Three-dimensional elastic analysis of cracked thick plates under bending fields

A three-dimensional analysis is presented for the bending problem of finite thick plates with through-the-thickness cracks. A general solution is obtained for Navier's equations of the theory of elasticity. It is found that the in-plane stresses and the transverse normal stress at the crack front are singular with an inverse square root singularity, while the transverse shear stresses are of the order of unity. Results from a numerical study indicate that the stress intensity factor, which varies across the thickness, is influenced by the thickness ratio in a significant manner. Results from a parametric study and those from a comparative study with existing finite element values are presented.

Distribution of the angle of rotation plane random walks

We study the probability distribution of the angle by which the tangent to the trajectory rotates in the course of a plane random walk. It is shown that the determination of this distribution function can be reduced to an integral equation, which can be rigorously transformed into a differential equation of Hill's type. We derive the asymptotic distribution for very long walks.

Some Exact-Solutions Describing Unsteady Plane Gas-Flows With Shocks

A new class of exact solutions of plane gasdynamic equations is found which describes piston-driven shocks into non-uniform media. The governing equations of these flows are taken in the coordinate system used earlier by Ustinov, and their similarity form is determined by the method of infinitesimal transformations. The solutions give shocks with velocities which either decay or grown in a finite or infinite time depending on the density distribution in the ambient medium, although their strength remains constant. The results of the present study are related to earlier investigations describing the propagation of shocks of constant strength into non-uniform media.

Out-of-plane deformation and failure of masonry walls with various forms of reinforcement

Out-of-plane behaviour of mortared and mortarless masonry walls with various forms of reinforcement, including unreinforced masonry as a base case is examined using a layered shell element based explicit finite element modelling method. Wall systems containing internal reinforcement, external surface reinforcement and intermittently laced reinforced concrete members and unreinforced masonry panels are considered. Masonry is modelled as a layer with macroscopic orthotropic properties; external reinforcing render, grout and reinforcing bars are modelled as distinct layers of the shell element. Predictions from the layered shell model have been validated using several out-of-plane experimental datasets reported in the literature. The model is used to examine the effectiveness of two retrofitting schemes for an unreinforced masonry wall.

Water-wave scattering by two submerged plane vertical barriers-Abel integral-equation approach

The classical problem of surface water-wave scattering by two identical thin vertical barriers submerged in deep water and extending infinitely downwards from the same depth below the mean free surface, is reinvestigated here by an approach leading to the problem of solving a system of Abel integral equations. The reflection and transmission coefficients are obtained in terms of computable integrals. Known results for a single barrier are recovered as a limiting case as the separation distance between the two barriers tends to zero. The coefficients are depicted graphically in a number of figures which are identical with the corresponding figures given by Jarvis (J Inst Math Appl 7:207-215, 1971) who employed a completely different approach involving a Schwarz-Christoffel transformation of complex-variable theory to solve the problem.

An explicit finite element modelling method for masonry walls under out-of-plane loading

An explicit finite element modelling method is formulated using a layered shell element to examine the behaviour of masonry walls subject to out-of-plane loading. Masonry is modelled as a homogenised material with distinct directional properties that are calibrated from datasets of a “C” shaped wall tested under pressure loading applied to its web. The predictions of the layered shell model have been validated using several out-of-plane experimental datasets reported in the literature. Profound influence of support conditions, aspect ratio, pre-compression and opening to the strength and ductility of masonry walls is exhibited from the sensitivity analyses performed using the model.

Gravity-induced coronal plane joint moments in adolescent idiopathic scoliosis

Background Adolescent Idiopathic Scoliosis is the most common type of spinal deformity, and whilst the risk of progression appears to be biomechanically mediated (larger deformities are more likely to progress), the detailed biomechanical mechanisms driving progression are not well understood. Gravitational forces in the upright position are the primary sustained loads experienced by the spine. In scoliosis they are asymmetrical, generating moments about the spinal joints which may promote asymmetrical growth and deformity progression. Using 3D imaging modalities to estimate segmental torso masses allows the gravitational loading on the scoliotic spine to be determined. The resulting distribution of joint moments aids understanding of the mechanics of scoliosis progression. Methods Existing low-dose CT scans were used to estimate torso segment masses and joint moments for 20 female scoliosis patients. Intervertebral joint moments at each vertebral level were found by summing the moments of each of the torso segment masses above the required joint. Results The patients’ mean age was 15.3 years (SD 2.3; range 11.9 – 22.3 years); mean thoracic major Cobb angle 52° (SD 5.9°; range 42°-63°) and mean weight 57.5 kg (SD 11.5 kg; range 41 – 84.7 kg). Joint moments of up to 7 Nm were estimated at the apical level. No significant correlation was found between the patients’ major Cobb angles and apical joint moments. Conclusions Patients with larger Cobb angles do not necessarily have higher joint moments, and curve shape is an important determinant of joint moment distribution. These findings may help to explain the variations in progression between individual patients. This study suggests that substantial corrective forces are required of either internal instrumentation or orthoses to effectively counter the gravity-induced moments acting to deform the spinal joints of idiopathic scoliosis patients.

