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Cold spraying (CS) is a coating technique, which has developed rapidly in the last two decades and shows great potential in the industrial community due to its advantages of low temperature deposition as well as no oxides forming in the coating. This review’s focus is on the behaviour of particles impacting and the prediction of critical velocity for particle deposition during CS as calculated by numerical simulations according to the open literature. The first part presents an introduction of CS and its particle bonding mechanism. The second part briefly introduces the typically employed numerical computation methods and compares these methods. The third part discusses the effect of particle parameters on particle deformation behaviour. Finally, the current problems and prospects existing in numerical simulations of the impact of CS particles are explored.

During friction stir welding (FSW) of AA2024-T3 sheets, composite backing plates (CBP) made out of the combination of pure copper and medium carbon steel were employed aiming at enhancing the joint mechanical properties. Three different CBP designs were used. Microstructure and mechanical properties of the welded joints were examined. Results reveal that the grains under CBP have been noticeably refined compared to those under a monolithic steel backing plate typically used in FSW. In addition, using the CBP effectively prevents the dissolution of Guinier–Preston–Bagaryatskii (GPB) zones in the HAZ. Superior strength–ductility synergy was obtained under CBP-3. Those joints exhibit more high-angle grain boundaries, ultrafine grains of about 980 nm, more GPB zones and optimum hardness distribution, resulting in a tensile strength of 442 MPa and an elongation of as much as 16.2%.

This study was aimed at characterizing microstructural change and fatigue properties of linear friction welded (LFWed) Ti6Al4V joints with special attention to the relationship between the microstructure and cyclic deformation behavior. The welding process resulted in a remarkable microstructure change across the LFWed joint. The microstructure of the joint consisted of fine subgrains in the weld zone (WZ) and elongated grains in the thermomechanically affected zone (TMAZ), leading to a significantly higher hardness in the WZ. Both the base metal (BM) and joint exhibited essentially symmetrical hysteresis loops and equivalent fatigue life, while the cyclic strain hardening exponent of the welded joint was lower. Cyclic stabilization appeared at lower strain amplitudes up to 0.6% in both the BM and joint, however, cyclic softening occurred at higher strain amplitudes. Fatigue failure was observed to occur in the BM, and fatigue crack initiated from the specimen surface or near-surface defect. Fatigue crack propagation was basically characterized by fatigue striations, together with some secondary cracks.

A two-dimensional axisymmetric model for the inertia friction welding (IFW) of a nickel-based superalloy was developed. The influences from the axial pressure, initial rotational speed, and moment of inertia of the flywheel on the interface temperature and axial shortening were systemically examined. The analysis shows that the mechanical energy mainly depends on the initial rotational speed, and a relatively high axial pressure will increase conversion efficiency from mechanical energy to effective welding heat. The axial shortening is found to be approximately proportional to the square of initial rotational speed while logarithmical to the axial pressure. Based on this work, the weldability criteria for IFW nickel-based superalloy was established. Additionally, the approach for welding parameter optimization was performed considering the evolution of temperature profiles from various parameters. The results show that the axial pressure has a more obvious effect on the width of high-temperature zone than the rotational speed during the quick shortening stage.

The present paper used an Eulerian model to study effects of the substrate material and the substrate temperature on the particle deformation behaviour in cold spraying dissimilar particle/substrate combinations. Results show that the deformation pattern of the particle presents a spreading and penetration way for soft/hard and hard/soft particle/substrate material combinations respectively. In addition, preheating the substrate can achieve a coordinated deformation pattern for the soft/hard particle/substrate material combination and a maximum steady PEEQ ranging in 3·2–3·5 in the present study.

In this paper, the previously developed Eulerian model (Yu et al., J Therm Spray Technol 21(3):745-752, 2012), which could well predict the critical velocity and erosion velocity, was extended to other commonly used materials such as aluminum, iron, nickel, stainless steel 316, and Inconel718 for studying the influence of material property and establishing a generalized window of critical velocity. Results show that the deformation behavior of the used materials could be classified as coordinated deformation (copper, iron, nickel) and uncoordinated deformation patterns (aluminum, stainless steel, and Inconel718). However, it was found that the steady maximum equivalent plastic strain values at the critical velocity for each material concentrate in the extent of 2.6-3.0 regardless of deformation pattern. Dimensionless analysis shows that, the calculated critical velocity increases with the increase of material characteristic velocity, and this relationship can be primarily used to predict the critical velocity.

