Analytical Solution for Buckling Behavior of FGM Plate Considering Surface Effect Based on General Third-Order Plate Theory and Non-local Theory

2020 ◽  
Vol 20 (11) ◽  
pp. 2050125
Author(s):  
J. R. Zhong
Keyword(s):  
Surface Effect ◽  
Plate Theory ◽  
Plate Thickness ◽  
Surface Elasticity ◽  
Local Theory ◽  
Solution Technique ◽  
Surface Residual Stress ◽  
Third Order ◽  
Stress Surface ◽  
Non Local

In this paper, the buckling characteristic of FGM plate considering the surface effect is studied based on general third-order plate theory and non-local theory. The surface effect of FGM plate is captured by the surface elasticity theory. The Kirchhoff hypothesis is released by employing parabolic variation of transverse shear strains. By using Navier solution technique, analytical solutions of buckling loads of FGM plate with surface effect are given, and detailed parametric studies are presented to show the relationship between surface effects and the plate thickness, power-law index, surface residual stress, surface moduli and non-local parameter. Furthermore, the surface effect on the buckling characteristic of FGM plate is also discussed.

Surface Effects on Large Deflection of Nanobeams Subjected to a Follower Load

2020 ◽  
Vol 12 (06) ◽  
pp. 2050067
Author(s):  
Yun Xing ◽  
Yi Han ◽  
Hua Liu ◽  
Jialing Yang
Keyword(s):  
Large Deformation ◽  
Surface Stress ◽  
Large Deflection ◽  
Surface Effect ◽  
Surface Elasticity ◽  
Surface Effects ◽  
Surface Residual Stress ◽  
Residual Surface Stress ◽  
Deformation Problem ◽  
Cross Sectional Dimension

As a basic element of the micro/nanodevices, nanobeams have remarkable physical properties and have attracted considerable attention in the previous studies. However, previous publications did not study the large deformation problem of nanobeams under follower loading when the surface effect becomes significant and especially for the influence of surface effect on mechanical behaviors of the nanobeams under follower loading remains unclear. In this paper, we investigated the large deformation behavior of nanobeams subjected to follower loads in consideration of the surface effects. The mechanical model of large deflection of extensible cantilever nanobeams under follower loading is presented in combination with the surface elasticity and residual surface stress, and then a MATLAB program of shooting method with a technique for determining the initial value was developed to solve the problems. The results indicate that the surface effects have an important influence on the large deflection of nanobeams under follower loading: when the surface residual stress is positive, the maximums of displacement in horizontal and vertical directions and the rotation angle of the free end become lager, but the corresponding follower force related to those maximums becomes smaller. When the residual surface stress is negative, the results are the opposite. In addition, the influence of the cross-sectional dimension of the nanobeams under follower loading on surface effects was discussed. This work is beneficial to understand the mechanism of large deformation of nanobeams with surface effects subjected to follower loads, and can also provide inspirations to design advanced nanomaterials and nanoscaled devices.

Non-linear vibration analysis of specially orthotropic tapered micro-plates with arbitrary located crack: A non-classical analytical approach

2021 ◽  
pp. 095440622110197
Author(s):  
Bhupesh K Chandrakar ◽  
NK Jain ◽  
Ankur Gupta
Keyword(s):  
Governing Equation ◽  
Orthotropic Plate ◽  
Multiple Scales ◽  
Plate Theory ◽  
Couple Stress Theory ◽  
Plate Thickness ◽  
Solution Technique ◽  
Classical Plate Theory ◽  
Non Linear ◽  
The Impact

The present work aims to study the non-linear vibrations in a cracked orthotropic tapered micro-plate. Linear and parabolic variation in the plate thickness is assumed in one as well as two directions. The partial crack is located in the centre, and it is continuous; this crack’s location is arbitrary and can be varied within the centre-line. Based on classical plate theory, the equilibrium principle is applied, and the governing equation of tapered orthotropic plate is derived. Additionally, the microstructure’s effect has been included in the governing equation using the non-classical modified couple stress theory. The simplified line spring model is used to consider the impact of partial crack on the plate dynamics and is incorporated using in-plane forces and bending moments. The introduction of Berger’s formulation brings the non-linearity in the model in terms of in-plane forces. Here, Galerkin’s method has been chosen for converting the derived governing equation into time-dependent modal coordinates, which uses an approximate solution technique to solve the non-linear Duffing equation. The crack is considered along the fibres and across the fibres to show the effect of orthotropy. Results are presented for an orthotropic cracked plate with non-uniform thickness. The effects of the variation of taper constants, crack location, crack length, internal material length scale parameter on the fundamental frequency are obtained for two different boundary conditions. The non-linear frequency response curves are plotted to show the effect of non-linearity on the system dynamics using the method of multiple scales, and the contribution of taper constants and crack parameters on non-linearity is shown with bending-hardening and bending-softening phenomenon. It has been found that vibration characteristics are affected by the taper parameters and fibre direction for a cracked orthotropic plate.

