A localized differential quadrature method (LDQM) is introduced for buckling analysis of axially functionally graded nonuniform columns with elastic restraints. Weighting coefficients of differential quadrature discretization are obtained making use of neighboring points in forward and backward type schemes for the reference grids near the beginning and end boundaries of the physical domain, respectively, and central type scheme for the reference grids inside the physical domain. Boundary conditions are directly implemented into weighting coefficient matrices, and there is no need to use fictitious points near the boundaries. Compatibility equations are not required because the governing differential equation is discretized only once for each reference grid using neighboring points and variation of flexural rigidity is taken to be continuous in the axial direction. A large case of columns having different variations of cross-sectional profile and modulus of elasticity in the axial direction are considered. The results for nondimensional critical buckling loads are compared to the analytical and numerical results available in the literature. Some new results are also given. Comparison of the results shows the potential of the LDQM for solving such generalized eigenvalue problems governed by fourth-order variable coefficient differential equations with high accuracy and less computational effort.

Free vibration behavior of short beams made of axially layered functionally graded material (FGM) was investigated experimentally and numerically. Beams, which have gradation of the material properties in the axial direction, are fabricated by powder metallurgy technique using different weight fractions of aluminum and silicon carbide powders. In order to determine elasticity modulus of axially layered functionally graded (FG) beams, homogeneous beams containing different weight fractions of Al (aluminum) and SiC (silicon carbide) are produced, and these homogeneous beams are subjected to tensile tests. Density of each homogeneous layer is also calculated experimentally. After determination of the mechanical properties of each layer of the FG beams, they are modeled in a finite element program (ANSYS) according to Timoshenko beam theory, and free vibration analyses are performed. Fundamental frequencies of the axially layered FG beams produced are also calculated experimentally. FG beams with clamped-free boundary conditions are considered. Layers of the axially FG beams are considered to have symmetric configurations. Effect of the change in weight fractions of SiC particles and sorting order of layers to fundamental frequency of the beam is investigated. Experimental results obtained are compared with numerical results.

In this experimental and statistical study, free vibration behavior of laminated composite beams with functionally graded fiber orientation angles was investigated under clamped-free boundary conditions. The beams were manufactured using E-glass/epoxy. Fiber orientation angles of the beams were analyzed based on Taguchi’s L9 (33) orthogonal array. The effect of fiber orientation angles and beams with optimum levels were assessed using analysis of signal-to-noise ratio. Significant laminates of the beams and their percent contributions on the free vibration responses were obtained using analysis of variance. According to this study, the increase of fiber orientation angle from 0° to 80° causes a decrease in the fundamental frequency behavior of laminated composite beams. The most effective control factors were found to be the first and the second laminates symbolized as L1 with 85.86% contribution, the third and the fourth laminates symbolized as L2 with 12.29% contribution, the fifth and the sixth laminates symbolized as L3 with 1.84% contribution, respectively. This study can be used as a reference for free vibration analysis of cantilever laminated composite beams made of functionally graded fiber orientation angles as experimentally and statistically.

The deflection response of cantilever laminated composite square plates subjected to the weight of itself was analyzed using finite element and Taguchi methods.  The plates with 12 plies were made of glass fiber reinforced polymer composites (GFRP).  The arrangements and fiber orientation angles of the plies were conducted using Taguchi's L9 (3 3) orthogonal array.  Analysis of signal-to-noise (S/N) ratio was used to evaluate the control factors with the optimum levels for minimum deflection response.  Analysis of variance was carried out to analyze the powerful influential control factors and their percent contributions on responses.

In this numerical study, natural frequency analysis of the layered functionally graded beams in the thickness direction for clamped-clamped and clamped-free boundary conditions was investigated using finite element software ANSYS and the effects of the layers on natural frequency analysis for first mode were evaluated under clamped-free boundary condition. The layer arrangements of the beams were performed according to Taguchi L9 (3x3) orthogonal array. Mechanical properties of the layers made of different volume fractions of Ti-6Al-4V and ZrO2 materials was assumed as control factors. In order to determine the optimum layers and their levels, signal-to-noise (S/N) ratio analysis was used. Significant layers and their percent contributions on the first mode natural frequency were carried out using Analysis of Variance (ANOVA). In addition, the effects of the boundary conditions (B.C.) such as clamped-free (C-F) and clamped-clamped (C-C) and positions of the optimum layers were evaluated. According to results observed, maximum first mode natural frequency for C-F boundary condition using optimum layers were found using the FG beams with top and bottom layers with ceramic-rich and middle layer with metalrich. The most effective layers on the responses was obtained as L1 with 48.4523%, L2 with 16.1547% and L3 with 34.9839%. Layer arrangements for C-F boundary condition play important role on the natural first mode frequency.