Exact solution for simply supported multiferroic laminates with imperfect interfaces

2009 ◽  
Author(s):  
Yun-ying Zhou ◽  
Wei-qiu Chen ◽  
Chao-feng Lu
Keyword(s):  
Exact Solution ◽  
Simply Supported ◽  
Imperfect Interfaces

The Buckling of a Reinforced Circular Plate under Uniform Radial Thrust

1961 ◽  
Vol 12 (4) ◽  
pp. 337-342 ◽  
Author(s):  
I. T. Cook ◽  
H. W. Parsons
Keyword(s):  
Exact Solution ◽  
Circular Plate ◽  
Central Region ◽  
Clamped Plate ◽  
Simply Supported ◽  
Thin Circular Plate ◽  
Radial Thrust ◽  
Thickness Function

SummaryAn exact solution for the symmetrical buckling under uniform radial thrust is obtained for a thin circular plate having a particular type of thickness function for the cases in which the edge of the plate is either clamped or simply-supported. In both cases it is found that the critical thrust necessary to produce buckling can be increased from its value for the uniform circular plate of the same material and volume by concentrating material in the central region of the plate. For the clamped plate the increase is about 18 per cent and for the simply-supported plate about 29 per cent.

Cylindrical bending analysis of a layered two-dimensional piezoelectric quasicrystal nanoplate

2018 ◽  
Vol 29 (12) ◽  
pp. 2660-2676 ◽  
Author(s):  
Yang Li ◽  
Lianzhi Yang ◽  
Yang Gao ◽  
Ernian Pan
Keyword(s):  
Exact Solution ◽  
Piezoelectric Effect ◽  
Nonlocal Parameter ◽  
Nonlocal Theory ◽  
Stacking Sequence ◽  
Two Dimensional ◽  
Cylindrical Bending ◽  
Simply Supported ◽  
Propagator Matrix ◽  
Numerical Modeling And Simulation

The piezoelectric effect is a significant property of quasicrystal. In this article, the exact solution is derived for a layered piezoelectric quasicrystal nanoplate with nonlocal effect in cylindrical bending. Based on the nonlocal theory and the pseudo-Stroh formalism, the exact solution for a homogeneous simply supported nanoplate is obtained. With the aid of the propagator matrix, the exact solution for a multilayered nanoplate is achieved. Numerical examples are carried out to reveal the influences of span-to-thickness ratio, nonlocal parameter, and stacking sequence on piezoelectric quasicrystal nanoplates with their top surface subjected to two loadings. One is a z-direction mechanical loading and the other is an electric potential loading. These results can be served as benchmarks for the design, numerical modeling, and simulation of layered two-dimensional piezoelectric quasicrystal nanoplates under cylindrical bending.

Static Analysis of Thick Laminated Circular Cylindrical Shells

1993 ◽  
Vol 115 (2) ◽  
pp. 193-200 ◽  
Author(s):  
K. Chandrashekhara ◽  
B. S. Kumar
Keyword(s):  
Exact Solution ◽  
Cylindrical Shell ◽  
Approximate Solution ◽  
Circular Cylindrical Shell ◽  
Simply Supported ◽  
Hybrid Laminates ◽  
Shell Panel ◽  
Circular Cylindrical Shells ◽  
Shear Deformation Theories ◽  
Asymmetric Load

An approximate solution for a thick laminated simply supported circular cylindrical shell of revolution and shell panel subjected to asymmetric load has been obtained using elasticity approach. The results obtained from this analysis have been compared with the exact solution. Numerical results have been presented for 3-ply hybrid laminates and (0/90/0) laminates subjected to patch loads. The results have also been compared with some available classical and shear deformation theories to assess the accuracy of these theories.

