Large displacement static analysis of a cantilever Timoshenko beam composed of functionally graded material

Abstract

In this study, non-linear static analysis of a cantilever Timoshenko beam composed of functionally graded material (FGM) under a non-follower transversal uniformly distributed load is studied with large displacements and large rotations. Material properties of the beam change in the thickness direction according to a power-law function. In this study, the finite element of the beam is constructed by using the total Lagrangian Timoshenko beam element approximation. The non-linear problem is solved by using the incremental displacement-based finite element method in conjunction with the Newton-Raphson iteration method. To use the solution procedures of the Newton-Raphson method, there is a need to linearize equilibrium equations, which can be achieved through the linearization of the principle of virtual work. In this study, the effects of large deflections, large rotations and various material distributions on displacements and normal stress and shear stress distributions through the thickness of the beam are investigated in detail. The convergence study is performed for various numbers of finite elements. In addition, some of the particular results of the present study which are obtained for the homogeneous material case are compared with the results of the SAP2000 packet program. Numerical results show that geometrical non-linearity and material distribution play very important roles in the static responses of FGM beams.

Bi-directional functionally graded materials (BDFGMs) for free and forced vibration of Timoshenko beams with various boundary conditions

“…Since material properties exhibit a smooth and continuous variation from one surface to another in FGMs, the main advantages of FGMs over the classical composites are that cracking and delamination phenomenon, stress concentrations and residual stresses can be avoided, and thus structural integrity can be maintained to a desirable level. Due to the wide applications of FGMs in engineering structures, static [1][2][3][4][5][6], buckling [7][8][9][10], free and forced [32][33][34][35][36] vibration behavior of FG structures have been examined extensively by several researchers. On the other hand, since the temperature field in advanced machines such as modern aerospace shuttles and craft develops in two or three directions, conventional FG materials may not be useful in the design of such structures [37].…”

Buckling Temperature and Natural Frequencies of Thick Porous Functionally Graded Beams Resting on Elastic Foundation in a Thermal Environment

“…Investigations into the dynamic characteristics of FG structures have been an area of intensive research over the last decade (see Refs. [2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18]).…”

Post-Buckling Analysis of Axially Functionally Graded Three-Dimensional Beams

“…Su et al [2010] studied post-buckling of FG Timoshenko beams with surface-bonded piezoelectric layers subjected to temperature rise and electric field. Kocatürk et al [2011] investigated nonlinear static analysis of a cantilever FG Timoshenko beam by using Total Langragian finite element approximation. Akbaş and Kocatürk [2011] studied the post-buckling behavior of axially functionally graded Timoshenko beam under the influence of temperature.…”