A Lie-group adaptive differential quadrature method to identify an unknown force in an Euler–Bernoulli beam equation

We recover an unknown space–time-dependent force in an Euler–Bernoulli beam vibration equation by an effective combination of the Lie-group adaptive method (LGAM) and the differential quadrature method (DQM). The layer-stripping technique is used to simplify this identification problem. The DQM is a feasible tool to semi-discretize the Euler–Bernoulli beam equation into a system of ordinary differential equations (ODEs) in time. Then, we can develop a two-point Lie-group equation to recover the unknown force through a few iterations. The success of the present method hinges on a rationale that the local in time ODEs and the global in time algebraic Lie-group equation have to be self-adapted during the iteration processes. The feasibility, accuracy and efficiency of the present method are assessed by comparing the estimated results with some exact solutions.     

A Hermite DRK interpolation-based collocation method for the analyses of Bernoulli–Euler beams and Kirchhoff–Love plates

A Hermite differential reproducing kernel (DRK) interpolation-based collocation method is developed for solving fourth-order differential equations where the field variable and its first-order derivatives are regarded as the primary variables. The novelty of this method is that we construct a set of differential reproducing conditions to determine the shape functions of derivatives of the Hermite DRK interpolation, without directly differentiating it. In addition, the shape function of this interpolation at each sampling node is separated into a primitive function possessing Kronecker delta properties and an enrichment function constituting reproducing conditions, so that the nodal interpolation properties are satisfied for the field variable and its first-order derivatives. A weighted least-squares collocation method based on this interpolation is developed for the static analyses of classical beams and plates with fully simple and clamped supports, in which its accuracy and convergence rate are examined, and some guidance for using this method is suggested.     

A note on the integrability of a remarkable static Euler–Bernoulli beam equation

It has recently been shown that the fourth-order static Euler–Bernoulli ordinary differential equation, where the elastic modulus and the area moment of inertia are constants and the applied load is a function of the normal displacement, in the maximal case has three symmetries. This corresponds to the negative fractional power law y ^?5/3, and the equation has the nonsolvable algebra ${sl(2, \mathbb{R})}$ . We obtain new two- and three-parameter families of exact solutions when the equation has this symmetry algebra. This is studied via the symmetry classification of the three-parameter family of second-order ordinary differential equations that arises from the relationship among the Noether integrals. In addition, we present a complete symmetry classification of the second-order family of equations. Hence the admittance of ${sl(2, \mathbb{R})}$ remarkably allows for a three-parameter family of exact solutions for the static beam equation with load a fractional power law y ^?5/3.     

A general method for analyzing moderately large deflections of a non-uniform beam: an infinite Bernoulli–Euler–von Kármán beam on a nonlinear elastic foundation

The present paper concerns a semi-analytical procedure for moderately large deflections of an infinite non-uniform static beam resting on a nonlinear elastic foundation. To construct the procedure, we first derive a nonlinear differential equation of a Bernoulli–Euler–von Kármán “non-uniform” beam on a “nonlinear” elastic foundation, where geometrical nonlinearities due to moderately large deflection and beam non-uniformity are effectively taken into account. The nonlinear differential equation is transformed into an equivalent system of nonlinear integral equations by a canonical representation. Based on the equivalent system, we propose a method for the moderately large deflection analysis as a general approach to an infinite non-uniform beam having a variable flexural rigidity and a variable axial rigidity. The method proposed here is a functional iterative procedure, not only fairly simple but straightforward to apply. Here, a parameter, called a base point of the method, is also newly introduced, which controls its convergence rate. An illustrative example is presented to investigate the validity of the method, which shows that just a few iterations are only demanded for a reasonable solution.     

The method of fundamental solutions with dual reciprocity for diffusion and diffusion–convection using subdomains

The method of fundamental solutions (MFS), first proposed in the 1960s, has recently reappeared in the literature and solutions of an extraordinary accuracy have been reported using relatively few data points. The method requires no mesh and therefore no integration, and has been recently combined with dual reciprocity method (DRM) for treating inhomogeneous terms. The objective of this paper is the combination of the two methods for treating convective terms which are derivatives of the problem variable. First the formulation of the methods for mixed Neumann–Dirichlet boundary conditions is considered, as both these types of boundary condition are necessary for this type of problem. Next a formulation for the usual Crank–Nickleson and Galerkin time-stepping procedures is obtained for both diffusion and diffusion–convection and the use of the subdomain technique with MFS is considered. Finally results obtained for some test problems are presented including a diffusion convection problem with variable velocity using both a single domain and a division into subregions, the convective terms being modeled using DRM. Results are compared with exact solutions and in some cases with DRBEM examples from the literature.     