In cold spraying (CS), critical velocity of particles is one of the most important parameters. The impacting particle and substrate inevitably undergo a strong thermomechanical coupling process at the contacting interface and serious plastic deformation in a very short time. In this paper, a coupled thermomechanical Eulerian (CTM-Eulerian) model was, for the first time, developed for CS particles to investigate plastic deformation and heat conduction within the bulk, and to predict the critical velocity. Results show that heat conduction has a significant effect on the temperature distribution within the particle which will influence the atom diffusion at the impacting interface, while a little influence on plastic deformation. Moreover, based on the deformed particle shapes and plastic strain analysis, a calculated critical velocity of about 300 m/s for copper is obtained. Finally, this CTM-Eulerian model is extended to other commonly sprayed materials and the predicted critical velocities of Fe, Ni, SS304, Al, In718, and TC4 are about 350, 380, 395, 410, 490, and 500 m/s, respectively.

Aimed at the real-time request of dynamic scheduling to product resource, an optimization method of parallel dynamic chain real-time available resources was put forward. Proceed from real-time tracing of resource information influencing scheduling tasks dynamic property, established a resource informations real-time tracing back and optimization model, which used module and parallel process mechanism to different kinds of real-time traced back resource information. The mechanism processed global dynamic feedback tracing for every module and optimized available resources primarily, on this basis, graded the primary available resources and gave a real-time candidate resource set. Through one example of one gear production scheduling, the methods validity was tested.

AZ91D/SiCp composite coatings were fabricated on AZ31 magnesium alloy substrates using cold spraying. The effects of SiC volume fraction and particle size on the deposition behavior, microhardness, and bonding strength of coatings were studied. The mean sizes of SiC particles tested were 4, 14, and 27 μm. The results show that fine SiC particles (d 0.5 = 4 μm) are difficult to be deposited due to the bow shock effect. The volume fraction of SiC particles in composite coatings increases with the increasing SiC particle size. The microhardness and bonding strength of composite coatings also show increases compared with AZ91D coatings. The volume fractions of SiC particles in the original powder were set at 15, 30, 45, and 60 vol.%. The corresponding contents in composite coatings are increased to 19, 27, 37, and 51 vol.%, respectively. The microhardness of composite coatings also increases as the volume fraction of SiC particles increases.

The height of rectangular nozzle's exit, throat and powder injector is changed systematically while the nozzle expansion ratio remains constant in order to study their effects on the distribution and velocity of magnesium (Mg) particles using three-dimensional models of cold spraying system. The effect of particle size on the particle distribution is also studied. It is found that the particle distribution is mainly influenced by the turbulent kinetic energy of the carrier gas flow at the nozzle exit. Changing the height of the exit or throat can control the particle distribution. The height of powder injector only influences the particle velocity.

The cold spray process usually involves preheating particle and increasing particle impact velocity to improve the deposition efficiency. In the present study, the effect of particle and substrate preheating on the deformation behavior of cold sprayed particle was investigated using the Eulerian formulation available in software of ABAQUS/Explicit with typical copper material. Preheating ways were used by realizing different temperatures on the substrate, particle and both. Calculated results show that different preheating ways result in different deformation patterns, the flattening ratio and compression ratio of Cu particle and the maximum equivalent plastic strain. Preheating whole model, substrate and particle shows a coordinated deformation pattern, penetration way and spreading way, respectively.

SiC reinforced Al 5056 composite coatings were prepared by cold spraying. Effects of gas temperature and SiC content in the composite coatings on microstructure and microhardness of the coatings were studied. Results show that the gas temperature improves the coating deposition efficiency, but has no effect on the volume fraction of SiC in the coatings and thus no influence on the coating microhardness. Cold spraying pure SiC powder shows deposition behaviors of SiC particles during the formation of composite coatings, i.e., cracking, embedment and rebounding.

