Semi-Analytical Study of a Functionally Graded Open Cellular Porous Beam to Analyze Its Nonlinear Bending Characteristics

The present investigation reports a semi-analytical analysis of a open cellular porous beam for the study of nonlinear bending characteristics when subjected to transverse loading in the form of uniform or patch. The porous beam is mathematically modeled in programming software (MATLAB) using first-order shear deformation theory (FSDT) in conjunction with von-Kármán nonlinearity. Firstly, the porosity of the beam is distributed throughout the thickness in the form of three distribution systems, i.e., either uniformly or non-uniform symmetrically or non-uniform unsymmetrically. Secondly, implementing minimization of total potential energy principle the partial differential equations (PDEs) of the beam is derived. These PDEs are simplified into nonlinear algebraic equations via. Galerkin’s method. Later, these equations are solved using the Newton–Raphson method to plot the load-deformation curves. Moreover, a parametric study is also reported to observe the characteristic of nonlinear bending with variation in different parameters like, types of porosity distribution, porosity coefficient, aspect ratio, different types of transverse loading, which may help the designers for appropriate design against large deformation.