Nonlocal elasticity analysis of moderately thick porous functionally graded plates in a hygro-thermal environment

In this article, a highly efficient quasi-three-dimensional theory has been used to study the nonlinear hygro-thermo-mechanical bending analysis of a very thick functionally graded material (FGM) r...

A comprehensive study on nonlinear hygro-thermo-mechanical analysis of thick functionally graded porous rotating disk based on two quasi three-dimensional theories

The bending analysis of moderately thick elliptic plates weakened by an eccentric circular hole has been investigated in this article. The nonlinear governing equations have been presented by considering the von-Karman assumptions and the first-order shear deformation theory in cylindrical coordinates system. Semi-analytical polynomial method (SAPM) which had been presented by the author before has been used. By applying SAPM method, the nonlinear partial differential equations have been transformed to the nonlinear algebraic equations system. Then, the nonlinear algebraic equations have been solved by using Newton–Raphson method. The obtained results of this study have been compared with the results of other references and the accuracy of the results has been shown. The effect of some important parameters on the results such as the location of the circular hole, the ratio of major to minor radiuses of elliptical plate, the size of circular hole and boundary conditions have been studied. It is concluded that applying the presented method is very convenient and efficient. So, it can be used for analyzing the mechanical behavior of elliptical plates, instead of relatively complicated formulations in elliptic coordinates system.

http://jsm.iau-arak.ac.ir/article_544403_3bc6d0710e1f14a64435dfe287fd8a1b.pdf

New Method for Large Deflection Analysis of an Elliptic Plate Weakened by an Eccentric Circular Hole

There are many materials that the linear elasticity theory cannot predict their mechanical behavior against applied loads. This research proposes a comprehensive theoretical method to obtain the mechanical response of hyperelastic models (with nonlinear elastic deformations) such as polymers and rubbers. They are vital in the design phase of complicated engineering structures like engine mounts and structural bearings in aerospace and automotive industries. The presented theory is implemented in detail and has no limitations in analyzing geometrically and physically nonlinear materials. As a test case, the governing equations of a sheet made of nonlinear elastic material are derived within the framework of this new approach. The derived governing equations are completely nonlinear in all major directions. Consequently, results can be one of the most accurate mathematical simulation results for nonlinear elastic material structures. Then, the obtained equations are solved using a meshless solution method named the semi-analytical polynomial method. The stress and deformation results of the structure under uniform and non-uniform transverse external loadings are obtained for different types of boundary conditions, loading, and material properties. Consequently, this research can be widely used as a suitable essential reference for researchers studying the mechanical behavior of nonlinear elastic structures. 

A Novel Nonlinear Elasticity Approach for Analysis of Nonlinear and Hyperelastic Structures

On the Vibration Characteristics of Graphene Platelet Reinforced Composite Super-elliptical Plates via Chebyshev-Ritz Method

In present study, thermo-elastic buckling analysis of multi-layer orthotropic annular/circular graphene sheets is investigated based on Eringen’s theory. The moderately thick and also thick nano-plates are considered. Using the non-local first and third order shear deformation theories, the governing equations are derived. The van der Waals interaction between the layers is simulated for multi-layer sheets. The stability governing equations are obtained according to the adjacent equilibrium estate method. The constitutive equations are solved by applying the differential quadrature method (DQM). Applying the differential quadrature method, the ordinary differential equations are transformed to algebraic equations. Then, the critical temperature is obtained. Since there is not any research in thermo-elastic buckling analysis of multi-layer graphene sheets, the results are validated with available single layer articles. The effects of non-local parameter, the values of van der Waals interaction between the layers, third to first order shear deformation theory analyses, non-local to local analyses, different values of Winkler and Pasternak elastic foundation and analysis of bi-layer and triple layer sheets are investigated. It is concluded that the critical temperature increases and tends to a constant value along the rise of van der Waals interaction between the layers.

http://jsm.iau-arak.ac.ir/article_527096_1714adc86fb1958d7fab51cf8e705d7c.pdf

Non-Local Thermo-Elastic Buckling Analysis of Multi-Layer Annular/Circular Nano-Plates Based on First and Third Order Shear Deformation Theories Using DQ Method

This study is the first report of numerical solution of nonlinear bending analysis for annular and circular plates based on 3D elasticity theory with asymmetric boundary conditions using semi-analytical polynomial method (SAPM). Orthotropic annular and circular plates are subjected to transverse loading and 3D bending analysis in the presence of symmetric and asymmetric boundary conditions is studied. For asymmetry cases, the plate boundaries are divided to two or three parts and various boundary conditions such as clamped, simply-supported and free edges are defined for each part. The asymmetry in one and two directions is studied. The influence of elastic foundations, mechanical and thermo-mechanical loadings are examined. Regarding this fact that no study has been done in the case of asymmetric boundary conditions, the obtained results are compared with FEM results by ABAQUS. The results show good agreement with the literatures and FEM results, which it shows that the presented method can use to analyze the 3D bending of plates under asymmetric conditions. Also, it is observed that 3D elasticity estimates some higher deflections than other theories. But, the obtained results by 3D elasticity theory and those obtained by FEM analysis in the case of asymmetric conditions are so close.

http://jsm.iau-arak.ac.ir/article_666765_23ea251bf2fe19f026f3a108db8062b2.pdf

A Novel Method for Numerical Analysis of 3D Nonlinear Thermo-Mechanical Bending of Annular and Circular Plates with Asymmetric Boundary Conditions Using SAPM

Sh Dastjerdi

Papers

Non-Local Thermo-Elastic Buckling Analysis of Multi-Layer Annular/Circular Nano-Plates Based on First and Third Order Shear Deformation Theories Using DQ Method

New Method for Large Deflection Analysis of an Elliptic Plate Weakened by an Eccentric Circular Hole

A Novel Method for Numerical Analysis of 3D Nonlinear Thermo-Mechanical Bending of Annular and Circular Plates with Asymmetric Boundary Conditions Using SAPM