Background Deficits in verbal working memory (VWM) have consistently been observed in schizophrenia, ranging from impairments in capacity, encoding, to irregular semantic organisation. However, syntactic deficits are less well-characterised, despite its crucial role in language construction. This study examines the role of simple syntactic structure (basis of the “sentence superiority effect”) in VWM of patients with psychotic disorders. Methods Patients with schizophrenia-spectrum disorders (n = 40) and healthy controls matched on age, sex and education (n = 40) were administered an auditory serial recall task containing word lists with low semantic coherence and either syntactically familiar structure (noun-verb-noun sequence) or syntactically unfamiliar structure. Other neurocognitive measures, symptoms and social functioning of patients were also assessed. Results A 4-way analysis of variance (group × version × list type × serial position) indicated that patients had significantly worse performance overall, suggesting a generalised verbal memory impairment. In addition, a significant interaction was found for list type and Group, demonstrating that healthy controls, but not patients, had superior performance in syntactically familiar word lists. A subgroup analysis of high-performing patients revealed that the interaction was not an artefact of poor verbal memory, but a selective deficit in syntactic facilitation. Conclusions Our findings may suggest segregated mechanisms for maintenance and computational aspects of VWM, and show that even simple syntactic structure facilitates recall of syntactically unfamiliar words lists. Additionally, schizophrenic patients show difficulty utilising syntactic information, which highlights the need to understand the neuropsychological basis of working memory and linguistic impairments in psychosis.

A coupled thermomechanical three-dimensional finite element model was developed for friction stir welding in the ABAQUS environment using Johnson–Cook material law and Johnson–Cook failure model. The temperature evolution during the plunge, dwell and moving stages of a friction stir welded 7050 aluminium alloy and the effect of heat conduction by the back plate were investigated. Results show that the temperature almost symmetrically distributes across the plate cross-section, and the temperature contour in the weld nugget zone presents a V type shape after the plunge stage. In the dwell stage, the frictional heat conducts around to preheat the plate. While in the moving stage, the heat gradually accumulates until a quasi-stable temperature field is formed. Moreover, it is shown that the heat conduction through the back plate has a significant effect on the temperature field. With the increasing heat convective coefficient of the back plate, the temperature field remarkably shrinks.

In this study, post-weld heat treatment of linear friction welded Ti17 (Ti–5Al–2Sn–2Zr–4Mo–4Cr) titanium alloy joints was performed at 530, 610 and 670°C for 4 h followed by air cooling. Results show that with increasing treatment temperature, the recrystallisation extent of the α and β phases in the weld and deformation zones increases significantly. The overall property of the joint is remarkably improved, and the fracture behaviour of the tensile and impact samples changes from brittle failure to a ductile one. After treatment at 670°C, the impact toughness of the joint is 93·3% of the parent metal, and the failure of the tensile samples occurs in the parent metal far away from the weld. According to these findings, a treatment temperature slightly lower than 670°C but higher than 610°C would be a good value for linear friction welding Ti17 joints.

In this study, an investigation on the impacting behavior of cold-sprayed particles using the Eulerian formulation available in ABAQUS/Explicit was conducted with typical copper material. The results show that a jet cannot be formed at an impact velocity less than about 290 m/s, while a continuous jet composed of both particle and substrate materials begins to initially form at about 290 m/s and a maximum equivalent plastic strain plateau can be found, which could be the approximate critical velocity. In addition, the jet presents discontinuities and the splashing causes the loss of material as the impact velocity exceeds the velocity extent of 290-400 m/s. Therefore, through theoretical analysis of the jet morphology, the Eulerian model could provide a prediction of the critical velocity.

In this paper, dense AZ91D/SiC composite coatings were fabricated by cold spraying. The microstructure and microhardness of the as-sprayed coatings were investigated. The results show that the content of SiC particles in the composite coating was 23.6 ± 7.5 vol.%. The microhardness of the composite coating was improved to 140 HV0.3 due to the enhancement of SiC particles, compared to 98 HV0.3 for the pure AZ91D coating. The wear behavior of the composite coating in an ambient condition was studied through a ball-on-disc dry sliding test system. The composite coating showed higher friction coefficient and lower wear rate than the pure AZ91D coating. The wear mechanism of the composite coating was discussed.

The orthogonal experimental design was conducted for linear friction welding of Ti-6Al-4V titanium alloy (TC4). The friction power and joint temperature were collected during the welding process. The influence of process parameters on the axial shortening was analyzed. The suitable process parameters were determined by investigating the joint appearance, the requirement of axial shortening and welding variables during welding. The results provide important reference for establishing process parameters of linear friction welding in practice.

