Irradiance formations of on-axis Lambertian pointlike sources in polygonal total-internal-reflection straight light pipes

Different geometric shapes of light pipes cause different irradiance distributions. We analytically explore the irradiance distributions of on-axis Lambertian pointlike sources in polygonal total-internal-reflection (TIR) straight light pipes. It is analytically shown that the irradiance of pentagonal light pipes concentrates on the center of the exit plane. Numerical verifications are also provided, and experimental explorations with different shapes of acrylic light pipes are carried out for comparison. We also analyze the influence of light-pipe length on distribution uniformity and deduce the smallest uniform-mixing length/circumradius ratios for polygonal light pipes.     

Cyclic tearing and crack growth in circumferentially cracked straight pipes

Earthquake load, which is cyclic in nature and of short duration, is the main design basis accident load for designing the primary heat transport (PHT) piping components of Nuclear Power Plants. Adequate protection of piping components from the effects of earthquake requires detailed knowledge of strength and deformation characteristics of the components and assemblies making up the piping system. Fracture behaviour of 23 pipes was studied by conducting cyclic tests under four‐point bending. Fifteen pipes were of carbon steel (SA333 Grade 6) of 219 mm, 324 mm and 406 mm ODs and eight pipes were of stainless steel (AISI Type 304LN) of 168 mm OD with through‐wall circumferential crack. Six pipes were tested under displacement control and the rest under load control. The effect of various parameters such as location and size of initial crack in base metal and weld metal, cyclic load range and displacement increment on crack growth and number of cycles for failure was investigated. The investigations showed significant reduction in the fracture resistance under cyclic loading conditions. Crack growth equations have been proposed for carbon steel pipes with and without weld under cyclic tearing.     

Thermal stresses and couple-stresses in square cylinder with a circular hole

This article deals with the effect of couple-stresses on thermal stress distribution in a square cylinder with a central circular hole under steady state temperature distribution. The analysis is developed by the point-matching technique.From our calculation, it may be concluded that stress concentration around a circular hole, taking couple-stress into account, results in lower values than those accepted heretofore.     

Design of Stark-tuned far-infrared laser with circular hollow waveguide

A novel design of a Stark-tuned far-infrared laser using a circular hollow dielectric waveguide is proposed, and its characteristics are studied. Supplementary electrodes are inserted inside the circular hollow dielectric tube to suppress charge accumulation while keeping field uniformity. In what is believed to be a new design, the mode property is found to be improved, and the angular dependency of the attenuation loss according to the beam polarization is estimated to be much smaller than that of the conventional rectangular hybrid waveguide design. In this new design, DeltaM=0 far-infrared (FIR) transition as well as DeltaM=+/-1 transition can be observed, and the power enhancement for the DeltaM=0 FIR transition is expected.     

Dynamic progressive buckling of circular and square tubes

A series of over 120 axial crushing tests were conducted on circular and square steel tubes loaded either statically or dynamically. Approximate theoretical predictions for static and dynamic progressive buckling are developed. Fair agreement with the experimental results is achieved provided the effective crushing distance is taken into account and the infuence of material strain rate sensitivity is retained for dynamic loads.     

Behaviour of pipes with a circular hole subjected to compressive loading

In the fabrication of offshore structures, cutouts are often made on pipes to allow access to the interior of the pipes for maintenance and servicing. Thus, there is a necessity to investigate the effects of cutouts on the buckling load of pipes. Both the finite element and experimental techniques have been employed to investigate several series of pipes with and without cutouts. The results obtained were in reasonably good agreement with those obtained by the semiempirical solution.     

Effect of frictional constraints on the barreling formations in cylinder upsetting with a hollow die

The objective of this study is to investigate the material flow characteristics associated with solid cylinder upsetting using a hollow die subjected to different combinations of frictional constraints. During the upsetting process, obviously two barrels are formed along the lateral-free surface of the workpiece and correspond to some specific combination of frictional constraints. A finite element based methodology is utilized to examine the radii of curvature of the barrels and the height of the top free surface that is extruded into the aperture of the die. In addition, the effect of various combinations of interface friction at the top- and bottom- die surfaces on both the effective stress and strain distributions are also investigated.     

