An efficient 4‐node facet shell element for the modified couple stress elasticity

2021 ◽  
Author(s):  
Yan Shang ◽  
Huan‐Pu Wu ◽  
Song Cen ◽  
Chen‐Feng Li
Keyword(s):  
Couple Stress ◽  
Shell Element ◽  
Couple Stress Elasticity ◽  
Modified Couple Stress

scholarly journals A Modified Couple Stress Elasticity for Non-Uniform Composite Laminated Beams Based on the Ritz Formulation

Molecules ◽  
2020 ◽  
Vol 25 (6) ◽  
pp. 1404 ◽  
Author(s):  
Farajollah Zare Jouneghani ◽  
Hamidraza Babamoradi ◽  
Rossana Dimitri ◽  
Francesco Tornabene
Keyword(s):  
Boundary Conditions ◽  
Couple Stress ◽  
Scale Parameter ◽  
Laminated Composite ◽  
Length Scale Parameter ◽  
Smart Devices ◽  
Small Scale ◽  
Length Scale ◽  
Couple Stress Elasticity ◽  
Modified Couple Stress

Due to the large application of tapered beams in smart devices, such as scanning tunneling microscopes (STM), nano/micro electromechanical systems (NEMS/MEMS), atomic force microscopes (AFM), as well as in military aircraft applications, this study deals with the vibration behavior of laminated composite non-uniform nanobeams subjected to different boundary conditions. The micro-structural size-dependent free vibration response of composite laminated Euler–Bernoulli beams is here analyzed based on a modified couple stress elasticity, which accounts for the presence of a length scale parameter. The governing equations and boundary conditions of the problem are developed using the Hamilton’s principle, and solved by means of the Rayleigh–Ritz method. The accuracy and stability of the proposed formulation is checked through a convergence and comparative study with respect to the available literature. A large parametric study is conducted to investigate the effect of the length-scale parameter, non-uniformity parameter, size dimension and boundary conditions on the natural frequencies of laminated composite tapered beams, as useful for design and optimization purposes of small-scale devices, due to their structural tailoring capabilities, damage tolerance, and their potential for creating reduction in weight.

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.

FGM micro/nano-plates within modified couple stress elasticity

2020 ◽  
Vol 245 ◽  
pp. 112294
Author(s):  
V. Sladek ◽  
J. Sladek ◽  
M. Repka ◽  
L. Sator
Keyword(s):  
Couple Stress ◽  
Couple Stress Elasticity ◽  
Modified Couple Stress

First-order shear deformation theory for orthotropic doubly-curved shells based on a modified couple stress elasticity

2018 ◽  
Vol 73 ◽  
pp. 129-147 ◽  
Author(s):  
Farajollah Zare Jouneghani ◽  
Payam Mohammadi Dashtaki ◽  
Rossana Dimitri ◽  
Michele Bacciocchi ◽  
Francesco Tornabene
Keyword(s):  
Shear Deformation ◽  
Couple Stress ◽  
Deformation Theory ◽  
Shear Deformation Theory ◽  
First Order ◽  
Doubly Curved Shells ◽  
Couple Stress Elasticity ◽  
Modified Couple Stress ◽  
Doubly Curved
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