The distribution of mechanical property in the weld zone of friction stir welded 7050 aluminum alloy joint along the plane perpendicular to the welding direction was experimentally investigated by the non-contact measurement method. The results show that the elastic modulus presents a W-shape distribution across the weld zone. The elastic modulus in the weld nugget zone is increased due to the grain refinement. In addition, the elastic modulus in the advancing side is slightly less than that in the retreating side possibly because of the relatively higher temperature in the advancing side during the welding process. The strength in the vicinity of weld center is decreased while the ductility is enhanced. The tensile strength and yield strength in the weld nugget zone and thermo-mechanically affected zone are significantly decreased while the elongation is increased due to the change of strengthening mechanism. In the heat affected zone the strength is decreased compared to the base material because the second phase grows up.

Linear friction welding (LFW), as a relatively new solid-state joining technique, has great potentials in welding of non-axisymmetric components, especially for cost-effectively machining blade/disc (blisks) assemblies. In this study, Ti–6Al–4V alloy was jointed by the LFW process under the appropriate processing parameters developed before. The microstructure, impact toughness and fracture characteristics of LFW Ti–6Al–4V joint were investigated. The results showed that a sound weld was obtained consisting of a superfine α + β microstructure in the weld center (about 70 μm thickness). The weld presents a higher impact toughness (61.3 ± 5.8 J/cm 2 ) than the parent Ti–6Al–4V because of the superfine microstructure formed in the weld. The fracture surface exhibits three typical regions: the thin fibrous zone close to the notch, the radiation zone in the middle and the shear lip zone at the other three sides, corresponding to the crack initiation, propagation and shear failure zones, respectively. The crack develops a short distance along the weld center and thermomechanically affected zone after its initiation, and then extends into the parent metal due to the lowest impact toughness of the parent.

Pure titanium TA2 and 1Cr18Ni9Ti stainless steel were vacuum diffusion bonded using Nb + Ni foils as interlayers, where Nb foil was adjacent to TA2 and Ni foil adjacent to 1Cr18Ni9Ti. The samples were heated to a temperature of 800°C at a pressure of 10 MPa and kept for 60 min, and then to a temperature of 900°C at a pressure of 1 MPa and kept for 30 min. The mechanical properties of the joint were characterized by the tensile strength test. The average tensile strength of the joints was about 398 MPa. The fracture characteristics of the joint were investigated using scanning electron microscope. The fracture of tensile test samples occurred in the Ni3Nb intermetallic compound formed in the interlayers.

The investigation of the plunge stage of the tool during friction stir welding (FSW) is the basis of understanding the nature of FSW, which is especially important for friction stir spot welding. In this study, the plunge stage of FSW tool was numerically examined by dynamic explicit finite element method with more attention to the temperature evolution. It was found that the high temperature region around the stirred zone extended with increasing the rotation speed. The heat affected zone expanded with the increase of inserting time, but the highest temperature around the stirred zone changed little. The range of the stirred zone changed little with the variations of the rotation speed and inserting time. The simulation result on the temperature field was in comparable agreement with the experimental one.

Large single crystals of 5,5′-distyryl-2,2′-bithiophene (DS-2T) were grown from tetrahydrofurane (THF) solution, and the crystal structure was analyzed by x-ray diffractometry. In-situ observation of crystal growth in solution was performed, and a unique change in the crystal habit depending on growth conditions is found. The change in crystal habit from a truncated parallelogram shape to a slender hexagonal shape with re-entrant angles at the both side can be explained as the consequence of kinetic roughing and Berg effect.