Optimised inner boundary shapes in circular rings under diametral compression

Using a method developed by the authors, the configuration of the inside boundary of circular rings, subjected to diametral compression, has been optimised, keeping cleared the space enclosed by the original circular inside boundary. The range of diameters studied was 0.33ID/OD0.7. In comparison with circular rings of the same ID/OD, the stress concentrations have been reduced by about 30%, the weight has been reduced by about 10% and coefficients of efficiency of about 0–96 have been attained. The maximum values of compressive and tensile stresses on the edge of the hole, are approximately equal, there are practically no gradients of stress along the edge of the hole, and sharp corners exhibit zero stress. The geometries for each ID/OD design are given in detail.     

Assessing the accuracy of fatigue life in surface‐cracked straight pipes

The demonstration of leak before brake (LBB) based on fracture mechanics requires information on the initial size of a defect, initiation of crack growth from the inherent defect and subsequent crack growth rates. In the present paper the prediction methodologies have been tested for three different full scale pipes geometry experimentally tested data. The prediction accuracy of two SIF solutions available in the literature has also been judged. The effect of fatigue crack closure and corrections needed in the numerical prediction methodology using FEM have also been included. The results showed that the FEM could fairly predict the fatigue crack initiation and crack growth life of full‐scale piping components having a constant depth crack profile.     

Transmission of light through right-angle corners in hollow light guides

Transmission of light through the corners in hollow light guides is compared for a new type of corner that is based on a laser-cut light-deflecting panel and for a flat, 45°, mirror-type corner. Corner efficiency is defined, and an experimental method for the measurement of the corner efficiency versus the angular width of the input light is described. Measured corner efficiencies were found to be nearly independent of the angular width of the incident light for metallic hollow light guides, with the average efficiency of the laser-cut-panel corner (65%) lower than that of the mirror corner (80%).     

Compact lens with circular spot profile for square die LEDs in multi-LED projectors

In the stage illumination industry, LED technology is promising both in terms of energy use and novel features, but it also has inherent issues. This paper presents a solution to the poor color homogeneity arising when multiple rectangular images formed from LED dies are combined into a circular spot profile. Using ray tracing, a nonrotationally symmetric collimating lens was optimized to round off such die images. The result is a high-output lens with an almost perfectly circular spot. In a simulated red green blue color mixing projector with seven LEDs, the lens reduced measurable color inhomogeneity by ≈24.1%, with a 5.3% luminous gain, compared to the best rotationally symmetric benchmark lens.     

Stress-intensity factors for circular hollow section V-joints with a rack-plate chord

This study investigates the fatigue crack‐driving force, measured by the linear‐elastic stress‐intensity factors (SIFs), for a surface crack at the root of the welds in a thick‐walled, circular hollow section (CHS) V‐shape joint, typically installed in modern offshore jack‐up platforms. The primary (chord) member of the V‐joint consists of two half CHSs welded to both sides of a thick rack plate, while the secondary (brace) member adopts thick‐walled CHSs. The surface‐breaking crack considered in this study locates at the interface between the rack plate and the weld metal joining the half CHS, and represents an initial flaw introduced by lack of penetration in the welding procedure. The finite‐element model incorporates a very detailed, local crack‐front mesh in a global continuous mesh through a mesh‐tying procedure, which ensures displacement continuity between the independent master surface and the dependent slave surface. A simple plate model verifies the mesh‐tying procedure in computing the linear‐elastic stress‐intensity factors for two remote loading conditions. The computation of the stress‐intensity factors employs a linear‐elastic interaction integral approach. The comparison of the computed SIF values with a previous experimental measurement for a CHS T‐joint verifies the accuracy and feasibility of the interaction integral approach in computing SIF values for surface cracks in welded tubular connections. Subsequent numerical analysis on the gapped V‐joints examines the mixed‐mode SIF values for different loading conditions and includes an array of practical joint geometric parameters and crack sizes. The nondimensional mode I stress‐intensity factors generally increases with the following variations in the joint geometric parameters: an increase in the chord radius to the wall thickness ratio (γ=d₀/2t₀) , an increase in the brace diameter to the chord diameter ratio (β=d₁/d₀) , a decrease in the crack depth ratio (a/t) or an increase in the crack length c. The current study identifies a practical group of V‐joints that requires detailed treatment in the fatigue assessment procedure. These V‐joints adopt a large β ratio and demonstrate high mode‐mixity angles [ψ= tan^?1(K_II/K_I)] with correspondingly high mode I and mode II stress‐intensity factors.     

