A higher-order nonlocal strain gradient mass sensor based on vibrating heterogeneous magneto-electro-elastic nanoplate via third-order shear deformation theory

2018 ◽  
Vol 133 (12) ◽  
Author(s):  
S. Ghahnavieh ◽  
Sh. Hosseini-Hashemi ◽  
K. Rajabi ◽  
S. Ghahnavieh
Keyword(s):  
Shear Deformation ◽  
Strain Gradient ◽  
Deformation Theory ◽  
Shear Deformation Theory ◽  
Higher Order ◽  
Mass Sensor ◽  
Third Order ◽  
Nonlocal Strain Gradient

A New Hyperbolic Two-Unknown Beam Model for Bending and Buckling Analysis of a Nonlocal Strain Gradient Nanobeams

2019 ◽  
Vol 57 ◽  
pp. 175-191 ◽  
Author(s):  
Wafa Adda Bedia ◽  
Mohammed Sid Ahmed Houari ◽  
Aicha Bessaim ◽  
Abdelmoumen Anis Bousahla ◽  
Abdelouahed Tounsi ◽  
...  
Keyword(s):  
Shear Deformation ◽  
Strain Gradient ◽  
Deformation Theory ◽  
Shear Deformation Theory ◽  
Beam Theory ◽  
Higher Order ◽  
Buckling Analysis ◽  
Strain Gradient Theory ◽  
Beam Model ◽  
Nonlocal Strain Gradient

In present paper, a novel two variable shear deformation beam theories are developed and applied to investigate the combined effects of nonlocal stress and strain gradient on the bending and buckling behaviors of nanobeams by using the nonlocal strain gradient theory. The advantage of this theory relies on its two-unknown displacement field as the Euler-Bernoulli beam theory, and it is capable of accurately capturing shear deformation effects, instead of three as in the well-known first shear deformation theory and higher-order shear deformation theory. A shear correction factor is, therefore, not needed. Equations of motion are obtained via Hamilton’s principle. Analytical solutions for the bending and buckling analysis are given for simply supported beams. Efficacy of the proposed model is shown through illustrative examples for bending buckling of nanobeams. The numerical results obtained are compared with those of other higher-order shear deformation beam theory. The results obtained are found to be accurate. Verification studies show that the proposed theory is not only accurate and simple in solving the bending and buckling behaviour of nanobeams, but also comparable with the other shear deformation theories which contain more number of unknowns

scholarly journals Third-Order Theory for the Bending Analysis of Laminated Thin and Thick Plates Including the Strain Gradient Effect

Materials ◽  
2021 ◽  
Vol 14 (7) ◽  
pp. 1771
Author(s):  
Michele Bacciocchi ◽  
Angelo Marcello Tarantino
Keyword(s):  
Shear Deformation ◽  
Strain Gradient ◽  
Deformation Theory ◽  
Plate Theory ◽  
Shear Deformation Theory ◽  
Laminated Composite ◽  
Composite Plates ◽  
Order Theory ◽  
Third Order ◽  
Starting Point

The aim of the paper is the development of a third-order theory for laminated composite plates that is able to accurately investigate their bending behavior in terms of displacements and stresses. The starting point is given by the corresponding Reddy’s Third-order Shear Deformation Theory (TSDT). This model is then generalized to consider simultaneously the Classical Laminated Plate Theory (CLPT), as well as the First-order Shear Deformation Theory (FSDT). The constitutive laws are modified according to the principles of the nonlocal strain gradient approach. The fundamental equations are solved analytically by means of the Navier methodology taking into account cross-ply and angle-ply lamination schemes. The numerical applications are presented to highlight the nonlocal effects on static behavior.

Two-Dimensional Electro-Elastic Analysis of FG-CNTRC Cylindrical Laminated Pressure Vessels With Piezoelectric Layers Based on Third-Order Shear Deformation Theory

2019 ◽  
Vol 142 (2) ◽  
Author(s):  
Masoud Mohammadi ◽  
Mohammad Arefi ◽  
Sara Amir Ahmadi
Keyword(s):  
Shear Deformation ◽  
Deformation Theory ◽  
Constitutive Relations ◽  
Shear Deformation Theory ◽  
Pressure Vessels ◽  
Higher Order ◽  
Functionally Graded ◽  
Numerical Results ◽  
Third Order ◽  
Piezoelectric Layers

Abstract The purpose of this paper is to show the electro-elastic static behavior of cylindrical sandwich pressure vessels integrated with piezoelectric layers. The core is made of functionally graded carbon nanotube-reinforced composite (FG-CNTRC). The cylinder is embedded between two piezoelectric layers made of PZT-4. The effective material properties of reinforced core with carbon nanotubes (CNTs) are calculated based on rule of mixture. The constitutive relations are developed in cylindrical coordinate system based on a higher-order shear deformation theory for both core and piezoelectric layers. The employed higher-order theory is based on third-order variation of deformations along the thickness direction to improve the accuracy of numerical results. The method of eigenvalue–eigenvector is used for solution of system of governing equations along the longitudinal direction. The numerical results are provided along the longitudinal and radial directions in terms of significant parameters such as various patterns of CNTs, various volume fractions of CNTs, various elastic foundation coefficients, and various applied electrical potentials.

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

A New Nonlinear Higher-Order Shear Deformation Theory for Nonlinear Vibrations of Laminated Shells

2010 ◽  
Author(s):  
M. Amabili ◽  
J. N. Reddy
Keyword(s):  
Shear Deformation ◽  
Deformation Theory ◽  
Nonlinear Vibrations ◽  
Circular Cylindrical Shell ◽  
Shear Deformation Theory ◽  
Higher Order ◽  
Curvilinear Coordinates ◽  
Geometrically Nonlinear ◽  
Geometric Imperfections ◽  
Laminated Shells

A consistent higher-order shear deformation nonlinear theory is developed for shells of generic shape; taking geometric imperfections into account. The geometrically nonlinear strain-displacement relationships are derived retaining full nonlinear terms in the in-plane displacements; they are presented in curvilinear coordinates in a formulation ready to be implemented. Then, large-amplitude forced vibrations of a simply supported, laminated circular cylindrical shell are studied (i) by using the developed theory, and (ii) keeping only nonlinear terms of the von Ka´rma´n type. Results show that inaccurate results are obtained by keeping only nonlinear terms of the von Ka´rma´n type for vibration amplitudes of about two times the shell thickness for the studied case.

Sign in / Sign up

Export Citation Format

Share Document