We carry out the static, free vibration, and buckling analyses of porous
two-directional functionally graded (2D FG) beams using a Ritz-based analytical
solution method based on the parabolic shear deformation theory. The choice of
solution functions used in the Ritz method distinguishes different approaches
and determines the accuracy of the analytical solution. Polynomial series
functions suitable for various boundary conditions were proposed. It was also
assumed that the material properties of the beam vary along both the thickness
(-axis) and
length (-axis)
directions according to a power-law distribution. The beam cross-section was
considered with three different types of porosity distributions. The equations of
motion were derived using Lagrange’s principle. The analysis results were obtained in
a nondimensional form depending on various boundary conditions, grading indices
,
, porosity coefficient
, porosity distribution,
and slenderness ratios
.
First, the suitability of the proposed polynomial series functions for this problem was
verified by comparison with the literature, and the obtained results were found to be
in good agreement with existing studies. Then, the static, free vibration, and
buckling analyses of porous two-directional functionally graded beams were
performed in detail, and the results obtained with the proposed method were
presented through tables and graphs.