Thermal stress in rotating functionally graded hollow circular disks

The analysis of thermoelastic problem of a rotating functionally graded hollow circular disk is made. The hollow disk is assumed to have varying material properties along the radial direction. An analytical method is presented to investigate steady thermal stresses in a functionally graded circular annulus rotating with constant angular velocity about its central axis. The associated boundary value problem is reduced to a Fredholm integral equation. The thermal stresses and radial displacement are obtained by numerically solving the resulting equation. A comparison of the numerical results with the exact ones for material properties of special power-law profile confirms the effectiveness of the method. For generally varying material parameters, numerical results are presented graphically to show the effects of gradient parameter, temperature change, angular velocity and thickness of the disk on the distribution of thermal stresses and radial displacement.     

方钢管焊接空心球节点的弹性有限元分析及试验

通过有限元系统分析方钢管焊接空心球节点在轴力作用下的受力性能。建立采用实体单元的有限元模型,对轴力作用下的方钢管焊接空心球节点进行弹性有限元分析,给出轴力作用下方钢管焊接空心球节点的应力和变位分布规律,并对它的力学性能进行分析。将弹性有限元结果与试验结果进行比较,两者符合很好,验证了有限元分析的正确性。     

Bismuth oxychloride hollow microspheres with high visible light photocatalytic activity

Hollow microspheres of two bismuth oxychlorides, BiOCl and Bi₂₄O₃₁Cl₁₀, were successfully synthesized using carbonaceous microsphere sacrificial templates. The phase evolution from BiOCl to Bi₂₄O₃₁Cl₁₀ was easily realized by heating the former at 600 °C. With a uniform diameter of about 200 nm, an average shell thickness of 40 nm, and basic nanosheets of <20 nm, the hollow microspheres of both BiOCl and Bi₂₄O₃₁Cl₁₀ showed high visible light photocatalytic activity towards the degradation of Rhodamine B (RhB). Besides the effective photosensitization process and efficient photointroduced carrier separation, the high photocatalytic activity was believed to result from their hollow-structure-dependent large visible light absorption. Moreover, as a chlorine-deficient analogue, the Bi₂₄O₃₁Cl₁₀ hollow spheres possessed a narrower band gap, more dispersive band structure, and higher photocarrier conversion efficiency, which further helped them to exhibit better photocatalytic activity.

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Tensile behaviour of anchored blind bolts in concrete filled square hollow sections

In this paper, the tensile behaviour of a new type of blind bolt, the anchored blind bolt, has been studied. This type of bolt consists of a conventional blind bolt with a headed stud extension that anchors it into the infill concrete. It has been developed for use in moment-resisting connections between I-beams and concrete-filled hollow section columns. The behaviour of these connections is highly dependent on the tensile behaviour of the anchored blind bolts. Hence, the fundamental mechanics of this behaviour has been studied here, both experimentally and in simulations using FE models. The complex interactions between the headed stud anchorage, the concrete infill, and the steel tube have been examined in detail. The experimental and numerical findings were used to understand the influence of important parameters in the tensile behaviour of the anchored blind bolts. It was found that the location of the bolt with respect to the side walls of the tube had a substantial influence on the behaviour of the anchored blind bolts. All the bolts located close to the side walls of the square hollow sections reached the ultimate tensile capacity of the equivalent structural bolts. This was due to the development of a concrete strut which transferred the load to the corner of the steel section. The bolt diameter also had a significant influence on the stiffness and strength of the anchored blind bolts.