Elastostatic behaviour of functionally graded porous beams: novel Kuhn Tucker conditions with R program for mathematical computing

Pores affect functionally graded materials. Further characteristics may be added if pores expand from the surface to the interior. Functionally graded porous beam (FGPB) bending response is analyzed using a specific shear shape function that accounts for both uniform and uneven porosity distributions. Power law changes the material characteristics of FGPBs with uniform and uneven porosity distributions along length and thickness. In order to determine the maximum transverse deflections, axial stresses, transverse shear stresses, and normal stresses in simply-supported and clamped-clamped beams, numerical calculations are performed with various gradation exponents, aspect ratios (L/h), and porosity levels (both even and uneven). The obtained results are compared with earlier investigations and justified.