Transient responses of laminated anisotropic piezothermoelastic plates and cylindrical shells with interfacial diffusion and sliding in cylindrical bending

2018 ◽  
Vol 24 (4) ◽  
pp. 1065-1090 ◽  
Author(s):  
Xu Wang
Keyword(s):  
Exact Solution ◽  
State Space ◽  
Relaxation Times ◽  
The State ◽  
Laminated Plate ◽  
Interfacial Diffusion ◽  
Cylindrical Bending ◽  
Simply Supported ◽  
Elegant Method ◽  
Space Equation

With aid of the Stroh-type formalism and the state-space approach, a simple and elegant method is presented to obtain an exact solution for the time-dependent problem of a simply-supported laminated anisotropic piezothermoelastic plate in cylindrical bending with interfacial diffusion and sliding. The Stroh-type formalism is used to obtain the general solution of the thermoelectroelastic field in a certain layer. The state-space equation is then constructed for a laminated plate. The relaxation times and the transient thermoelectroelastic response of the laminated plate can be determined by solving the state-space equation via an analysis of a generalized eigenvalue problem. By using a similar method, we also derive an exact solution for a simply-supported laminated anisotropic piezothermoelastic cylindrical shell with interfacial diffusion and sliding under cylindrical bending.

Exact Solution of Thermoelastic Damping and Frequency Shifts in a Nano-Beam Resonator

2015 ◽  
Vol 15 (06) ◽  
pp. 1450082 ◽  
Author(s):  
Ibrahim A. Abbas
Keyword(s):  
Exact Solution ◽  
Natural Frequencies ◽  
Thermoelastic Damping ◽  
Frequency Shifts ◽  
Beam Resonator ◽  
Simply Supported ◽  
Thermoelastic Vibration ◽  
Modes Of Vibration ◽  
Generalized Thermoelastic ◽  
Analytical Expressions

In this study, we consider the problem of a generalized thermoelastic vibration of a bounded nano-beam resonator in the context of Green and Naghdi theory (GNIII). The first four modes of vibration in the nano-beam resonator are investigated for the beam under clamped and simply supported conditions. Analytical expressions for the deflection, temperature change, frequency shifts, and thermoelastic damping in the beam are derived. The numerical results have been presented graphically in respect of natural frequencies, thermoelastic damping and frequency shift.

Exact analysis of simply supported rhombic plates under uniform pressure

1974 ◽  
Vol 76 (1) ◽  
pp. 381-388 ◽  
Author(s):  
K. Rajaiah ◽  
Akella Kameswara Rao
Keyword(s):  
Exact Solution ◽  
Complex Variables ◽  
Transverse Load ◽  
Uniform Pressure ◽  
Approximate Methods ◽  
Simply Supported ◽  
Series Form ◽  
Exact Analysis ◽  
Present Solution

AbstractThe simply supported rhombic plate under transverse load has received extensive attention from elasticians, applied mathematicians and engineers. All known solutions are based on approximate procedures. Now, an exact solution in a fast converging explicit series form is derived for this problem, by applying Stevenson's tentative approach with complex variables. Numerical values for the central deflexion and moments are obtained for various corner angles. The present solution provides a basis for assessing the accuracy of approximate methods for analysing problems of skew plates or domains.

scholarly journals Buckling of double-walled carbon nanotubes

2012 ◽  
Vol 34 (4) ◽  
pp. 217-224 ◽  
Author(s):  
Isaac Elishakoff ◽  
Kévin Dujat ◽  
Maurice Lemaire
Keyword(s):  
Carbon Nanotubes ◽  
Exact Solution ◽  
Approximate Solution ◽  
Carbon Nanotube ◽  
Finite Difference ◽  
Finite Difference Method ◽  
Simply Supported ◽  
The Finite Difference Method ◽  
Double Walled Carbon Nanotubes ◽  
Walled Carbon Nanotubes

In this note we deal with the approximate solution of the buckling problem of a clamped-free double-walled carbon nanotube. First the finite difference method is utilized to solve this case. Then this approach is verified by solving the buckling problem of a double-walled carbon nanotube that is simply supported at both ends for which the exact solution is available.

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