Micrometer-size pits on the surface of a polymer (polyallyldiglycol carbonate or PADC) substrate created by alpha-particle irradiation and subsequent chemical etching were used to study the topographical effects alone on cell behavior. Vinculin, the cell adhesion and membrane protrusion protein, was used as an indicator of cytoskeletonal reorganization on the substrate and localization of vinculin was used to demonstrate the presence of focal adhesions. In our experiments, vinculin expressed in epithelial HeLa cells cultured on PADC films with track-etch pits, but not in cells cultured on the raw or chemically etched blank films. In other words, vinculin expression was induced by the topography of track-etch pits, while etching of the substrate alone (without alpha-particle irradiation) did not cause up-regulation of vinculin protein expression. HeLa cells cultured on PADC films with track-etch pits also showed changes in cell proliferation, cell area and cell circularity, and were largely contained by the pits. In other words, the cell membrane edges tended to be in contact with the pits. By comparing the correlation between the positions of HeLa cells and the pits, and that between the positions of cells and computer-simulated pits, the tendency for membrane edges of HeLa cells to be in contact with the pits was recognized. This could be explained by inhibition of membrane protrusion at the pits. In conclusion, substrate track-etch pits were an important determinant of epithelial cell behaviors.

Ti-6Al-4V was successfully jointed by linear friction welding (LFW). A sound weld of thickness of 65-115 $m was obtained under the present conditions. The weld consisted of the superfine α+β structure, which is associated with the rapid heating and cooling processes involved in LFW. The thermomechanically affected zone (TMAZ) was limited and comprised of the severely deformed α and β grains. In the flash, a gradual microstructure was formed from the weld edge to the flash edge. A martensite structure (α’) was formed besides the acicular α+β in the flash edge owing to the fast cooling rate.

In this work, the effects of sliding velocity and applied load on the tribological characteristics, i.e. friction coefficient and wear rate, of an amorphous poly-ether–ether–ketone (PEEK) coating was examined. Friction tests were performed on a ball-on-disc apparatus. Based on analyses of the worn tracks, a comprehensive attempt is made to approach the tribological mechanism of amorphous PEEK. A hypothesis is proposed that the tribological behaviour of the amorphous PEEK is closely related to its viscoelastic behaviour. The sliding velocity plays significant roles on the tribological characteristics by influencing the interface temperature and strain rate of the PEEK surface layer involved in the friction process. The applied load influences the tribological performance by varying the strain range in the surface layer.

The influence of friction time on the flash (upset metal) shape and axial shortening during linear friction welding of 45 steel under an appropriate welding condition was examined. It was found that a sound weld with the fine structures could be formed as the friction time not less than 3 s. The axial shortening was exponentially increased with increasing the friction time. The periodical ridges presented in the flash were formed through the reciprocating motion and expelling of the plasticized materials. The flash in the friction direction presents an undulating-ribbon structure, while that in the vertical direction looks like a little curly swirl. The curved ridges were caused by the non-uniform extrusion rates of materials in the middle and edge resulting from the non-uniform temperatures.

Alpha-particle radiobiological experiments involve irradiating cells with alpha particles and require thin biocompatible materials which can record alpha-particle traversals as substrates for cell cultures. The biocompatibilities of chemically etched CR-39 solid-state nuclear track detectors (SSNTDs) using aqueous NaOH or NaOH/ehtanol are studied through the abundance and morphology of the cultured HeLa cells. The wetting properties of these etched CR-39 SSNTDs are also studied. The moderately hydrophobic CR-39 SSNTDs as well as the hydrophobic NaOH/ethanol-etched CR-39 SSNTDs are more biocompatible than the hydrophilic aqueous-NaOH-etched SSNTDs. Too small water contact angles, too large surface energy (γs) or the polar component γ s p do not favor the cell culture. On the other hand, the dispersive component γ s d of the surface energy and the ratio γ s p / γ s d do not seem to significantly affect the biocompatibility.

An analytic model of a bonding layer for a fiber Bragg grating (FBG) bonded on a substrate was developed to predict the strain transfer from the substrate to the FBG when the substrate is subjected to external forces. This model provides a guide on how to bond an FBG on a substrate as a strain sensor or as a chirp FBG spectrum-tuning device used in telecommunications. In addition, an inverse approach based on an optimization technique was developed to investigate which part of the strain distribution along the FBG causes sidebands and ripples when an FBG is stretched to become a chirped FBG (CFBG) using the substrate-straining technique. Results show that the primary influence of an unacceptable bonding layer on the strain transfer from the substrate to the FBG is near the two ends of the FBG, which causes sidebands in the reflective spectrum. Using a glue with a high shear modulus, we can increase the bonding length and reduce the bonding-layer thickness to effectively improve the strain transmissibility of the bonding layer. However, if the strain transfer from the substrate to the FBG exhibits fluctuations due to an improper bonding process or a deteriorating bonding layer, ripples occur in the corresponding wavelength spectra. The number and amplitude of the ripples correlate strongly to those of strain fluctuations in the FBG.

