Equilibrium of transversely isotropic FGM plates with an elliptical hole: 3D elasticity solutions

2016 ◽  
Vol 86 (8) ◽  
pp. 1391-1414 ◽  
Author(s):  
B. Yang ◽  
W. Q. Chen ◽  
H. J. Ding
Keyword(s):  
Elliptical Hole ◽  
Transversely Isotropic ◽  
Elasticity Solutions ◽  
3D Elasticity

Extensional Waves in a Sandwich Plate With Interface Slip

2015 ◽  
Vol 137 (3) ◽  
Author(s):  
Peng Li ◽  
Feng Jin ◽  
Weiqiu Chen ◽  
Jiashi Yang
Keyword(s):  
Sandwich Plate ◽  
Collective Motion ◽  
Three Dimensional ◽  
Elastic Plates ◽  
Plate Equations ◽  
Elasticity Solutions ◽  
Interface Elasticity ◽  
Shear Motion ◽  
3D Elasticity ◽  
The Individual

The two-dimensional (2D) equations for thin elastic plates are used to study extensional motions of a sandwich plate with weak interfaces. The interfaces are governed by the shear-slip model that possesses interface elasticity and allows for a discontinuity of the tangential displacements at the interfaces. Equations for the individual layers of the sandwich plate are coupled by the interface conditions. Through a procedure initiated by Mindlin, the layer equations can be written into equations for the collective motion of the layers representing the extensional motion of the sandwich plate, and equations for the relative motions of the layers with respect to each other representing the symmetric thickness-shear motion of the sandwich plate. The use of plate equations results in relatively simpler models compared to the equations of three-dimensional (3D) elasticity. Solutions to a few useful problems are presented. These include the propagation of straight-crested waves in an unbounded plate with weak interfaces, the reflection of extensional waves at the joint between a perfectly bonded sandwich plate and a sandwich plate with weak interfaces, and the vibration of a finite sandwich plate with weak interfaces.

Plane Electromechanical Fields in a Piezoelectric Material Containing an Elliptical Hole

2008 ◽  
Vol 33-37 ◽  
pp. 539-544
Author(s):  
Yan Liang Du ◽  
Shu Hong Liu ◽  
Shi Jie Duan ◽  
Yan Qiang Li
Keyword(s):  
Boundary Conditions ◽  
Piezoelectric Material ◽  
Electric Displacement ◽  
Elliptical Hole ◽  
Transversely Isotropic ◽  
Complex Potentials ◽  
Two Dimensional ◽  
Displacement Fields ◽  
Transversely Isotropic Piezoelectric Material

A two-dimensional electromechanical analysis is performed on a transversely isotropic piezoelectric material containing an elliptical hole, which is subjected to uniform compressive forces with intensity q acting on the edge of the hole and uniform electric displacement fields at infinity. Based on the impermeable electric boundary conditions, general electromechanical fields solution are obtained in the form of complex potentials.

Wrinkled and slack membranes: nonlinear 3D elasticity solutions via smooth DMS-FEM and experiment

2012 ◽  
Vol 90 (10) ◽  
pp. 1233-1260
Author(s):  
N. Sunilkumar ◽  
G. Lalmoni ◽  
D. Roy ◽  
S. R. Reid ◽  
R. M. Vasu
Keyword(s):  
Elasticity Solutions ◽  
3D Elasticity

Stress Distribution in a Piezoelectric Material with an Elliptical Hole Subjected to Remote Uniform Shear Mechanical and Electric Loads

2010 ◽  
Vol 97-101 ◽  
pp. 956-959
Author(s):  
Min Juan Zhou ◽  
Shi Jie Duan ◽  
Yan Ping Kong ◽  
Shu Hong Liu
Keyword(s):  
Electric Field ◽  
Piezoelectric Material ◽  
Elliptical Hole ◽  
Transversely Isotropic ◽  
Shielding Effect ◽  
Stress Distributions ◽  
Uniform Shear ◽  
Sharp Stress ◽  
Close Form ◽  
Electric Loads

A two-dimensional electro-elastic analysis is performed on a transversely isotropic piezoelectric material with an elliptical hole, which is subjected to remote uniform shear forces, and remote electric field. Based on the impermeable electric boundary conditions, close form solutions are obtained by using the complex potentials method. Taking PZT-4 ceramic into consideration, the stress distributions around the neighborhood of the elliptical hole are given. It is shown that the hole geometry and the electric field are responsible for the shielding effect, there are sharp stress concentration near the hole.

Radial Deformation of Cylinders Due to Torsion

2012 ◽  
Vol 79 (6) ◽  
Author(s):  
Srikant Sekhar Padhee ◽  
Dineshkumar Harursampath
Keyword(s):  
Isotropic Material ◽  
Ad Hoc ◽  
Solid Mechanics ◽  
Transversely Isotropic ◽  
Analytic Solutions ◽  
Radial Deformation ◽  
Classical Literature ◽  
Cross Sectional ◽  
Closed Form Solutions ◽  
3D Elasticity

Classical literature on solid mechanics claims existence of radial deformation due to torsion but there is hardly any literature on analytic solutions capturing this phenomenon. This paper tries to solve this problem in an asymptotic sense using the variational asymptotic method (VAM). The method makes no ad hoc assumptions and hence asymptotic correctness is assured. The VAM splits the 3D elasticity problem into two parts: A 1D problem along the length of the cylinder which gives the twist and a 2D cross-sectional problem which gives the radial deformation. This enables closed form solutions, even for some complex problems. Starting with a hollow cylinder, made up of orthotropic but transversely isotropic material, the 3D problem has been formulated and solved analytically despite the presence of geometric nonlinearity. The general results have been specialized for particularly useful cases, such as solid cylinders and/or cylinders with isotropic material.

A Higher Order Theory for Bending of Cross Ply Laminated Cylindrical Shell under Hygrothermal Loads

2015 ◽  
Vol 1115 ◽  
pp. 509-512 ◽  
Author(s):  
J.S. Mohamed Ali ◽  
Saleh Alsubari ◽  
Yulfian Aminanda
Keyword(s):  
Shear Deformation ◽  
Deformation Theory ◽  
Shear Deformation Theory ◽  
Order Theory ◽  
Higher Order ◽  
Graphical Form ◽  
Laminated Shells ◽  
Elasticity Solutions ◽  
3D Elasticity ◽  
Higher Order Theory

The combined effect of moisture and temperature on the bending behaviour of simply supported cross ply composite laminated shells has been investigated. A 13 term accurate higher order shear deformation theory with zigzag function is used in this analysis in which the effects of transverse shear deformation are taken into account. The results are presented for thermal load cases are validated against available 3D elasticity solutions in the literature and useful results for combined hygrothermal loading are presented in tabular and graphical form.

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