The size effects that reveal the dramatic changes of mechanical behaviour at nanoscales have traditionally been analysed for regular beam systems. Here, the method of using finite-element analysis is explored with the intention of evaluating the size effects for complex nanostructures. The surface elasticity theory and generalized Young-Laplace equation are integrated into a beam element to acc...

Based on generalized laminate plate theory, the formulation of a one-dimensional beam finite element with layer-wise constant shear (BLCS) is presented. The linear layer-wise representation of in-plane displacements permit accurate computation of normal stresses and transverse shear stresses on each layer for laminated beams with dissimilar ply stiffnesses. The BLCS formulation is equivalent to...

In the present paper, electrical energy harvesting from random vibrations of an Euler-Bernoulli nano-beam with two piezoelectric layers is investigated. The beam is composed of an aluminum layer together with two piezoelectric ceramic layers (PZT 5A) serving as energy harvesting sensors. In the proposed method, the equations governing the bimorph nano-beam will be analytically derived using cla...

We calculate the tensile and shear moduli of a series of boron nitride nanotubes and their piezoelectric response to applied loads. We compare in detail results from a simple molecular mechanics (MM) potential, the universal force field, with those from the atomistic finite element method (AFEM) using both Euler-Bernoulli and Timoshenko beam formulations. The MM energy minimisations are much mo...

In this article thermoelastic damping in nano-beam resonators is investigated based on nonlocal theory of elasticity and the Euler-Bernoulli beam assumptions. The governing equation of deflection of the beam is obtained from shear and moment resultants and stress–strain relationship of the nonlocal elasticity model and also the governing equations of thermoelastic damping are established by usi...

A complete investigation on the free vibration and stability analysis of beams made of functionally graded materials (FGMs) containing open edge cracks utilizing four beam theories, Euler-Bernoulli, Rayleigh, shear and Timoshenko, is performed in this research. It is assumed that the material properties vary along the beam thickness exponentially and the cracked beam is modeled as two segments ...

We consider an elastic model for a curved rod with arbitrary threedimensional geometry, incorporating shear and membrane as well as bending and torsion effects. We define an approximation procedure based on a discretization by linear Timoshenko beam elements. Introducing an equivalent mixed problem, we establish optimal error estimates independent of the thickness, thereby proving that shear an...