Nonlinear Mechanical Analysis Of Functionally Graded Porous Structures

This paper presents the nonlinear behavior of functionally graded porous structures (beam and circular plate) with Model I which density gradient symmetric along thickness or Model II which non-symmetric along thickness. A further study is carried out to investigate the effects of porosity coefficient, boundary conditions and the mechanical load on the bending, buckling and post-buckling characteristics of functionally graded structures. The main contents are as follows:1) The analytical method is employed to research the nonlinear behavior of functionally graded porous beam. In the analysis, based on the classical beam theory (CBT), first-order shear deformation beam theory(FBT), respectively, and the physical neutral surface concept, governing equations for the nonlinear static response behavior of functionally graded porous beams subjected to the thermal or axial and transverse loading are derived using the energy method, then, the nonlinear equation is directly solved and a closed-form solution is obtained. The exact solutions obtained herein can be used to analyze the effects of density gradient index, density distribution patterns, slenderness ratio and loading on the bending, buckling and post-buckling behavior of functionally graded porous beam subjected to both clamped and simply supported boundary conditions in detail. The results show that under thermal loading, a functionally graded porous beam which simply supported at both ends do exhibit some characteristics that are quite different from those of a functionally graded porous beam clamped at both ends; Porosity coefficient and density distribution patterns play important roles in the bending and post-buckling of functionally graded porous beams. An increase in the slenderness ratio results in a reduction in the influence of the transverse shear deformation. As a consequence, the dimensionless critical buckling load of classical beams is higher than those of shear deformable beams. In contrast with this, the deflection of classical beams is lower than that of shear deformable beams.2) The shooting method is employed to numerically study the nonlinear behavior of functionally graded porous circular plate. In the analysis, based on the classical plate theory (CPT), governing equations for the nonlinear static response behavior of functionally graded porous circular plate subjected to the axial and transverse loading are derived , then, the resulted equations are numerically solved using the shooting method. The exact solutions obtained herein can be used to analyze the effects of porosity coefficient , density distribution patterns, slenderness ratio and loading on the bending, buckling and post-buckling behavior of functionally graded porous axisymmetric plates subjected to both clamped and simply supported boundary conditions in detail. The results show that porosity coefficient and density distribution patterns play important roles in the bending and post-buckling of functionally graded porous circular plates. The proper selection of density distribution pattern and porosity coefficient on the structure performance is highlighted to shed important insights into the porosity design to effectively achieve improved mechanical properties of beams and circular plates.