Geometrically nonlinear polygonal finite element analysis of functionally graded porous plates

Abstract

In this study, an efficient polygonal finite element method (PFEM) in combination with quadratic serendipity shape functions is proposed to study nonlinear static and dynamic responses of functionally graded (FG) plates with porosities. Two different porosity types including even and uneven distributions through the plate thickness are considered. The quadratic serendipity shape functions over arbitrary polygonal elements including triangular and quadrilateral ones, which are constructed based on a pairwise product of linear shape functions, are employed to interpolate the bending strains. Meanwhile, the shear strains are defined according to the Wachspress coordinates. By using the Timoshenko's beam to interpolate the assumption of the strain field along the edges of polygonal element, the shear locking phenomenon can be naturally eliminated. Furthermore, the C 0-type higher-order shear deformation theory (C 0-HSDT), in which two additional variables are included in the displacement field, significantly improves the accuracy of numerical results. The nonlinear equations of static and dynamic problems are solved by Newton-Raphson iterative procedure and by Newmark's integration scheme in association with the Picard methods, respectively. Through various numerical examples in which complex geometries and different boundary conditions are involved, the proposed approach yields more stable and accurate results than those generated using other existing approaches.

Mechanical Behavior of Porous Functionally Graded Nanocomposite Materials

“…The results obtained in this case study are represented in Figure 7. The results obtained in this study are in agreement with the literature [26], denoting higher displacements for porous FGM plates when compared with non-porous. As can be seen for the same porosity volume fraction, the even porosity distribution model promotes a larger displacement.…”

“…Hence, the effects of this kind of defect need to be considered when studying the mechanical behavior of FGMs structures. With this concern, N. V. Nguyen et al [26] worked on the mechanical response of porous FGM plates, considering for this purpose two distinct porosity distributions along the thickness direction, namely even and uneven. Figure 4 illustrates these different porosity distributions in an FGM plate like the one represented in Figure 2a.…”

“…In both relations-(3) and (4)-α is a porosity volume fraction, so 0 ≤ α ≤ 1. For α = 0, the FGM plate has no porosities, which is usually called the perfect FGM plate [26]. Also, J. Kim et al [25] referred that, being fundamental elements in structural systems and others, the mechanical responses of beams, plates, and shells should be under investigation with regard to FGMs with distributed porosities.…”

Porous Functionally Graded Plates: An Assessment of the Influence of Shear Correction Factor on Static Behavior

“…Concerning porosity distributions, Nguyen et al [41] studied the mechanical behavior of porous FGPs. To this purpose they took into account two different porosity distributions, varying both through the thickness direction (namely, the so-called even and uneven distributions).…”

Isogeometric analysis for size-dependent nonlinear thermal stability of porous FG microplates

“…Nguyen et al [21] developed a polygonal finite element method for geometrical nonlinear analysis of porous FG plates. A 3-D exact solution was obtained by Zhao et al [22] for vibration analysis of porous FG rectangular plates with three different types of porosity distributions.…”