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The results obtained from beam and shell theories are compared, which leads to the determination of limits of tube parameters up to which beam theory gives valid results.
Viscoelastic material damping has been assumed and system loss factors have been determined for various modes, by using the complex modulus approach in the beam and shell theories.
The application of nonlocal continuum mechanics allowing for the small scale effects to the vibrational analysis of CNTs has been suggested by many research workers including both beam and shell theories [29, 30, 31, 32, 33, 34, 35].
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In comparing the results obtained from beam theory and shell theory, emphasis is given to possible explanations of the points of difference in terms of physical behavior of the shell.
Helically wound armours and tubulars are formulated by a combination of curved beam kinematics, thin shell theory and the principle of virtual displacements to obtain finite element equations.
The CAD model of the stent was meshed with beam and shell elements to discretise the stent struts and the stent graft, respectively.
The second type is continuum-based modeling, which includes elastic beam models (Yoon et al. 2005; Zhang et al. 2006; Wang et al. 2008; Kuang et al. 2009) and elastic shell theories (Yakobson et al. 1997; Nguyen et al. 2009; Yan et al. 2009; Liew & Wang 2007).
The building is modeled as a three-dimensional (3D) frame structure using frame elements for columns, longitudinal beams, and transverse beams and shell element for slabs.
The cylindrical shells are also analyzed using the Flügge and the Donnell shell theories.
The review mainly focus on the size-dependent beam, plate and shell models developed based on the nonlocal elasticity theory, modified couple stress theory and strain gradient theory due to their common use in predicting the global behaviour of small-scale structures.
In these calculations, beam, solid, and shell elements are used.
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