Bending Analysis of 2-D Functionally Graded Porous Beams Based on Novel High Order Theory

For modern structures and components, advanced engineering materials are preferred whose properties change continuously in more than one direction. In particular, the 2-D Functionally Graded Materials (2-D FGMs) have shown added effective properties, which will lead to avoid delamination and stress concentration. To research bending response of Functionally Graded Beams (FGBs), a novel shear strain shape function is chosen and considering the even and uneven porosity distributions. Material properties of even and uneven porosity distributions along the length and thickness directions of FGBs are varied in two directions by power-law. Present theory includes the influence of thickness stretching. This theory also fulfills the nullity of shear stresses in transverse direction on upper and lower side of the beam, thus avoiding use of a correction factor to accurately estimate shear stresses. The principle of virtual displacements is employed to develop equilibrium equations for porous FGBs. Navier’s method is used to obtain solutions to porous FGBs for Simply Supported (SS) boundary conditions. To ascertain accuracy, the developed theory is justified with numerical results of perfect and porous FGBs available in the open source. Influence of exponents, porosity volume fraction, thickness ratios, and aspect ratios on dimensionless deflections and stresses are studied. It can be observed that the effect of porosity coefficient on bending behavior of FG beams subjected to uniform transverse load, transverse deflection increases as the porosity coefficient increases and this effect is more prominent with high values of porosities from 20% to 30%. So the porosity parameter is a crucial parameter that must be considered in design of modern structures and the percentage of porosity in structure can be effected considerably in its performance and response. © 2022 School of Science, IHU. All rights reserved.