Piezoelectric ceramics (Na 0.5 Bi 0.5 ) 0.92 Ba 0.08 TiO 3 + x mol.% Mn (BNBT-Mn) with x ranging from 0 to 2.97 are synthesized by conventional solid state reaction. The sintered BNBT-Mn exhibited a single phase perovskite structure without detectable secondary phase from x =0 to x =2.6. With increasing amount of doped Mn, the Curie temperature ( T c ) of BNBT-Mn decreased rapidly, piezoelectric constants d 33 and k t increased promptly when x was lower than 0.56, taking the maximum value of 160×(10 −12 C/N) and 58.5%, respectively for x =0.56, then decreased slightly with x ranging from 0.56 to 2.6, and finally decreased rapidly for x >2.6, whereas Q m showed a different trend from d 33 and k t . Furthermore, k t had a relatively high value under the low poling field ( E p ) for x =0.56 owing to the reduced coercive field ( E c ). Possible mechanisms of the influence of Mn doping on the microstructure and piezoelectric properties are discussed.

This paper reports on the successful deposition of amorphous carbon nitride thin films (a-CN x ) and fabrication of ITO/a-CN x /Al Schottky thin-film solar cells by using the technique of ion beam sputtering. XPS and Raman spectra are used to characterize the deposited thin films. Nitrogen atoms are incorporated into the films in the form of carbon–nitrogen multiple bands. Their optical properties are also investigated using a spectroscopic ellipsometer and UV/VIS/NIR spectrophotometer. The refraction of the carbon nitride thin films deposited lies in the range of 1.7–2.1. The Tauc optical band gap is about 0.6 eV. The photovoltaic values of the device, short-circuit current and open-circuit voltage are 1.56 μA/cm 2 and 250 mV, respectively, when exposed to AM1.5 illumination (100 mW/cm 2 , 25°C).

In this research, the TRACE/PARCS model of Lungmen ABWR has been developed for verification of ultimate response guideline (URG) efficiency. This ultimate measure was named as DIVing plan, abbreviated from system depressurization, water injection and containment venting. The simulation initial condition is 100% rated power/100% rated core flow. This research focuses on the estimation of the time when the fuel might be damaged with no water injection by using TRACE/PARCS first. Then, the effect of the reactor core isolation system (RCIC), control depressurization and ac-independent water addition system (ACIWA), which can provide the injection with 950 gpm are also estimated for the station blackout (SBO) transient. &nbsp

cited By 15; International audience; SiC particle reinforced Al5056 composite coatings were prepared by cold spraying using initial powders containing 15, 30, 45 and 60 vol.% SiC. Effects of SiC content in the coating on microstructure, mechanical property and wear behavior of the coatings were studied. Experimental results show that the SiC particles in the coating improve the deformation of Al5056 particles and also increase the hardness of the coating. The cohesion strength of the composite coatings firstly increases and then decreases with the increase of SiC content in the coatings as a result of comprehensive effects of the SiC particles on improving the deformation of Al5056 particles and on reducing the effective contact area between the Al5056 particles. Finally, tribological tests show that the SiC particle and its content in the coatings would greatly influence the tribological behavior of the coatings. The worn tracks suggest that the delaminating wear is the wear mechanism of the Al5056 and Al5056/SiCp coatings at the present tribological condition. © 2013 Elsevier B.V.

Based on the displacement variational principle, a general method, called the spline finite member element method, is developed for lateral buckling analysis of thin-walled members. A transformed B3-spline function presented in the paper is used to simulate the longitudinal warping displacement field along the cross section of the thin-walled member. The analysis takes into account the effect of shearing strains of the middle surface of walls on the buckling, which reflects the shear lag phenomenon. Compared with the results from classical theory and other methods, the numerical results proposed in the paper demonstrate the versatility, accuracy and efficiency of the proposed method. The fast convergency, shown in numerical examples, predicts the reliability of the results.

