stability, bending, and free vibration analyses.…”