An Exact Three-Dimensional Solution for Simply Supported Rectangular Piezoelectric Plates

1996 ◽  
Vol 63 (3) ◽  
pp. 628-638 ◽  
Author(s):  
P. Bisegna ◽  
F. Maceri
Keyword(s):  
Isotropic Material ◽  
Piezoelectric Plate ◽  
Plate Thickness ◽  
Three Dimensional ◽  
Transversely Isotropic ◽  
Transversely Isotropic Material ◽  
Reference Case ◽  
Dimensional Solution ◽  
Simply Supported ◽  
Side Ratio

An exact three-dimensional solution for the problem of a simply supported rectangular homogeneous piezoelectric plate is obtained, in the framework of the linear theory of piezoelectricity. The plate is made of a transversely isotropic material, is earthed on the lateral boundary, and is subjected to prescribed surface charge and tractions on the end faces. The limit of this solution as the plate thickness aspect ratio approaches zero is explicitly carried out. The analytical results obtained may constitute a reference case when developing or applying two-dimensional plate theories for the analysis of more complex piezoelectric problems. A numerical investigation in the case of a square uniformly loaded plate is also performed, in order to evaluate the influence of the thickness-to-side ratio on the three-dimensional solution of the plate problem.

Stress Analysis and Failure Prediction in the Proximal Femur Before and After Total Hip Replacement

1986 ◽  
Vol 108 (1) ◽  
pp. 33-41 ◽  
Author(s):  
H. H. Vichnin ◽  
S. C. Batterman
Keyword(s):  
Bone Cement ◽  
Material Properties ◽  
Isotropic Material ◽  
Three Dimensional ◽  
Transversely Isotropic ◽  
Transversely Isotropic Material ◽  
Experimental Conditions ◽  
Failure Data ◽  
Cement Prosthesis ◽  
Failure Loads

An investigation was performed to determine the effects of the presence of two lengths of proximal Mu¨ller prosthesis on predicted failure loads, as compared to those for an intact femur. Three-dimensional stresses in a bone/cement/prosthesis system were determined using finite element methods, with both isotropic and transversely isotropic material properties used for the diaphyseal cortex. Significant increases in prosthesis stem stresses were found when the transversely isotropic material properties were employed in the diaphyseal cortex. This leads to the conclusion that accurate anisotropic material properties for bone are essential for precise stress determination and optimum design in prosthetic implants. Failure loads were also predicted for vertical compression and axial torque, similar to available experimental conditions, and were within the range of the experimental failure data found in the literature. The technique developed herein can be used to systematically assess existing as well as future implant designs, taking into account the complex three-dimensional interaction effects of the overall bone/cement/prosthesis system.

THE ANALYSIS OF DYNAMICAL RESPONSE OF TRANSVERSELY ISOTROPIC MATERIAL UNDER BLASTING LOAD

2008 ◽  
Vol 22 (09n11) ◽  
pp. 1443-1448
Author(s):  
YUE-XIU WU ◽  
QUAN-SHENG LIU
Keyword(s):  
Isotropic Material ◽  
Peak Velocity ◽  
Transversely Isotropic ◽  
Normal Direction ◽  
Dynamical Response ◽  
Transversely Isotropic Material ◽  
Peak Acceleration ◽  
Loading Direction ◽  
Blasting Load ◽  
Explosion Load

To understand the dynamic response of transversely isotropic material under explosion load, the analysis is done with the help of ABAQUS software and the constitutive equations of transversely isotropic material with different angle of isotropic section. The result is given: when the angle of isotropic section is settled, the velocity and acceleration of measure points decrease with the increasing distance from the explosion borehole. The velocity and acceleration in the loading direction are larger than those in the normal direction of the loading direction and their attenuation are much faster. When the angle of isotropic section is variable, the evolution curves of peak velocity and peak acceleration in the loading direction with the increasing angles are notching parabolic curves. They get their minimum values when the angle is equal to 45 degree. But the evolution curves of peak velocity and peak acceleration in the normal direction of the loading direction with the increasing angles are overhead parabolic curves. They get their maximum values when the angle is equal to 45 degree.

scholarly journals Elastic-plastic transition stresses in a transversely isotropic thick-walled cylinder subjected to internal pressure and steady-state temperature

2009 ◽  
Vol 13 (4) ◽  
pp. 107-118 ◽  
Author(s):  
Thakur Pankaj
Keyword(s):  
Steady State ◽  
Internal Pressure ◽  
Isotropic Material ◽  
Internal Surface ◽  
Transversely Isotropic ◽  
Percentage Increase ◽  
Transversely Isotropic Material ◽  
Elastic Plastic ◽  
Steady State Temperature ◽  
Walled Cylinder

Elastic-plastic transitional stresses in a transversely isotropic thick-walled cylinder subjected to internal pressure and steady-state temperature have been derived by using Seth's transition theory. The combined effects of pressure and temperature has been presented graphically and discussed. It has been observed that at room temperature, thick-walled cylinder made of isotropic material yields at a high pressure at the internal surface as compared to cylinder made of transversely isotropic material. With the introduction of thermal effects isotropic/transversely isotropic cylinder yields at a lower pressure whereas cylinder made of isotropic material requires less percentage increase in pressure to become fully-plastic from its initial yielding as compared to cylinder made of transversely isotropic material.

scholarly journals Three Dimensional Static Solution of Simply Supported Single Layer Piezoelectric Plate

2016 ◽  
Vol 82 (4) ◽  
Author(s):  
Sandeep S. Pendhari ◽  
Sameer S. Sawarkar ◽  
Yogesh M. Desai ◽  
Nilesh Patil
Keyword(s):  
Piezoelectric Plate ◽  
Three Dimensional ◽  
Single Layer ◽  
Static Solution ◽  
Simply Supported

An Analytical Solution for Transversely Isotropic Simply Supported Thick Rectangular Plates Using Displacement Potential Functions

2011 ◽  
Vol 46 (2) ◽  
pp. 121-142 ◽  
Author(s):  
M Nematzadeh ◽  
M Eskandari-Ghadi ◽  
B Navayi Neya
Keyword(s):  
Isotropic Material ◽  
Transversely Isotropic ◽  
Numerical Results ◽  
Potential Functions ◽  
Constant Thickness ◽  
Rectangular Plates ◽  
Displacement Potential ◽  
Simply Supported ◽  
Axial Forces ◽  
Internal Forces

Using a complete set of displacement potential functions, the exact solution of three-dimensional elasticity equations of a simply supported rectangular plates with constant thickness consisting of a transversely isotropic linearly elastic material subjected to an arbitrary static load is presented. The governing partial differential equations for the potential functions are solved through the use of the Fourier method, which results in exponential and trigonometric expression along the plate thickness and the other two lengths respectively. The displacements, stresses, and internal forces are determined through the potential functions at any point of the body. To prove the validity of this approach, the analytical solutions developed in this paper are degenerated for the simpler case of plates containing isotropic material and compared with the existing solution. In addition, the numerical results obtained from this study are compared with those reported in other researches for the isotropic material, where excellent agreement is achieved for both thin and thick plates. The results show that increasing the thickness ratios of the plate causes compressive axial forces and central shear forces inside the plate. Finally, the internal forces and displacement components are calculated numerically for several kinds of transversely isotropic materials with different anisotropies and are compared with a finite element (FE) solution obtained from the ANSYS software, where the high accuracy of the present method is demonstrated. The effects of the material anisotropy are clearly revealed in the numerical results presented.

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