Finite element based stress and vibration analysis of axially functionally graded rotating beams

Khalid H. Almitani,M.A. Eltaher,Alaa. A. Abdelrahman,Hanaa E. Abd-El-Mottaleb 국제구조공학회 2021 Structural Engineering and Mechanics, An Int'l Jou Vol.79 No.1

This study presents a comprehensive numerical dynamic finite element analysis to investigate the dynamic behavior and induced stresses of axially functionally graded rotating beam, for the first time. The material properties of the rotating beam are assumed to continuously vary nonlinearly along the longitudinal direction according to the power law. Based on Timoshenko beam theory (TBT), the Hamiltonian principle is applied to derive governing equations of motion. The dynamic finite element equation of motion for axially functionally straight rotating cantilever beam is derived. Both stress and vibration responses are detected and analyzed. The proposed computational procedure is verified by comparing the obtained results with the corresponding results in the literature and good agreement is observed. Effects of the material gradation index and the rotating speed on the dynamic behavior of functionally graded rotating cantilever are investigated and analyzed. The obtained results show the significant effect of the material gradation index and the rotating speed on the dynamic behavior of axially functionally graded beams. The proposed model can be used effectively in design of wind turbine, rotation shafts and turbomachinery systems.

On forced and free vibrations of cutout squared beams

Khalid H. Almitani,Alaa A. Abdelrahman,Mohamed A. Eltaher 국제구조공학회 2019 Steel and Composite Structures, An International J Vol.32 No.5

Perforation and cutouts of structures are compulsory in some modern applications such as in heat exchangers, nuclear power plants, filtration and microeletromicanical system (MEMS). This perforation complicates dynamic analyses of these structures. Thus, this work tends to introduce semi-analytical model capable of investigating the dynamic performance of perforated beam structure under free and forced conditions, for the first time. Closed forms for the equivalent geometrical and material characteristics of the regular square perforated beam regular square, are presented. The governing dynamical equation of motion is derived based on Euler-Bernoulli kinematic displacement. Closed forms for resonant frequencies, corresponding Eigen-mode functions and forced vibration time responses are derived. The proposed analytical procedure is proved and compared with both analytical and numerical analyses and good agreement is noticed. Parametric studies are conducted to illustrate effects of filling ratio and the number of holes on the free vibration characteristic, and forced vibration response of perforated beams. The obtained results are supportive in mechanical design of large devices and small systems (MEMS) based on perforated structure.

Stability of perforated nanobeams incorporating surface energy effects

Khalid H. Almitani,Alaa A. Abdelrahman,Mohamed A. Eltaher 국제구조공학회 2020 Steel and Composite Structures, An International J Vol.35 No.4

This paper aims to present an analytical methodology to investigate influences of nanoscale and surface energy on buckling stability behavior of perforated nanobeam structural element, for the first time. The surface energy effect is exploited to consider the free energy on the surface of nanobeam by using Gurtin-Murdoch surface elasticity theory. Thin and thick beams are considered by using both classical beam of Euler and first order shear deformation of Timoshenko theories, respectively. Equivalent geometrical constant of regularly squared perforated beam are presented in simplified form. Problem formulation of nanostructure beam including surface energies is derived in detail. Explicit analytical solution for nanoscale beams are developed for both beam theories to evaluate the surface stress effects and size-dependent nanoscale on the critical buckling loads. The closed form solution is confirmed and proven by comparing the obtained results with previous works. Parametric studies are achieved to demonstrate impacts of beam filling ratio, the number of hole rows, surface material characteristics, beam slenderness ratio, boundary conditions as well as loading conditions on the non-classical buckling of perforated nanobeams in incidence of surface effects. It is found that, the surface residual stress has more significant effect on the critical buckling loads with the corresponding effect of the surface elasticity. The proposed model can be used as benchmarks in designing, analysis and manufacturing of perforated nanobeams.

