Analysis of thick porous beams by a quasi-3D theory and isogeometric analysis

We analyze mechanical behavior of porous beams by an effective computational approach based on isogeometric analysis (IGA). The quasi-3D theory is employed to take into account not only both normal and shear deformations without any shear correction factor, but also the thickness stretching effect, while the use of NURBS basis functions within the IGA framework can directly meet the first-order derivative demand of the quasi-3D theory. To demonstrate the accuracy and performance of the quasi-3D theory-based isogeometric analysis, mechanical static bending and natural frequency of porous beams are investigated via the proposed method. In porous beams, porosities are assumed to vary along the thickness direction and to distribute in uniform, symmetric, and asymmetric configurations. The effects of porosity distribution, volume fraction of porosity, boundary condition, length-to-height ratio, etc., on deflections, stresses, and fundamental frequencies of porous beams are systematically analyzed. Numerical results indicate that the porosity distribution significantly alters the deflection and natural frequency of porous beams with large thickness and high volume fraction of pores. The present study, thus, provides an incisive approach for investigation on mechanical responses of porous structures and useful insights into the porosity design to achieve appropriately natural frequency and deflection responses.