A dual reciprocity boundary element formulation using the fractional step method for the incompressible Navier–Stokes equations

This paper presents a dual reciprocity boundary element solution method for the unsteady Navier–Stokes equations in two-dimensional incompressible flow, where a fractional step algorithm is utilized for the time advancement. A fully explicit, second-order, Adams–Bashforth scheme is used for the nonlinear convective terms. We performed numerical tests for two examples: the Taylor–Green vortex and the lid-driven square cavity flow for Reynolds numbers up to 400. The results in the former case are compared to the analytical solution, and in the latter to numerical results available in the literature. Overall the agreement is excellent demonstrating the applicability and accuracy of the fractional step, dual reciprocity boundary element solution formulations to the Navier–Stokes equations for incompressible flows.     

Failure mode and effects analysis using function–motion–action decomposition method and integrated risk priority number for mechatronic products

Failure mode and effects analysis is a widely applied risk assessment method in various engineering and management domains. However, the identification of failure modes is difficult and uncountable. Therefore, a function–motion–action (FMA) decomposition method is developed to identify failure modes from the perspective of motion and extraordinarily suitable for mechatronic products. In the typical risk assessment, the ranking orders of failure modes are determined by risk priority number (RPN), which has been criticized for several drawbacks and improved by some alternative RPNs, but some drawbacks still exist, such as duplicate values, narrow admissible value range, and missing failure modes’ and risk factors’ weights. This study formulates several alternative weighted RPNs to overcome the above drawbacks, and the final ranking orders of failure modes are garnered through the integrated RPN (IRPN). First, failure modes are identified via the proposed FMA decomposition method and evaluated with crisp values, whose weights are aggregated from the basic failure modes’ weights. Second, the weights of the basic failure modes, risk factors and different RPN methods are derived from analytic hierarchy process. Third, the conditional weights of risk factors are determined by incorporating risk factors’ weights and failure modes’ conditional weights deduced from Shannon entropy. Next, several alternative weighted RPNs and IRPN are formulated to rank failure modes’ risk levels. Finally, an illustrative example about computer numerical control machine center is presented to demonstrate the application and effectiveness of the proposed method.     

An experimental method for determining the total efficiency and the response function of a gamma-ray detector in the range 0.5–10 MeV

An experimental method is presented for the determination of the total efficiency and the response function of a γ-ray detector in the range 0.5–10 MeV. It consists of observing (p, γ) resonance reactions with two detectors: the one to be calibrated, in this case a cylindrical deuterated hexabenzene liquid scintillator, and a Ge detector used to select and resolve the main two-step cascades of the reaction. Efficiencies and response functions were obtained for thirteen γ-rays via the coincidence method, using targets of ²⁶Mg at proton energies of 1001 and 2220 keV, of ³⁰Si at 1398 keV and of ³⁴S at 1211 keV.The weighting function derived from these data was used to determine the capture area of the 1.15 keV neutron resonance in ⁵⁶Fe. By normalizing the data to the 5.2 eV resonance in ¹⁰⁹Ag, a value (gΓ_nΓ_γ/Γ) = 57.1 ± 2.1 meV was obtained, in excellent agreement with the result of recent transmission measurements.     

An analysis for the elasto-plastic problem of the moderately thick plate using the meshless local Petrov–Galerkin method

A meshless local Petrov–Galerkin method for the analysis of the elasto-plastic problem of the moderately thick plate is presented. The discretized system equations of the moderately thick plate are obtained using a locally weighted residual method. It uses a radial basis function (RBF) coupled with a polynomial basis function as a trial function, and uses the quartic spline function as a test function of the weighted residual method. The shape functions have the Kronecker delta function properties, and no additional treatment to impose essential boundary conditions. The present method is a true meshless method as it does not need any grids, and all integrals can be easily evaluated over regularly shaped domains and their boundaries. An incremental Newton–Raphson iterative algorithm is employed to solve the nonlinear discretized system equation. Numerical results show that the present method possesses not only feasibility and validity but also rapid convergence for the elasto-plastic problem of the moderately thick plate.     

