Bending, vibration and buckling of simply supported thick orthotropic rectangular plates and laminates

This paper presents a unified exact analysis for the statics and dynamics of a class of thick laminates. A three-dimensional, linear, small deformation theory of elasticity solution is developed for the bending, vibration and buckling of simply supported thick orthotropic rectangular plates and laminates. All the nine elastic constants of orthotropy are taken into account. The solution is formally exact and leads to simple infinite series for stresses and displacements in flexure, forced vibration and "beam-column" type problems and to closed form characteristic equations for free vibration and buckling problems. For free vibration of plates, the present analysis yields a triply infinite spectrum of frequencies instead of only one doubly infinite spectrum by thin plate theory or three doubly infinite spectra by Reissner-Mindlin type analyses. Some numerical results are presented for plates and laminates. Comparison of results from thin plate, Reissner and Mindlin analyses with these yield some important conclusions regarding the validity and effects of the assumptions made in the approximate theories.

An exact analysis for vibration of simply-supported homogeneous and laminated thick rectangular plates

A three-dimensional linear, small deformation theory of elasticity solution by the direct method is developed for the free vibration of simply-supported, homogeneous, isotropic, thick rectangular plates. The solution is exact and involves determining a triply infinite sequence of eigenvalues from a doubly infinite set of closed form transcendental equations. As no restrictions are placed on the thickness variation of stresses or displacements, this formulation yields a triply infinite spectrum of frequencies, instead of only one doubly infinite spectrum by thin plate theory and three doubly infinite spectra by Mindlin's thick plate theory. Further, the present analysis yields symmetric thickness modes which neither of the approximate theories can identify. Some numerical results from the two approximate theories are compared with those from the present solution and some important conclusions regarding the effect of the assumptions made in the approximate theories are drawn. The thickness variations of stresses and displacements are also discussed. The analysis is readily extended for laminated plates of isotropic materials. Numerical results are also given for three-ply laminates, and are used to assess the accuracy of thin plate theory predictions for laminates. Extension to general lateral surface conditions and forced vibrations is indicated.

Analysis of a thick plate with a circular hole resting on a smooth rigid bed and subjected to axisymmetric normal load

A solution for the stresses and displacements in an radially infinite thick plate having a circular hole, one face of which resting on a smooth rigid bed and the other face subjected to axisymmetric normal loading is given. The solution is obtained in terms of Fourier-Bessel series and integral for the Love's stress function. Numerical results are presented for one particular ratio of thickness of plate to the hole radius and loading. It is also shown that the Poisson's ratio has a predominant effect on certain stresses and displacements. The solution would be useful in the stress analysis of bolted joints.Eine Lösung für die Spannungen und Verschiebungen in einer radial, unendlich ausgedehnten, dicken Platte mit einem kreisförmigen Loch, wobei eine Seite auf einer ebenen, starren Unterlage aufliegt, die andere Seite durch eine achsensymmetrische Vertikallast belastet ist, wird angegeben. Die Lösung wird in Form von Fourier-Bessel-Reihen und Integralen der Loveschen Spannungsfunktion angegeben. Numerische Ergebnisse werden für ein bestimmtes Verhältnis der Plattendicke zum Lochradius sowie zur Belastung angegeben. Es wird auch gezeigt, daß das Poisssonsche Verhältnis einen besonderen Einfluß auf bestimmte Spannungen und Verschiebungen hat. Die Lösung ist anwendbar für die Spannungsermittlung von Bolzenverbindungen.

Dielectric properties of poly(vinylidene luoride)/CaCu3Ti4O12 nanocrystal composite thick films

The poly(vinylidene fluoride)/CaCu3Ti4O12 (CCTO) nanocrystal composite films (thickness approximate to 85 mu m) with relatively high dielectric permittivity (90 at 100 Hz) were prepared by the solution casting followed by spin coating technique. The structural, the microstructural and the dielectric properties of the composites were studied using X-ray diffraction, Scanning Electron Microscope, and Impedance analyzer respectively. The effective dielectric permittivity (e(eff)) of the composite increased with increase in the volume fraction of CCTO at all the frequencies (100 Hz to 1 MHz) under investigation. The room temperature dielectric permittivity which is around 90 at 100 Hz, has increased to about 290 at 125 degrees C (100 Hz). These results may be exploited in the development of high energy density capacitors.

