Free vibration analysis of porous functionally graded plates using a novel Quasi-3D hyperbolic high order shear deformation theory

In this study, a novel quasi-three dimensional hyperbolic high-order shear deformation theory (quasi-3D HHSDT) is developed for free vibration analysis of porous functionally graded plates (FGPs). There are six unknowns in the current displacement field, and no shear correction factor is required. The mechanical properties are varied continuously through the thickness of porous FG plates using a modified power law function while considering the effect of porosities on the plate�s structural integrity. Two distinct porosity distribution models are considered, including even and uneven porosity distributions. The Navier technique is employed to obtain the closed-form solutions of motion's equations. An exhaustive parametric study is presented to show the influence of the different parameters on the fundamental frequencies

A Novel Trigonometric High-Order Shear Deformation Theory for Free Vibration and Buckling Analysis of Carbon Nanotube Reinforced Beams Resting on a Kerr Foundation

This research is concerned with the free vibration and buckling analysis of carbon nanotube-reinforced beams (CNT-RBs) using a novel high-order shear deformation theory (HSDT). The current HSDT is modeled by a trigonometric function without a shear correction factor, and the displacement field has only four variables. Several different carbon nanotube distributions, including two uneven CNT distributions (X-CNT and O-CNT), are considered. The mixture rule is applied to express the effective material properties of carbon nanotube-reinforced beams. The CNTR beams are rested on two springs and a shear layer (Kerr foundation). Hamilton’s principle is employed to derive the governing equations, which are then solved using the Navier technique. The current theory and several parameter effects are studied and validated in comparison to benchmark studies and theories. The main purpose of this study is to enhance understanding of high-order shear theories, such as third order, sinusoidal, exponential, etc. In this context, our theory yields excellent results when compared to other theories. The difference between our theory and the exact solution is so minimal that it is superior to other theories. The second part of the study focuses on investigating the distribution of carbon nanotubes to enhance understanding. This knowledge can assist panel manufacturers in determining the appropriate distribution shape. Our results indicate that the third distribution (X-CNT) significantly influences mechanical behavior, unlike the first and second distributions (UD-CNT and O-CNT)

Quadrilateral membrane finite elements with rotational DOFs for the analysis of geometrically linear and nonlinear plane problems

International audienceIn this paper, we present the formulations of two four-node quadrilateral membrane finite elements with rotational degrees of freedom to analyze geometric linear and nonlinear plane problems. They are based on a plane adaptation of the space fiber rotation concept that considers virtual rotations of a nodal fiber within the element enhancing the displacement vector approximation of low-order elements. An updated Lagrangian approach is chosen to describe large displacement with small strain kinematics. Several geometric linear and nonlinear benchmarks are presented to assess the performance of the proposed membrane elements and the obtained results demonstrate their efficiency

Free vibration analysis of the structural integrity on the porous functionally graded plates using a novel Quasi-3D hyperbolic high order shear deformation theory

In this study, a novel quasi-three dimensional hyperbolic high-order shear deformation theory (quasi-3D HHSDT) is developed for free vibration analysis of porous functionally graded plates (FGPs). There are six unknowns in the current displacement field, and no shear correction factor is required. The mechanical properties are varied continuously through the thickness of porous FG plates using a modified power law function while considering the effect of porosities on the plate’s structural integrity. Two distinct porosity distribution models are considered, including even and uneven porosity distributions. The Navier technique is employed to obtain the closed-form solutions of motion's equations. An exhaustive parametric study is presented to show the influence of the different parameters on the fundamental frequencies