New Look at Kirchhoff's Theory of Plates

KIRCHHOFF’S theory [1] and the first-order shear deformation theory (FSDT) [2] of plates in bending are simple theories and continuously used to obtain design information. Within the classical small deformation theory of elasticity, the problem consists of determining three displacements, u, v, and w, that satisfy three equilibrium equations in the interior of the plate and three specified surface conditions. FSDT is a sixth-order theory with a provision to satisfy three edge conditions and maintains, unlike in Kirchhoff’s theory, independent linear thicknesswise distribution of tangential displacement even if the lateral deflection, w, is zero along a supported edge. However, each of the in-plane distributions of the transverse shear stresses that are of a lower order is expressed as a sum of higher-order displacement terms. Kirchhoff’s assumption of zero transverse shear strains is, however, not a limitation of the theory as a first approximation to the exact 3-D solution.

Fasteners in Composite Plates - Effects of Interfacial Friction

The effects of tangential friction at pin—hole interfaces are appropriately modelled for the analysis of fasteners in large composite (orthotropic) plate loaded along its edges. The pin—hole contact could be of interference, clearance or neat fit. When the plate load is monotonically increased, interference fits give rise to receding contact, whereas clearance fits result in advancing contact. In either case, the changing contact situations lead to non-linear moving boundary value problems. The neat fit comes out as a special case in which the contact and separation regions are invariant with the applied load level and so the problem remains linear. The description of boundary conditions in the presence of tangential friction, will depend on whether the problem is one of advancing or receding contact, advancing contact presenting a special problem. A model is developed for the limiting case of a rigid pin and an ideally rough interface (infinitely large friction coefficient). The non-linearity resulting from the continuously varying proportions of contact and separation at the interface, is handled by an “Inverse Formulation” which was successfully applied earlier by the authors for smooth (zero friction) interfacial conditions. The additional difficulty introduced by advancing contact is handled by adopting a “Marching Solution”. The modelling and the procedure are illustrated in respect of symmetric plate load cases. Numerical results are presented bringing out the effects of interfacial friction and plate orthotropy on load-contact relations and plate stresses.

Thermal Stability of Polystyrene Peroxide

It has been observed that poly(styrene peroxide) with a high molecular weight is thermally less stable than the same polymer with a low molecular weight. This has been explained as being due to the strain on the O-O bond due to the greater polymer chain length.

On vibration of eccentrically stiffened plates with varying stiffener length

Results of a study of the variation of natural frequencies with respect to the length of the stiffener of a square panel clamped all along its boundary and stiffened in the middle by a concentric stiffener were recently reported [ 11. Significant increases in certain frequencies, namely those with modes symmetric about both the medians of the plate, were observed when small gaps were not left between the plate boundary and the stiffener end. As an extension to that work, results of a study of the effect of the eccentricity of the stiffener on the frequency variation with the length of the stiffener are reported here.

Thermochemical and kinetic studies on the effects of cobalt salicylate on the oxidative degradation of polystyrene

The effect of cobalt salicylate on the oxidative degradation and ignition of polystyrene has been studied. It was found that cobalt salicylate sensitizes both the degradation and ignition of polystyrene by facilitating electron-transfer processes in the propagation step. From thermochemical and kinetic studies it was found that the cobalt ion, owing to its ability to exist in variable valence states, promotes electron transfer in the propagation step of polymer degradation, increasing the rate of propagation and consequently the overall rate. Using solid-phase thermal ignition theory, an attempt has been made to explain the sensitization of ignition by the cobalt ion.

Elastic analysis of pin joints in plates under some combined pin and plate loads

Joints are primary sources of weakness in structures. Pin joints are very common and are used where periodic disassembly of components is needed. A circular pin in a circular hole in an infinitely large plate is an abstraction of such a pin joint. A two-dimensional plane-stress analysis of such a configuration is carried out, here, subjected to pin-bearing and/or biaxial-plate loading. The pin is assumed to be rigid compared to the plate material. For pin load the reactive stresses at the edges of the infinite plate tend to zero though their integral over the external boundary equals to the pin load. The pin-hole interface is unbonded and so beyond some load levels the plate separates from the pin and the extent of separation is a non-linear function of load level. The problem is solved by inverse technique where the extent of contact is specified and the causative loads are evaluated directly. In the situations where combined load is acting the separation-contact zone specification generally needs two parameters (angles) to be specified. The present report deals with analysing such a situation in metallic (or isotropic) plates. Numerical results are provided for parametric representation and the methodology is demonstrated.

Pin-Loaded Holes in Large Orthotropic Plates

Pin-loaded holes commonly occur in engineering structures. However, accurate analysis of such holes presents formidable difficulties because of the load-dependent contact of the pin with the plate. Significant progress has recently been achieved in the analysis of holes in isotropic plates. This paper develops a simple and accurate method for the partial contact analysis of pin-loaded holes in composites. The method is based on an inverse formulation that seeks to determine loads in a given contact-separation configuration. A unified approach for all types of fit was used. Continuum solutions were obtained for infinitely large plates of various typical orthotropic properties with holes loaded by smooth rigid pins. These solutions were then compared with those for isotropic plates. The effects of orthotropy and the type of fit were studied through load-contact relationships, distribution of stresses and displacements, and their variation with load. The results are of direct relevance to the analysis and design of pin joints in composite plates.

