Numerical Prediction of Deflection and Stress Responses of Functionally Graded Structure for Grading Patterns (Power-Law, Sigmoid and Exponential) and Variable Porosity (Even/Uneven)

Abstract

The finite element solutions of static deflection and stress values are obtained in this article for the functionally graded structure considering variable grading patterns (power-law, sigmoid and exponential) including the porosity effect. The unknown values are obtained computationally via a customized computer code with the help of cubic-order displacement functions considering the varied distribution of porosity (even and uneven) through the panel thickness. Also, the values are simulated through design software (ANSYS) to establish the present numerical solution accuracy. The comparison as well as the element sensitivity behaviour of the present numerical model verified by solving different kinds of numerical examples available in the published domain. Lastly, the effect of several influential geometry relevant parameters (aspect ratio, curvature ratio, thickness ratio, porosity index, type of porosity, power-law exponent, geometrical configuration and support conditions) affecting the structural stiffness and the corresponding outcomes (deflection and stress) of the FG structure are computed through the presently derived numerical model.

An eigenvalue solution for nonlocal vibration of guide supported perfect/imperfect functionally graded power‐law and sigmoid nanobeams on one‐parameter elastic foundation

“…One of the two types of porosity to be examined is the porosity distribution called even type. The change of material properties of power-law FGM with even porosity distribution is given as follows [34,37,42]:…”

“…This type imperfect FG power-law nanobeam will be called IPU-PL-FGM in this study. The change of material properties of power-law FG beam with uneven porosity distribution is written as [34,37]:…”

“…The ceramic volume fraction obeys sigmoid function given in Equation ( 8) is not given as a single expression like powerlaw function, but as two different expressions in two different regions. The material properties for the imperfect FG sigmoid nanobeam with evenly distributed porosities are stated as [34,37,40]:…”

“…Scholar have studied macro, micro, or nano FG material structures with different forms or effects. Some researchers have analyzed these structures with porosity [31][32][33][34][35][36][37][38][39][40][41][42][43], cracks [44,45], foundation effects [46][47][48], thermal effect [49,50], and combined effects [51][52][53][54][55][56][57][58][59][60]. As can be understood, the analysis of structural elements consisting of FG composite materials has attracted considerable attention.…”

Assessment of non‐polynomial shear deformation theories for the free vibration and transient analysis of plates with functionally‐graded materials supported on an elastic foundation

“…The static deflection increases by 25%-86% due to the porosities, as reported in the article. Further, Ramteke et al [38] presented the stress analysis of various even and uneven types of porosity-dependent FGM panels with power-law, exponential and sigmoid material distributions. Ramteke and Panda [39,40] derived a finite element model for the free vibration responses of porous multi-directional FGM panels using a polynomial HSDT.…”