Strength and ductility of FRP web-bonded RC beams for the assessment of retrofitted beam–column joints

It is generally accepted that beam–column joints are critical elements of reinforced concrete (RC) buildings subjected to lateral loads, and that they may require specific design treatment following the accepted design philosophy of the strong-columnweak-beam. In earthquake-prone regions, the joints must be designed to allow the dissipation of large amounts of energy into the neighbouring elements without a significant loss of strength and ductility. The frames are often designed carefully based on the strong-column–weak-beam concept and their joints detailed accordingly. Sometimes, though, the detailing is inadequate (example, RC joints designed to earlier codes have insufficient lateral resistance). Web-bonded FRP (fibre reinforced plastic) is one of the few possible strengthening methods that can be used when an inadequately detailed joint is damaged causing severe degradation of the joint’s structural strength. In this paper, the results of some tests on FRP strengthened specimens are presented. The results show that the method is effective and capable of restoring or even upgrading the strength of the system. In addition, using the basic principles of equilibrium and compatibility, an analytical model is presented that simplifies the analysis and design of this strengthening scheme. Based on the model, a range of design graphs are presented for selection of the type and the amount of FRP required upgrading an existing joint to a specified moment capacity and curvature ductility.     

A numerical method based on the boundary integral equation and dual reciprocity methods for one-dimensional Cahn–Hilliard equation

This paper describes a numerical method based on the boundary integral equation and dual reciprocity methods for solving the one-dimensional Cahn–Hilliard (C–H) equation. The idea behind this approach comes from the dual reciprocity boundary element method that introduced for higher order dimensional problems. A time-stepping method and a predictor–corrector scheme are employed to deal with the time derivative and the nonlinearity respectively. Numerical results are presented for some examples to demonstrate the usefulness and accuracy of this approach. For these problems the energy functional dissipation and the mass conservation properties are investigated.     

A study aimed at determining and understanding the fracture behaviour of an Al–Li–Cu–Mg–Zr alloy 8090

The S-L fracture toughness of aluminium–lithium based alloys is generally poor and this has limited their applicability, particularly in aerospace where good damage tolerance is required. The low S-L toughness has been attributed variously to grain boundary precipitation, planar slip and lithium segregation. This work examined the S-L fracture behaviour of an 8090 Al–Li-based alloy in 34–45mm plate. The results confirmed that the S-L fracture toughness decreases from the centre to the surface of plate material and increases with double ageing. Fracture is principally intergranular, with both ductile and brittle components occurring, but some transgranular fracture also occurs and this produces steps in the fracture plane. Changes in the relative proportions of brittle and ductile intergranular fracture, as well as in the amount of transgranular fracture, accompany the changes in toughness. However, the decrease in fracture toughness across the plate is accompanied principally by an increase in the relative proportion of brittle intergranular fracture, while the toughening produced by double ageing is accompanied principally by an increase in the amount of transgranular fracture. Evidence of coarse slip, indicative of slip planarity, was seen from slip steps and dislocation structures. However, planar slip was seen only towards the centre of the plate and not towards the surface. The level of planar slip was not reduced markedly by double ageing. Texture varied with position across the plate. There were also a larger number of low angle boundaries towards the centre of the plate than towards the surface. The hardness did not change across the plate. The results could not be explained fully in terms of either the grain boundary precipitate theory or the planar slip model, but were generally consistent with the lithium segregation model. However, the basic tenet of this model is that the level of embrittlement is influenced by the grain boundary structure, and the results did not indicate a substantial difference between the boundaries that failed in a ductile manner and those which failed by brittle fracture. This suggests that the factors which affect lithium segregation may be more complex than originally envisaged.     

