An algorithm for the complete symmetry classification of differential equations based on Wu’s method

In this paper, an alternative algorithm which uses Wu’s method (differential characteristic set algorithm) for the complete symmetry classification of (partial) differential equations containing arbitrary parameter is proposed. The classification is determined by decomposing the solution set of determining equations into a union of a series of zero sets of differential characteristic sets of the corresponding differential polynomial system of the determining equations. Each branch of the decomposition yields a class of symmetries and associated parameters. The algorithm makes the classification become direct and systematic. This is also a new application of Wu’s method in the field of differential equations. As illustrative examples of our algorithm, the complete potential symmetry classifications of linear and nonlinear wave equations with an arbitrary function parameter and both classical and nonclassical symmetries of a parametric Burgers equation are presented.     

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.     

A fast multipole boundary element method based on the improved Burton–Miller formulation for three-dimensional acoustic problems

A fast multipole boundary element method (FMBEM) based on the improved Burton–Miller formulation is presented in this paper for solving large-scale three-dimensional (3D) acoustic problems. Some improvements can be made for the developed FMBEM. In order to overcome the non-unique problems of the conventional BEM, the FMBEM employs the improved Burton–Miller formulation developed by the authors recently to solve the exterior acoustic problems for all wave numbers. The improved Burton–Miller formulation contains only weakly singular integrals, and avoids the numerical difficulties associated to the evaluation of the hypersingular integral, it leads to the numerical implementations more efficient and straightforward. In this study, the fast multipole method (FMM) and the preconditioned generalized minimum residual method (GMRES) iterative solver are applied to solve system matrix equation. The block diagonal preconditioner needs no extra memory and no extra CPU time in each matrix–vector product. Thus, the overall computational efficiency of the developed FMBEM is further improved. Numerical examples clearly demonstrate the accuracy, efficiency and applicability of the FMBEM based on improved Burton–Miller formulation for large-scale acoustic problems.     

An experimental study on the mechanical properties of rat brain tissue using different stress–strain definitions

There are different stress–strain definitions to measure the mechanical properties of the brain tissue. However, there is no agreement as to which stress–strain definition should be employed to measure the mechanical properties of the brain tissue at both the longitudinal and circumferential directions. It is worth knowing that an optimize stress–strain definition of the brain tissue at different loading directions may have implications for neuronavigation and surgery simulation through haptic devices. This study is aimed to conduct a comparative study on different results are given by the various definitions of stress–strain and to recommend a specific definition when testing brain tissues. Prepared cylindrical samples are excised from the parietal lobes of rats’ brains and experimentally tested by applying load on both the longitudinal and circumferential directions. Three stress definitions (second Piola–Kichhoff stress, engineering stress, and true stress) and four strain definitions (Almansi–Hamel strain, Green-St. Venant strain, engineering strain, and true strain) are used to determine the elastic modulus, maximum stress and strain. The highest non-linear stress–strain relation is observed for the Almansi–Hamel strain definition and it may overestimate the elastic modulus at different stress definitions at both the longitudinal and circumferential directions. The Green-St. Venant strain definition fails to address the non-linear stress–strain relation using different definitions of stress and triggers an underestimation of the elastic modulus. The results suggest the application of the true stress–true strain definition for characterization of the brain tissues mechanics since it gives more accurate measurements of the tissue’s response using the instantaneous values.     

Effects of Dy substitution for Sn on the solderability and mechanical property of the standard near eutectic Sn–Ag–Cu alloy

In this study, the solderability of Sn–3.5Ag–0.5Cu–xDy solders were investigated and the shear strength properties of joints with Cu substrate were investigated. The results indicated that a small amount Dy addition can improve the solderability, and the optimal amount of Dy was 0.025 wt%. The maximum shear strength can be found with 0.025 wt% Dy addition, improved by 74%. With the observation of the fracture morphology, it was found that a small amount Dy can improve the ductility of the solder joints; but excessive amount of Dy would deteriorate the shear strength and form large dimples on the fracture surface.     

Design of lead-free candidate alloys for high-temperature soldering based on the Au–Sn system

Au–Sn based candidate alloys have been proposed as a substitute for high-lead content solders that are currently being used for high-temperature soldering. The changes in microstructure and microhardness associated with the alloying of Ag and Cu to the Au rich side as well to the Sn rich side of the Au–Sn binary system were explored in this work. Furthermore, the effects of thermal aging on the microstructure and microhardness of these promising Au–Sn based ternary alloys were investigated. For this purpose, the candidate alloys were aged at a lower temperature, 150 °C for up to 1 week and compared with aging at 200 °C for respective durations. It was determined in this work that the candidate alloys on the Sn rich side were relatively more stable, i.e. only the aging temperature had a substantial impact on the microstructure and not the aging duration. The candidate alloys aged at 200 °C were substantially softer on the Au rich side than the candidate alloys on the Sn rich side. However, the difference in hardness narrowed down considerably between the candidate alloys on the Au rich side and the Sn rich side when subjected to aging at 150 °C.     