Transient Response of a Circular Nanoplate Subjected to Low Velocity Impact

2017 ◽  
Vol 09 (08) ◽  
pp. 1750114 ◽  
Author(s):  
Jie Liu ◽  
Hua Liu ◽  
Jia-Ling Yang ◽  
Xi-Qiao Feng
Keyword(s):  
Transient Response ◽  
Plate Theory ◽  
Surface Elasticity ◽  
Expansion Method ◽  
Surface Effects ◽  
Dynamic Responses ◽  
Low Velocity Impact ◽  
Low Velocity ◽  
Surface Residual Stress ◽  
Impact Problems

The transient response of a circular nanoplate subjected to the normal impact by a nanosphere (e.g., C[Formula: see text]) is investigated theoretically. The nanoplate is modeled by the Kirchhoff thin plate theory. Gurtin–Murdoch’s theory is employed to account for the surface effects of the nanoplate with surface elasticity and surface residual stress. The van der Waals interaction between the nanosphere and the nanoplate is also taken into account. The governing equations for the vibration of the nanoplate impinged by a rigid nanosphere are established by using the Hamilton’s principle. The displacement field in the circular nanoplate is obtained by using the Fourier–Bessel expansion method. We reveal some physical mechanisms in the nanoimpact problem that are different from those in macroscopic impact problems, and surface effects have pronounced influences on the dynamic responses of a plate when its thickness shrinks to a few nanometers.

Elastic Analysis of Carbon Nanotube-Reinforced Composite Plates with Piezoelectric Layers Using Shear Deformation Theory

2017 ◽  
Vol 09 (01) ◽  
pp. 1750011 ◽  
Author(s):  
Mohammad Zamani Nejad ◽  
Tahereh Taghizadeh ◽  
Saeed Jafari Mehrabadi ◽  
Saeed Herasati
Keyword(s):  
Carbon Nanotube ◽  
Shear Deformation ◽  
Volume Fraction ◽  
Plate Theory ◽  
Plate Thickness ◽  
Composite Plates ◽  
Third Order ◽  
Reinforced Composite ◽  
Shear Deformation Plate Theory ◽  
Piezoelectric Layers

This paper investigates the deflection and stress behavior of composite plates reinforced by single-walled carbon nanotubes (SWCNTs) with piezoelectric layers which are under transverse mechanical load. Two kinds of carbon nanotube-reinforced composite (CNTRC) plates, namely uniformly distributed (UD) and functionally graded (FG) along the plate thickness, are considered. The extended rule of mixture approach is used to estimate the effective material properties. The governing equations are derived using the Hamilton approach based on the first-order shear deformation plate theory (FSDT) and third-order shear deformation plate theory (TSDT). In addition, the Navier technique is employed to obtain the deflection and stress response of the nanocomposite plates. The results of present work are also compared with those available in the literature and show good agreement. The effects of applied force, volume fraction of CNT, distribution of CNT, thickness of piezoelectric layer, thickness to width ratio and aspect ratio on the static behavior are studied. In previous studies, deflection and stress analysis of nanocomposite plate with piezoelectric layers based on third-order shear deformation plate theory has not investigated.

Using phase field and third-order shear deformation theory to study the effect of cracks on free vibration of rectangular plates with varying thickness

2020 ◽  
Vol 71 (7) ◽  
pp. 853-867
Author(s):  
Phuc Pham Minh
Keyword(s):  
Free Vibration ◽  
Shear Deformation ◽  
Phase Field ◽  
Deformation Theory ◽  
Plate Thickness ◽  
Shear Deformation Theory ◽  
Rectangular Plates ◽  
Equilibrium Equations ◽  
Third Order ◽  
Free Vibration Frequency

The paper researches the free vibration of a rectangular plate with one or more cracks. The plate thickness varies along the x-axis with linear rules. Using Shi's third-order shear deformation theory and phase field theory to set up the equilibrium equations, which are solved by finite element methods. The frequency of free vibration plates is calculated and compared with the published articles, the agreement between the results is good. Then, the paper will examine the free vibration frequency of plate depending on the change of the plate thickness ratio, the length of cracks, the number of cracks, the location of cracks and different boundary conditions

scholarly journals Perturbative linearization of super-Yang-Mills theories in general gauges

2021 ◽  
Vol 2021 (6) ◽  
Author(s):  
Hannes Malcha ◽  
Hermann Nicolai
Keyword(s):  
Large Class ◽  
Fourth Order ◽  
Landau Gauge ◽  
Third Order ◽  
Yang Mills ◽  
Free Theory ◽  
Non Linear ◽  
Functional Measure ◽  
Non Local ◽  
Jacobi Determinant