A 50Ni–50Ti powder was produced by solid state synthesis via mechanical alloying from elemental Ti and Ni powders. The product was characterized using X-ray diffraction, scanning electron microscopy and optical microscopy. Cold spraying makes possible to deposit the coating of temperature sensitive materials, such as nanostructured material, without any significant change in the microstructure of feedstock. The preliminary results of this work showed that the ball milled Ni–Ti coating can be deposited by cold spraying. The coating presents a multilayer structure consisting of the alternate flattened Ni and Ti particles.

To our knowledge, apart from a closed-form solution for a simply supported I-beam subjected to uniform moment, most buckling loads are obtained by numerical methods. By using Galerkin's method of weighted residuals, an accurate approximate solution for lateral buckling of simply supported I-beam is proposed in this paper. Due to fast convergence of the method, the solution can be written in closed form. The results compare well with the previous work including experimental results and optimal and finite element analytical results.

Based on the displacement variational principle, a general method, called spline finite member element method, is developed for buckling analysis of thin-walled members with arbitrary cross sections under pure bending in the present paper. A transformed spline function is used to simulate the warping displacements along the cross section of the thin-walled member. The analysis takes into account the shear lag effect. Compared with the results from classical theory and the package ‘COSMOS/M’ (a finite element analysis program), the versatility, accuracy and efficiency of the proposed method are fully demonstrated. The fast convergency shown in numerical examples predicts the reliability of the results.

By introducing an important modification into Vlasov theory [1], a general displacement variational method is proposed for free vibration analysis of thin walled members to take into account the shear effect. The differential equations obtained are solved by the Galerkin method. The method can be applied to arbitrary cross sections including open and closed section thin walled structures and tube-in-tube structures. The results compare well with those of other authors and of a general finite element program COSMOS [2] in which the rigid section assumption and shear effect have also been considered. The method requires less computer time than the standard finite element method and even the finite strip method.

A semi-discrete displacement-based variational method is proposed to analyse tube-in-tube structures. The framed tube is substituted by an equivalent continuous orthotropic tube. The framed tube and core wall are connected by continuous in-plane rigid floor slabs. The commonly transverse displacement {vo} and the individual longitudinal displacement {w} of the outer and inner tubes are taken as primary unknown functions, where {w} expressed by [φ(s)]{w(z)} and [φ(s)] are assumed to be interpolation functions along the outer and inner cross-sections respectively. The ordinary differential equations of the tube-in-tube structure and the relevant boundary conditions are derived by the variational principle. The solutions are obtained directly by using the ordinary differential equation solver, which is a general-purpose program developed for solving various ODEs.

Based on the complementary energy principle, a simplified method applied to arbitrary cross-section thin-walled members under transverse and torsional loading is proposed in this paper. In this method, by considering the warping deformations of the cross-section and shearing deformations in the mid-surface of the thin wall, the shear lag phenomena can be reflected. The longitudinal stress is assumed to be the sum of two parts in the present method, i.e. the stress of the classical beam theory and a set of self-equilibrium stresses. The self-equilibrium stress is then assumed to be a B-3 spline function of s with unknown coefficients which are functions of z , where s is the curvilinear coordinate along the central line of the cross-section and z is the coordinate of the longitudinal axis of the thin-walled member. Finally, a group of ordinary differential equations can be obtained by means of the complementary energy principle. Solving these equations with related natural boundary conditions, a closed-form of solution can be obtained. Three numerical examples are reported to demonstrate the versatility and accuracy of the method. Because of significant reduction of computational time involved, when compared with the finite element method, the method will be very useful in practical design, especially at the preliminary stage.

The free vibration analysis of doubly curved shells is accomplished by the spline finite strip method. The method is quite general in that the shell surfaces can be of any shape but their boundaries have to be the co-ordinate lines: i.e., the principal curvature lines of the surfaces due to the strain-displacement formulations used in the present paper. Numerical examples of various shell surfaces are employed to demonstrate the accuracy and versatility of the method.

The space-time distribution of a pulsed magnetic field in the space within the waveguide-flanges boundary was calculated by the use of a nonuniform divided coil model and numerical method. The magnetic field line configuration was measured experimentally by the patterned iron powder. The results of calculations and measurements were discussed and a problem that should be noticed in the operational design of an intense pulsed electron beam accelerator was pointed out.