Analysis of a long thick orthotropic circular cylindrical shell panel

An exact three-dimensional elasticity solution has been obtained for an infinitely long, thick transversely isotropic circular cylindrical shell panel, simply supported along the longitudinal edges and subjected to a radial patch load. Using a set of three displacement functions, the boundary value problem is reduced to Bessel's differential equation. Numerical results are presented for different thickness to mean radius ratios and semicentral angles of the shell panel. Classical and first-order shear deformation orthotropic shell theories have been examined in comparison with the present elasticity solution.

Superconducting YBa2Cu3O7-delta thick films on Ba2RETaO6 (RE=Pr, Nd, Eu, and Dy) substrates

Thick films of YBa2Cu3O7-delta fabricated on polycrystalline Ba2RETaO6 (where RE= Pr, Nd, Eu, and Dy) substrates by dip-coating and partial melting techniques are textured and c-axis oriented, showing predominantly (00l) orientation. All the thick films show a superconducting zero resistance transition of 90 K. SEM studies clearly indicate platelike and needlelike grain growth over a wide area of the thick films. The values of the critical current density for these thick films are similar to 10(4) A/cm(2) at 77 K as determined by the nonresonant R.F. absorption method. Various processing conditions that affect the critical current density of thick films are also discussed.

Protection against UVB inactivation (in vitro) of rat lens enzymes by natural antioxidants

Oxidative damage, through increased production of free radicals, is believed to be involved in UV-induced cataractogenesis (eye lens opacification). The possibility of UVB radiation causing damage to important lenticular enzymes was assessed by irradiating 3 months old rat lenses (in RPMI-1640 medium) at 300 nm (100 mu Wcm(-2)) for 24 h, in the absence and presence of ascorbic acid, alpha-tocopherol acetate and beta-carotene. UVB irradiation resulted in decreased activities of hexokinase, glucose-6-phosphate dehydrogenase, aldose reductase, and Na, K- ATPase by 42, 40, 44 and 57% respectively. While endopeptidase activity (229%) and lipid peroxidation (156%) were increased, isocitrate dehydrogenase activity was not altered on irradiation. In the presence of externally added ascorbic acid, tocopherol and beta-carotene (separately) to the medium, the changes in enzyme activities (except endopeptidase) and increased lipid peroxidation, due to UVB exposure, were prevented. These results suggest that UVB radiation exerts oxidative damage on lens enzymes and antioxidants were protective against this damage.

Synergistic effect of UVB radiation and age on HMPS enzymes in rat lens homogenate

The behaviour of rat lenticular enzymes, glucose-6-phosphate dehydrogena.se (G6PD, EC: 1.1.1.49) and 6-phosphogluconate dehydrogenase (6PGD, EC: 1.1.1.44) as a function of age and UVB irradiation (in vitro) was investigated by irradiating the lens homogenate from 3-and 12-month-old rats at 300 nm (100 μW cm 2). In the 3-month-old group the specific activities of G6PD and 6PGD were reduced by 26% and 42%, respectively, after 24 h of irradiation, whereas in the 12-month-old group the decrease was 38% and 49% respectively, which suggests that the susceptibility of HMPS enzymes to UVB damage is higher in older lenses. The decrease in specitic activity was associated with a change in apparent Km and Vmax (marginal in 3 months and significant in 12 months) of these enzymes due to UVB irradiation. UVB irradiation also decreased the levels of NADPH and NADPH/NADP ratio. These changes, altered activities of G6PD and 6PGD and altered levels of NADPH. may in turn have a bearing on lens transparency.

A waveguide problem involving a thick iris in the theory of electromagnetism

The problem of electromagnetic wave propagation in a rectangular waveguide containing a thick iris is considered for its complete solution by reducing it to two suitable integral equations, one of which is of the first kind and the other is of the second kind. These integral equations are solved approximately, by using truncated Fourier series for the unknown functions. The reflection coefficient is computed numerically from the two integral equation approaches, and almost the same numerical results are obtained. This is also depicted graphically against the wave number and compared with thin iris results, which are computed by using complementary formulations coupled with Galerkin approximations. While the reflection coefficient for a thin iris steadily increases with the wave number, for a thick iris it fluctuates and zero reflection occurs. The number of zeros of the reflection coefficient for a thick iris increases with the thickness. Thus a thick iris becomes completely transparent for some discrete wave numbers. This phenomenon may be significant in the modelling of rectangular waveguides.