Royal Air Mail plane in Singapore Transportation

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Royal Air Mail plane in Singapore Transportation

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Immediate, cumulative and residual effects of short- and long-term low plane of nutrition on milk protein and casein composition

Immediate and residual effects of two lengths of low plane of nutrition (PON) on the synthesis of milk protein and protein fractions were studied at the Mutdapilly Research Station, in south-east Queensland. Thirty-six multiparous Holstein-Friesian cows, between 46 and 102 days in milk (DIM) initially, were used in a completely randomised design experiment with three treatments. All cows were fed on a basal diet of ryegrass pasture (7.0 kg DM/cow.day), barley-sorghum concentrate mix (2.7 kg DM/cow.day) and a canola meal-mineral mix (1.3 kg DM/cow.day). To increase PON, 5.0 kg DM/cow.day supplemental maize and forage sorghum silage was added to the basal diet. The three treatments were (C) high PON (basal diet + supplemental silage); (L9) low PON (basal diet only) for a period of 9 weeks; and (L3) low PON (basal diet only) for a period of 3 weeks. The experiment comprised three periods (1) covariate – high PON, all groups (5 weeks), (2) period of low PON for either 3 weeks (L3) or 9 weeks (L9), and (3) period of high PON (all groups) to assess ability of cows to recover any production lost as a result of treatments (5 weeks). The low PON treatment periods for L3 and L9 were end-aligned so that all treatment groups began Period 3 together. Although there was a significant effect of L9 on yields of milk, protein, fat and lactose, and concentrations of true protein, whey protein and urea, these were not significantly different from L3. There were no residual effects of L3 or L9 on protein concentration or nitrogen distribution after 5 weeks of realimentation. There was no significant effect of low PON for 3 or 9 weeks on casein concentration or composition.

Synthesis of plane linkages to generate functions of two variables using point position reductionâII. Sliding inputs and outputs

The paper presents simple graphical procedures for the position synthesis of plane linkage mechanisms with sliding inputs and output to generate functions of two independent variables. The procedures are based on point position reduction and permit synthesis of the linkage to satisfy up to five arbitrarily selected precision positions.

A problem in micropolar elasticity

In this paper a three-dimensional analysis for statics and dynamics of a class of simply supported rectangular plates made up of micropolar elastic material is presented. The solution is in the form of series, in which each term is explicitly determined. For free vibrations, the frequencies are obtained by the solution of a closed form characteristic equation.

Studies on the out-of-plane behaviour of masonry walls

The prime aim of this PhD thesis is to contribute to the current body of knowledge on the out-of-plane performance of masonry walls through systematic investigation of the key parameters and provide insight into the design clauses of Australian Masonry Standard (AS3700-2011). The research work has been carried out through numerical simulation based on a 3D layered shell element model. The model demonstrated capability to simulate various forms of new and existing masonry systems commonly constructed in Australia such as unreinforced, internally and externally reinforced, confined and dry-stack masonry. In addition, the model simultaneously simulates in-plane and out-of-plane responses.

Impulse Voltage Breakdown Characteristics of Point-Plane Gaps at Low Pressures

Practical applications of vacuum as an insulator necessitated determining the low-pressure breakdown characteristics of long gap lengths of a point-plane electrode system. The breakdown voltage has been found to vary as the square root of the gap length. Further, with the point electrode as the anode, the values of the breakdown voltages obtained have been found to be larger than those obtained with a plane-parallel electrode system at a corresponding gap length. By applying the theory of the anode heating mechanism as the cause for breakdown, the results have been justified, and by utilizing a field efficiency factor which is the ratio of the average to maximum field, an empirical criterion has been developed. This criterion helps in calculating the breakdown voltage of a nonuniform gap system by the knowledge of the breakdown voltage of a plane-parallel electrode system.

A numerical method for separation of stresses in photo-orthotropic elasticity

A numerical method is suggested for separation of stresses in photo-orthotropic elasticity using the numerical solution of compatibility equation for orthotropic case. The compatibility equation is written in terms of a stress parameter S analogous to the sum of principal stresses in two-dimensional isotropic case. The solution of this equation provides a relation between the normal stresses. The photoelastic data give the shear stress and another relation between the two normal stresses. The accuracy of the numerical method and its application to practical problems are illustrated with examples.