scholarly journals Size-dependent vibration analysis of graphene-PMMA lamina based on non-classical continuum theory

2019 ◽  
Vol 26 (1) ◽  
pp. 491-501 ◽  
Author(s):  
Mehran Karimi Zeverdejani ◽  
Yaghoub Tadi Beni
Keyword(s):  
Natural Frequency ◽  
Couple Stress ◽  
Volume Fraction ◽  
Couple Stress Theory ◽  
Shear Deformation Theory ◽  
Continuum Theory ◽  
Dynamics Simulation ◽  
Physical Parameters ◽  
Stress Theory ◽  
Size Dependent

AbstractThis paper studies the free vibration of polymer nanocomposite reinforced by graphene sheet. In this work, the new size dependent formulation is presented for nanocomposites based on couple stress theory. For this purpose, the first shear deformation theory is applied. The effect of scale parameter is investigated based on anisotropic couple stress theory. Vibration equations of the composite lamina are extracted using Hamilton’s principle. Numerical results are provided for Poly methyl methacrylate/graphene composite.Mechanical properties of the composite are obtained from molecular dynamics simulation. Based on eigenvalue procedure, an analytical solution is obtained for the natural frequency of composite lamina. In the results section, the effect of dimensional and physical parameters are investigated on lamina natural frequency. It is observed that graphene defects caused to diminish the lamina frequency. Furthermore, it is revealed that the increase in graphene volume fraction leads to natural frequency be greater.

Size-dependent two-node axisymmetric shell element for buckling analysis with couple stress theory

2019 ◽  
Vol 233 (13) ◽  
pp. 4729-4741
Author(s):  
Iman Soleimani ◽  
Yaghoub Tadi Beni ◽  
Mohsen Botshekanan Dehkordi
Keyword(s):  
Couple Stress ◽  
Couple Stress Theory ◽  
Continuum Theory ◽  
Shell Element ◽  
Modified Couple Stress Theory ◽  
Element Formulation ◽  
Stress Theory ◽  
Size Dependent ◽  
Axisymmetric Shell ◽  
Modified Couple Stress

In this paper, two-node size-dependent axisymmetric shell element formulation is developed by using thin conical shell model in the place of the beam model, which is used in previous research and using the modified couple stress theory in the place of the classical continuum theory. Since classical continuum theory is unable to correctly compute stiffness and account for size effects in micro/nanostructures, higher order continuum theories such as modified couple stress theory have become quite popular. The mass stiffness matrix and geometric stiffness matrix for axisymmetric shell element are developed in this paper, and by means of size-dependent finite element formulation it is extended to more precisely account for nanotube buckling. The results have indicated using the two-node axisymmetric shell element, where the rigidity of the nano-shell is greater than that in the classical, and the critical axial buckling loads obtained from couple stress theory are greater than that of classical, which is due to the presence of one size parameter in couple stress theory. The findings also indicate that the developed size-dependent axisymmetric shell element is able to analyze the buckling of cylindrical and conical shells and also circular plate, which is reliable for simulating micro/nanostructures and can be used for the analysis of size effect and has desirable convergence characteristic. Besides, in addition to reducing the number of elements required, using axisymmetric shell element also increases convergence speed and accuracy.

A size-dependent model for shear deformable laminated micro-nano plates based on couple stress theory

2021 ◽  
Vol 259 ◽  
pp. 113457
Author(s):  
Zanhang He ◽  
Jianghong Xue ◽  
Sishi Yao ◽  
Yongfu Wu ◽  
Fei Xia
Keyword(s):  
Couple Stress ◽  
Couple Stress Theory ◽  
Stress Theory ◽  
Size Dependent ◽  
Dependent Model ◽  
Shear Deformable

Size-dependent bending behavior of three-layered doubly curved shells: Modified couple stress formulation

2018 ◽  
Vol 22 (7) ◽  
pp. 2210-2249 ◽  
Author(s):  
Mohammad Arefi
Keyword(s):  
Applied Voltage ◽  
Couple Stress ◽  
Virtual Work ◽  
Couple Stress Theory ◽  
Shear Deformation Theory ◽  
Small Scale ◽  
Size Dependent ◽  
Modified Couple Stress ◽  
Doubly Curved ◽  
Piezoelectric Shell

In this paper, modified couple stress formulation of a small scale doubly curved piezoelectric shell resting on Pasternak's foundation is presented based on first-order shear deformation theory. Size-dependent electro-elastic results of doubly curved shell are presented based on an analytical approach. The doubly curved piezoelectric shell is subjected to uniform transverse loads and applied voltage. To account the size dependency, modified couple stress theory is employed in conjunction with principle of virtual work. The numerical results are presented in both tabular and graphical forms to show the influence of small scale parameter, applied voltage, geometries and two parameters of Pasternak's foundation on the electro-elastic results of size-dependent doubly curved piezoelectric shell.

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