Effect of concentration and temperature on the properties of the microspheres prepared using an emulsion–solvent extraction process

Methylaluminoaxane (MAO) microspheres of average size smaller than 100 μm were prepared using a solvent extraction process; excess of perfluorocarbon (PFC) was added to the hydrocarbon-in-perfluorocarbon emulsion to solidify the MAO droplets. The effect of the MAO concentration in the dispersed phase, the temperature of the PFC added to the emulsion and the preparation temperature on the size, the size distribution and the morphology of the MAO microspheres was studied. MAO droplets broke up more easily with decreasing dispersed phase viscosity and hence the size of the MAO microspheres decreased. The temperature of the PFC added to the emulsion did not significantly affect the size and the morphology of the MAO microspheres. The size of the MAO microspheres increased with increasing preparation temperature. The main reason for the increased size of the MAO microspheres was the increased coalescence with increasing preparation temperature. In addition the porosity of the MAO microspheres increased with increasing preparation temperature.     

Synthesis of fullerene nanowhiskers using the liquid–liquid interfacial precipitation method and their mechanical,electrical and superconducting properties

Abstract

Fullerene nanowhiskers (FNWs) are thin crystalline fibers composed of fullerene molecules, including C₆₀, C₇₀, endohedral, or functionalized fullerenes. FNWs display n-type semiconducting behavior and are used in a diverse range of applications, including field-effect transistors, solar cells, chemical sensors, and photocatalysts. Alkali metal-doped C₆₀ (fullerene) nanowhiskers (C₆₀NWs) exhibit superconducting behavior. Potassium-doped C₆₀NWs have realized the highest superconducting volume fraction of the alkali metal-doped C₆₀ crystals and display a high critical current density (J_c) under a high magnetic field of 50 kOe. The growth control of FNWs is important for their success in practical applications. This paper reviews recent FNWs research focusing on their mechanical, electrical and superconducting properties and growth mechanisms in the liquid–liquid interfacial precipitation method.     

Synthesis of fullerene nanowhiskers using the liquid–liquid interfacial precipitation method and their mechanical,electrical and superconducting properties

Fullerene nanowhiskers (FNWs) are thin crystalline fibers composed of fullerene molecules, including C₆₀, C₇₀, endohedral, or functionalized fullerenes. FNWs display n-type semiconducting behavior and are used in a diverse range of applications, including field-effect transistors, solar cells, chemical sensors, and photocatalysts. Alkali metal-doped C₆₀ (fullerene) nanowhiskers (C₆₀NWs) exhibit superconducting behavior. Potassium-doped C₆₀NWs have realized the highest superconducting volume fraction of the alkali metal-doped C₆₀ crystals and display a high critical current density (J_c) under a high magnetic field of 50 kOe. The growth control of FNWs is important for their success in practical applications. This paper reviews recent FNWs research focusing on their mechanical, electrical and superconducting properties and growth mechanisms in the liquid–liquid interfacial precipitation method.     

Synthesis and electrochemical characterization of Li2MnO3–LiNixCOyMnzO2 cathode for lithium battery using co-precipitation method

The Li_xNi_0.23Co_0.12Mn_0.65O₂ electrode system with various compositions (x = 1.19, 1.33, 1.46, 1.58) was synthesized from a metal oxide precursor synthesized by co-precipitation method. The XRD patterns of the prepared powders revealed a hexagonal α-NaFeO₂ structure (space group: R-3m, 166) and the existence of a Li₂MnO₃ phase in the composite structure. In particular, the low Li content sample shows a three integrated structure (spinel, Li₂MnO₃, LiMO₂) for a Li/Metal(Ni/Co/Mn) mol ratio of 1.2. Scanning electron microscopy showed that all the synthesized samples contained spherical agglomerates with a size of 8–10 μm. Among the samples tested, Li_1.46Ni_0.23Co_0.12Mn_0.65O₂ shows relatively high charge and discharge capacity for the first cycle is 287, 192.9 mA h g^?1, respectively. Also, charge transfer resistance was also significantly improved compare with other samples.     

Strain–life curves of steels and methods for determining the curve parameters. Part 1. Conventional methods

The available publications give much consideration to strain–life curves which are usually described by the Basquin–Manson–Coffin equation. The parameters of this equation are related to those of the Ramberg–Osgood equation that represents the cyclic stress–strain diagram. Many different methods have been put forward for the assessment of parameters of these equations on the basis of static strength and plasticity characteristics. Most of the methods rely on a fairly small body of experimental evidence. Using the experimental data on static and cyclic strength and plasticity characteristics of about 200 various steels from the well-known publications, a statistical analysis of parameters of Basquin–Manson–Coffin and Ramberg–Osgood equations has been performed by each of the assessment methods, revealing their advantages and disadvantages.