Photoelastic determination of stress intensity factors in patched cracked plates

n this paper, the influence of patch parameters on stress intensity factors in edge cracked plates is studied by employing transmission photoelasticity. Edge cracked plates made of photo-elastic material are patched on one side only by E glass-epoxy and carbon-epoxy unidirectional composites. The patch is located on the crack in such a way that the crack tip is not covered. Magnified isochromatic fringes are obtained by using a projection microscope of magnification 50, converted into a polariscope. Irwin's method is used to compute stress intensity factors from photoelastic data. The reduction in stress intensity factors is presented in graphical form as a function of patch parameters, namely stiffness, location and length. An empirical equation connecting reduction in stress intensity factor and these patch parameters is presented.

Flexure of composite plates

A new higher order shear deformation theory of laminated composite plates is developed. The basic displacement variables in this theory are two partial normal displacements and two in-plane displacement parameters. The governing equations are presented in the form of four simultaneous partial differential equations. The shear deformation theories of Bhimareddy and Stevens, and of Reddy are special cases of this formulation. In their models, transverse shear strains will become zero at points in the plate where displacements are constrained to be zero such as those on fixed edges. This limitation has been overcome in the present formulation.

Studies on vacuum pyrolysis of ammonium perchlorate and ammonium perchlorate/polystyrene propellant in the presence of transition metal oxides

Vacuum pyrolysis of ammonium perchlorate (AP) and ammonium perchlorate/polystyrene (PS) propellant has been studied by differential thermal analysis (DTA) in order to observe the effect of transition metal oxides on sublimation. Sublimation and decomposition being competitive processes, their proportions depend on the pressure of the pyrolysis chamber. The enthalpies for complete decomposition and complete sublimation are available from the literature and by using these data together with DTA area measurements, the extents of sublimation and decomposition have been calculated for AP and the propellant system. The effect of the metal ions on the extent and rate of sublimation depends on their nature. For AP the extent of sublimation increases with a decrease in particle size. For the propellants the powder sublimes more readily than the bulk material, but in the presence of metal ions the bulk material sublimes more readily than the powder. To substantiate this finding, the effect of MnO2 on AP sublimation as a function of particle size was examined, and it was observed that the extent of sublimation decreases as the particle size decreases.

Mechanistic studies on the pyrolysis and combustion of polystyrene/ammonium perchlorate propellants in the presence of transition metal oxides

The effect of transition metal oxides (Fe2O3, MnO2, Ni2O3 and Co2O3) on polystyrene/ammonium perchlorate propellant systems has been examined. The mechanism of action of the oxides in increasing the burning rate was examined by studying the effect of the oxides on the thermal decomposition and combustion of the oxidizer and the propellant. It has been concluded that one of the mechanisms by which the oxides act is by promoting the charge-transfer process, which is indicated by the enhancement of the electron-transfer process in ammonium perchlorate and by the correlation between the redox potential of the metal ions and the corresponding burning rates of the propellant.

Steady-State Response of Thick Rectangular Plates

The classical theory of plates neglects the effects of rotatory inertia and shear deformation, and due to this assumption it is applicable only for thin plates. Mindlin presented an improved plate theory which is fairly accurate.

Studies on friction and formation of transfer layer when Al-4Mg alloy pins slid at various numbers of cycles on steel plates of different surface texture

In the present investigation, various kinds of textures, namely, unidirectional, 8-ground, and random were attained on the die surfaces. Roughness of the textures was varied using different grits of emery papers or polishing powders. Then pins made of Al-4Mg alloys were slid against steel plates at various numbers of cycles, namely 1, 2, 6, 10 and 20 under both dry and lubricated conditions using an inclined pin-on-plate sliding tester. The morphologies of the worn surfaces of the pins and the formation of transfer layer on the counter surfaces were observed using a scanning electron microscope. Surface roughness parameters of the plate were measured using an optical profilometer. It was observed that the coefficient of friction and formation of transfer layer during the first few cycles depend on the die surface textures under both dry and lubricated conditions. It was also observed that under lubricated condition, the coefficient of friction decreases with number of cycles for all kinds of textures. However, under dry condition, it ecreases for unidirectional and 8-ground surfaces while for random surfaces it increases with number of cycles

Influence of the electric field on the low-temperature thermal decomposition of ammonium perchlorate/polystyrene propellant

An electric field (100 V/cm at 230°C and 150°C) has been applied to ammonium perchlorate (AP)/polystyrene (PS) propellant mixtures in order to understand the low temperature decomposition behavior of the propellant. The charge-carrying species is anionic in nature at 230°C, which could be ClO4−, but is cationic at 150°C, which could be either NH4+ or H+. These results are parallel to that observed for pure ammonium perchlorate (AP) pellets [1]. The burning rate (r' ) of the propellant was found to follow the same trend as that for the thermal decomposition of the propellant on application of an electric field. At 150°C Image was higher at the −ve electrode than at the +ve electrode, but at 230°C just the opposite was observed. Kinetic studies have confirmed that the decomposition of the orthorhombic AP follows two mechanism corresponding to E = 30 kcal mol−1 (180–230°C) and E = 15 kcal mol−1 (150–180°C).

Analytical estimation of stress intensity factors in patched cracked plates

The fatigue and fracture performance of a cracked plate can be substantially improved by providing patches as reinforcements. The effectiveness of the patches is related to the reduction they cause in the stress intensity factor (SIF) of the crack. So, for reliable design, one needs an accurate evaluation of the SIF in terms of the crack, patch and adhesive parameters. In this investigation, a centrally cracked large plate with a pair of symmetric bonded narrow patches, oriented normally to the crack line, is analysed by a continuum approach. The narrow patches are treated as transversely flexible line members. The formulation leads to an integral equation which is solved numerically using point collocation. The convergence is rapid. It is found that substantial reductions in SIF are possible with practicable patch dimensions and locations. The patch is more effective when placed on the crack than ahead of the crack. The present analysis indicates that a little distance inwards of the crack tip, not the crack tip itself, is the ideal location, for the patch.