Abstract Supersymmetric Yang-Mills theories can be characterized by a non-local and non-linear transformation of the bosonic fields (Nicolai map) mapping the interacting functional measure to that of a free theory, such that the Jacobi determinant of the transformation equals the product of the fermionic determinants obtained by integrating out the gauginos and ghosts at least on the gauge hypersurface. While this transformation has been known so far only for the Landau gauge and to third order in the Yang-Mills coupling, we here extend the construction to a large class of (possibly non-linear and non-local) gauges, and exhibit the conditions for all statements to remain valid off the gauge hypersurface. Finally, we present explicit results to second order in the axial gauge and to fourth order in the Landau gauge.

scholarly journals Antiplane–inplane shear mode delamination between two second-order shear deformable composite plates

2016 ◽  
Vol 22 (3) ◽  
pp. 259-282 ◽  
Author(s):  
András Szekrényes
Keyword(s):  
Plate Theory ◽  
Plate Thickness ◽  
State Space Model ◽  
Boundary Surface ◽  
Plate Boundary ◽  
Composite Plates ◽  
Second Order ◽  
Shear Mode ◽  
Mode Iii ◽  
Double Plate System

The second-order laminated plate theory is utilized in this work to analyze orthotropic composite plates with asymmetric delamination. First, a displacement field satisfying the system of exact kinematic conditions is presented by developing a double-plate system in the uncracked plate portion. The basic equations of linear elasticity and Hamilton’s principle are utilized to derive the system of equilibrium and governing equations. As an example, a delaminated simply supported plate is analyzed using Lévy plate formulation and the state-space model by varying the position of the delamination along the plate thickness. The displacements, strains, stresses and the J-integral are calculated by the plate theory solution and compared with those by linear finite-element calculations. The comparison of the numerical and analytical results shows that the second-order plate theory captures very well the mechanical fields. However, if the delamination is separated by only a relatively thin layer from the plate boundary surface, then the second-order plate theory approximates badly the stress resultants and so the mode-II and mode-III J-integrals and thus leads to erroneous results.

Nonlinear Oscillations of a Composite Laminated Plate with Parametrically and Externally Excitations

2013 ◽  
Vol 699 ◽  
pp. 641-644
Author(s):  
Xiao Li Bian ◽  
Shuang Bao Li
Keyword(s):  
Thin Plate ◽  
Nonlinear Oscillations ◽  
Plate Theory ◽  
Laminated Plate ◽  
Rectangular Thin Plate ◽  
Third Order ◽  
Composite Laminated Plate ◽  
Strain Relationship ◽  
Relationship Of ◽  
Equations Of Motions

Nonlinear oscillations of a simply-supported symmetric cross-ply composite laminated rectangular thin plate are investigated in this paper. The rectangular thin plate is subjected to the transversal and in-plane excitations. Based on the Reddy’s third-order shear deformation plate theory and the stress-strain relationship of the composite laminated plate, a two-degree-of-freedom non-autonomous nonlinear system governing equations of motions for the composite laminated rectangular thin plate is derived by using the Galerkin’s method. Numerical simulations illustrate that there exist complex nonlinear oscillations for composite laminated rectangular thin plate.

scholarly journals Non-Local Buckling Analysis of Functionally Graded Nanoporous Metal Foam Nanoplates

Coatings ◽  
2018 ◽  
Vol 8 (11) ◽  
pp. 389 ◽  
Author(s):  
Yanqing Wang ◽  
Zhiyuan Zhang
Keyword(s):  
Metal Foam ◽  
Plate Theory ◽  
Constitutive Relations ◽  
Equations Of Motion ◽  
Local Buckling ◽  
Functionally Graded ◽  
Small Scale ◽  
Refined Plate Theory ◽  
Nanoporous Metal ◽  
Non Local

In this study, the buckling of functionally graded (FG) nanoporous metal foam nanoplates is investigated by combining the refined plate theory with the non-local elasticity theory. The refined plate theory takes into account transverse shear strains which vary quadratically through the thickness without considering the shear correction factor. Based on Eringen’s non-local differential constitutive relations, the equations of motion are derived from Hamilton’s principle. The analytical solutions for the buckling of FG nanoporous metal foam nanoplates are obtained via Navier’s method. Moreover, the effects of porosity distributions, porosity coefficient, small scale parameter, axial compression ratio, mode number, aspect ratio and length-to-thickness ratio on the buckling loads are discussed. In order to verify the validity of present analysis, the analytical results have been compared with other previous studies.

Sign in / Sign up

Export Citation Format

Share Document