Static, Vibration, and Buckling Analysis of Nanobeams

Static, vibration, and buckling analysis of nanobeams is studied based on modified couple stress theory (MCST) in this chapter. The inclusion of an additional material parameter enables the new beam model to capture the size effect. The new nonclassical beam model reduces the classical beam model when the length scale parameter is set to zero. The finite element formulations are derived for static, free vibration, and buckling problems of nanobeams within MCST and the Euler‐Bernoulli beam theory. The effect of the material length scale parameter and geometry parameters on the static, vibration, and buckling responses of the nanobeam is investigated in both the classical beam theory (CBT) and MCST by using finite element method. Also, the difference between the classical beam theory (CBT) and modified couple stress theory is investigated

Hygro-Thermal Nonlinear Analysis of a Functionally Graded Beam

Nonlinear behavior of a functionally graded cantilever beam is analyzed under non-uniform hygro-thermal effect. To solve this problem, finite element method is applied within plane solid continua. Total Lagrangian approach is utilized in the nonlinear kinematic relations. Newton-Raphson method with incremental displacement is used in nonlinear solution. Comparison study is performed. Effects of material distribution, temperature and moisture changes on nonlinear deflections of the functionally graded beam are presented and discussed

Stability of A Non-Homogenous Porous Plate by Using Generalized Differantial Quadrature Method

This paper presents stability analysis of a non-homogeneous plate wit porosity effect. Material properties of the plate vary in the thickness direction and depend on the porosity. In the solution of the problem, the Generalized Differential Quadrature method is used. In the porosity model, uniform porosity distribution is considered. The effects of the porosity and material distribution parameters on the critical buckling of the non-homogeneous plate are investigated

Vibration and Static Analysis of Functionally Graded Porous Plates

This research deals with free vibration and static bending of a simply supported functionally graded (FG) plate with the porosity effect. Material properties of the plate which are related to its change are position-dependent. Governing equations of the FG plate are obtained by using the Hamilton’s principle within first-order shear deformation plate theory. In solving the problem, the Navier solution is also used. In this study, the effect of the porosity and material distribution parameters on the static and vibration responses of the FG plate is presented and discussed

Wave propagation analysis of edge cracked circular beams under impact force.

This paper presents responses of an edge circular cantilever beam under the effect of an impact force. The beam is excited by a transverse triangular force impulse modulated by a harmonic motion. The Kelvin-Voigt model for the material of the beam is used. The cracked beam is modelled as an assembly of two sub-beams connected through a massless elastic rotational spring. The considered problem is investigated within the Bernoulli-Euler beam theory by using energy based finite element method. The system of equations of motion is derived by using Lagrange's equations. The obtained system of linear differential equations is reduced to a linear algebraic equation system and solved in the time domain by using Newmark average acceleration method. In the study, the effects of the location of crack, the depth of the crack, on the characteristics of the reflected waves are investigated in detail. Also, the positions of the cracks are calculated by using reflected waves

Geometrically Nonlinear Static Analysis of Edge Cracked Timoshenko Beams Composed of Functionally Graded Material

Geometrically nonlinear static analysis of edge cracked cantilever Timoshenko beams composed of functionally graded material (FGM) subjected to a nonfollower transversal point load at the free end of the beam is studied with large displacements and large rotations. Material properties of the beam change in the height direction according to exponential distributions. The cracked beam is modeled as an assembly of two subbeams connected through a massless elastic rotational spring. In the study, the finite element of the beam is constructed by using the total Lagrangian Timoshenko beam element approximation. The nonlinear problem is solved by using incremental displacement-based finite element method in conjunction with Newton-Raphson iteration method. The convergence study is performed for various numbers of finite elements. In the study, the effects of the location of crack, the depth of the crack, and various material distributions on the nonlinear static response of the FGM beam are investigated in detail. Also, the difference between the geometrically linear and nonlinear analysis of edge cracked FGM beam is investigated in detail

Transverse displacement at the free end of the beam.

<p>a) Intact beam, b) <i>a/D</i> = 0.2, c) <i>a/D</i> = 0.3, d) <i>a/D</i> = 0.4, e) <i>a/D</i> = 0.6 and f) <i>a/D</i> = 0.8.</p

A circular beam with an open edge crack subjected to an impact force.

<p>A circular beam with an open edge crack subjected to an impact force.</p

The relationship between first non-dimensional natural frequency and the crack depth ratio for different crack locations.

<p>a) <i>L₁/L</i> = 0.2, b) <i>L₁/L</i> = 0.4.</p

The shape of the excitation impulse in the a) time domain and b) frequency domain [13].

<p>The shape of the excitation impulse in the a) time domain and b) frequency domain <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0100496#pone.0100496-Ostachowicz1" target="_blank">[13]</a>.</p