Dynamic vibration response of functionally graded porous nanoplates in thermal and magnetic fields under moving load

Ismail Esen,Mashhour A. Alazwari,Khalid H. Almitani,Mohamed A Eltaher,A. Abdelrahman Techno-Press 2023 Advances in nano research Vol.14 No.5

In the context of nonclassical nonlocal strain gradient elasticity, this article studies the free and forced responses of functionally graded material (FGM) porous nanoplates exposed to thermal and magnetic fields under a moving load. The developed mathematical model includes shear deformation, size-scale, miscorstructure influences in the framework of higher order shear deformation theory (HSDT) and nonlocal strain gradient theory (NSGT), respectively. To explore the porosity effect, the study considers four different porosity models across the thickness: uniform, symmetrical, asymmetric bottom, and asymmetric top distributions. The system of quations of motion of the FGM porous nanoplate, including the effects of thermal load, Lorentz force, due to the magnetic field and moving load, are derived using the Hamilton's principle, and then solved analytically by employing the Navier method. For the free and forced responses of the nanoplate, the effects of nonlocal elasticity, strain gradient elasticity, temperature rise, magnetic field intensity, porosity volume fraction, and porosity distribution are analyzed. It is found that the forced vibrations of FGM porous nanoplates under thermal and live loads can be damped by applying a directed magnetic field.

Characterization and behaviors of single walled carbon nanotube by equivalent-continuum mechanics approach

Eltaher, Mohamed A.,Almalki, Talaal A.,Ahmed, Khaled I.E.,Almitani, Khalid H. Techno-Press 2019 Advances in nano research Vol.7 No.1

This paper focuses on two main objectives. The first one is to exploit an energy equivalent model and finite element method to evaluate the equivalent Young's modulus of single walled carbon nanotubes (SWCNTs) at any orientation angle by using tensile test. The calculated Young's modulus is validated with published experimental results. The second target is to exploit the finite element simulation to investigate mechanical buckling and natural frequencies of SWCNTs. Energy equivalent model is presented to describe the atomic bonding interactions and their chemical energy with mechanical structural energies. A Program of Nanotube modeler is used to generate a geometry of SWCNTs structure by defining its chirality angle, overall length of nanotube and bond length between two adjacent nodes. SWCNTs are simulated as a frame like structure; the bonds between each two neighboring atoms are treated as isotropic beam members with a uniform circular cross section. Carbon bonds is simulated as a beam and the atoms as nodes. A finite element model using 3D beam elements is built under the environment of ANSYS MAPDL environment to simulate a tensile test and characterize equivalent Young's modulus of whole CNT structure. Numerical results are presented to show critical buckling loads, axial and transverse natural frequencies of SWCNTs with different orientation angles and lengths. The understanding of mechanical behaviors of CNTs are essential in developing such structures due to their great potential in wide range of engineering applications.

Nonlocal strain gradient theory for buckling and bending of FG-GRNC laminated sandwich plates

Muhammad Basha,Ahmed Amine Daikh,Ammar Melaibari,Ahmed Wagih,Ramzi Othman,Khalid H. Almitani,Mostafa A. Hamed,Alaa Abdelrahman,Mohamed A Eltaher 국제구조공학회 2022 Steel and Composite Structures, An International J Vol.43 No.5

The bending and buckling behaviours of FG-GRNC laminated sandwich plates are investigated by using novel fivevariables quasi 3D higher order shear deformation plate theory by considering the modified continuum nonlocal strain gradient theory. To calculate the effective Young’s modulus of the GRNC sandwich plate along the thickness direction, and Poisson’s ratio and mass density, the modified Halpin-Tsai model and the rule of the mixture are employed. Based on a new field of displacement, governing equilibrium equations of the GRNC sandwich plate are solved using a developed approach of Galerkin method. A detailed parametric analysis is carried out to highlight the influences of length scale and material scale parameters, GPLs distribution pattern, the weight fraction of GPLs, geometry and size of GPLs, the geometry of the sandwich plate and the total number of layers on the stresses, deformation and critical buckling loads. Some details are studied exclusively for the first time, such as stresses and the nonlocality effect.