In this work, various higher-order shear deformation plate theories for wave propagation in functionally graded plates are developed. Due to porosities, possibly occurring inside functionally graded materials (FGMs) during fabrication, it is therefore necessary to consider the wave propagation in plates having porosities in this study. The developed refined plate theories have fewer number of unknowns and equations of motion than the first-order shear deformation theory, but accounts for the transverse shear deformation effects without requiring shear correction factors. The rule of mixture is modified to describe and approximate material properties of the functionally graded plates with porosity phases. The governing equations of the wave propagation in the functionally graded plate are derived by employing the Hamilton

Wave propagation in functionally graded plates with porosities using various higher-order shear deformation plate theories

Analytical solutions for bending and buckling of functionally graded nanobeams based on the nonlocal Timoshenko beam theory

In the present work, a simple and refined trigonometric higher-order beam theory is developed for bending and vibration of functionally graded beams The beauty of this theory is that, in addition to modeling the displacement field with only 3 unknowns as in Timoshenko beam theory, the thickness stretching effect (ez ≠ 0) is also included in the present theory Thus, the present refined beam theory has fewer number of unknowns and equations of motion than the other shear and normal deformations theories, and it considers also the transverse shear deformation effects without requiring shear correction factors The neutral surface position for such beams in which the material properties vary in the thickness direction is determined Based on the present refined trigonometric higher-order beam theory and the neutral surface concept, the equations of motion are derived from Hamilton's principle Numerical results of the present theory are compared with other theories to show the effect of the inclusion of transverse normal strain on the deflections and stresses

A new simple shear and normal deformations theory for functionally graded beams

https://northumbria-test.eprints-hosting.org/id/document/265204

A review of continuum mechanics models for size-dependent analysis of beams and plates

A review on nonlocal elastic models for bending, buckling, vibrations, and wave propagation of nanoscale beams

The thermal buckling properties of double-walled carbon nanotubes (DWCNTs) are studied using nonlocal Timoshenko beam model, including the effects of transverse shear deformation and rotary inertia. The DWCNTs are considered as two nanotube shells coupled through the van der Waals interaction between them. The geometric nonlinearity is taken into account, which arises from the mid-plane stretching. Considering the small-scale effects, the governing equilibrium equations are derived and the critical
buckling temperatures under uniform temperature rise are obtained. The results show that the critical buckling temperature can be overestimated by the local beam model if the nonlocal effect is overlooked for long nanotubes. In addition, the effect of shear deformation and rotary inertia on the buckling temperature is more obvious for the higher-order modes. The investigation of the thermal buckling properties of DWCNTs may be used as a useful reference for the application and the design of nanostructures in which DWCNTs act as basic elements.

/pdf/nonlocal-effects-on-thermal-buckling-properties-of-double-2j084dqtnp.pdf

Nonlocal effects on thermal buckling properties of double-walled carbon nanotubes

In this paper, the mechanical buckling properties of a zigzag double-walled carbon nanotube (DWCNT) with both chirality and small scale effects are studied. Based on the nonlocal continuum theory and the Timoshenko beam model, the governing equations are derived and the critical buckling loads under axial compression are obtained. The DWCNTs are considered as two nanotube shells coupled through the van der Waals interaction between them. The equivalent Young’s modulus and shear modulus for zigzag DWCNT are derived using an energy-equivalent model. The results show that the critical buckling load can be overestimated by the local beam model if the small-scale effect is overlooked for long nanotubes. In addition, significant dependence of the critical buckling loads on the chirality of zigzag carbon nanotube is confirmed. These findings are important in mechanical design considerations of devices that use carbon nanotubes.

Chirality and scale effects on mechanical buckling properties of zigzag double-walled carbon nanotubes

This paper presents an efficient higher-order nonlocal beam theory for the thermal buckling of nanobeams. The displacement field is chosen based on assumptions that the in-plane and transverse displacements consist of bending and shear components, and the shear components of in-plane displacements give rise to the parabolic variation of shear strain through the thickness in such a way that shear stress vanishes on the nanobeam surfaces. Therefore, there is no need to use a shear correction factor. The present model is capable of capturing both the small-scale effect and transverse shear deformation effects of nanobeams, and it has strong similarities with the nonlocal Euler–Bernoulli beam theory in aspects such as equations of motion, boundary conditions, and stress resultant expressions. Using the nonlinear strain–displacement relations, the equilibrium and stability equations of nanobeams are derived. The theoretical development presented herein may serve as a reference for nonlocal theories as ...

https://ascelibrary.org/doi/pdf/10.1061/%28ASCE%29NM.2153-5477.0000057

Thermal Buckling Behavior of Nanobeams Using an Efficient Higher-Order Nonlocal Beam Theory

In this paper, unified nonlocal shear deformation theory is proposed to study bending, buckling and free vibration of nanobeams This theory is based on the assumption that the in-plane and transverse displacements consist of bending and shear components in which the bending components do not contribute toward shear forces and, likewise, the shear components do not contribute toward bending moments In addition, this present model is capable of capturing both small scale effect and transverse shear deformation effects of nanobeams, and does not require shear correction factors The equations of motion are derived from Hamilton\'s principle Analytical solutions for the deflection, buckling load, and natural frequency are presented for a simply supported nanobeam, and the obtained results are compared with those predicted by the nonlocal Timoshenko beam theory and Reddy beam theories

Abdelwahed Semmah

Papers

Nonlocal effects on thermal buckling properties of double-walled carbon nanotubes

Chirality and scale effects on mechanical buckling properties of zigzag double-walled carbon nanotubes

Thermal Buckling Behavior of Nanobeams Using an Efficient Higher-Order Nonlocal Beam Theory

Comparison of various refined nonlocal beam theories for bending, vibration and buckling analysis of nanobeams

The thermal effect on vibration of zigzag single walled carbon nanotubes using nonlocal Timoshenko beam theory