Nanocomposites based on MWCNT and styrene–butadiene–styrene block copolymers: Effect of the preparation method on dispersion and polymer–filler interactions

Composites of Kraton-D® 1102 BT (a styrene–butadiene–styrene block copolymer) and multi-walled carbon nanotubes (MWCNTs) were prepared by melt mixing. The composites were characterized by electrical conductivity measurements (Coleman’s method), mechanical properties (DMA and stress–strain tests), thermal stability (thermogravimetry) and morphology of dispersion (SEM). Finally, the resulting composites were compared with those made by the solution casting method. The results showed a strong influence of the preparation methodology on the final properties of the composites due to changes in morphology. Composites prepared by casting showed a higher electrical conductivity than extruded ones; the composites with 6 wt.% of MWCNT prepared by extrusion presented conductivity of the same order of magnitude as the composite with 1 wt.% of MWCNT prepared by casting – 10⁻³ to 10⁻⁴ S cm⁻¹. However, the extruded samples presented better mechanical properties than the casting ones.     

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.     

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.     

Design of lead-free candidate alloys for low-temperature soldering applications based on the hypoeutectic Sn–6.5Zn alloy

The coupling effect of both minor alloying addition and reducing the amount of Zn phase have been proposed as an important strategy to improve the integrity and reliability of eutectic Sn–9Zn solder joints. In this work, the changes in microstructures, thermal behaviors and mechanical properties associated with the alloying of Ni and Sb to eutectic Sn–Zn after reducing the amount of Zn phase were explored. Thermal analysis confirmed that Ni and Sb additions being effective in reducing the amount of undercooling, while the melting temperature and pasty range remained at the hypoeutectic Sn–6.5Zn level. The resulting ultimate (UTS), yield tensile strength (YS) and elongation (El) of Sn–6.5Zn–0.5Ni and Sn–6.5Zn–0.5Sb alloys were experimentally determined and compared with the corresponding results of plain Sn–6.5Zn solder alloy. It was found that the Sn–6.5Zn–0.5Ni and Sn–6.5Zn–0.5Sb alloys examined comply with the compromise between high mechanical strength and ductility. Microstructural analysis revealed that the origin of change in mechanical properties was attributed to the enhanced solid solution effect of Sb and the flower shaped (Ni, Zn)₃Sn₄ intermetallics (IMC) phase produced by Ni addition. The Sn–6.5Zn–0.5Sb alloy has the highest UTS and appropriate ductility of all alloys examined. This finding indicates the capability of newly developed ternary solder alloys to serve a much wider array of value-added applications.     

A comparative study of the physical and mechanical properties of three natural corals based on the criteria for bone–tissue engineering scaffolds

Coral has been used for bone grafts since 1970. Because coral has the advantages of good osteoconduction, biocompatibility, and biodegradation, it is also suitable for scaffolds used in bone–tissue engineering. However, the skeletons of different species of corals often vary significantly, and very few studies focus on the assessment of the permeability and mechanical properties of coral structure. In order to better understand the use of coral in bone tissue–engineering, we selected three typical models (Acropora sp., Goniopora sp., and Porites sp.) to analyze for pore size, porosity, permeability, and mechanical strength. We found Goniopora and Porites had homogenous structure and Acropora had oriented pores and irregular pore size. Acropora had the largest permeability, however, the transverse section was closed and the useful size was limited because of its habitat type. Porites had the smallest pore size and had the lowest permeability. Our data indicated that Goniopora sp. can be considered as the most promising source of scaffolds for bone–tissue engineering because of its high porosity (73%) and that its permeability and mechanics were similar to those in human cancellous bone. In conclusion, we analyzed the impact of the macroporous structure of coral on the permeability and mechanical properties that provide indicators for designing the optimal scaffold for bone–tissue engineering.     

A BEM formulation based on Reissner's hypothesis for analysing the coupled stretching–bending problem of building floor structures

In this work, a plate bending formulation of the boundary element method (BEM) based on the Reissner's hypothesis to perform linear analysis of plates reinforced by rectangular beams is extended to consider the beams not displayed over their middle surface. Therefore eccentricity effects are taken into account. The building floor structure is modelled as a stiffened plate which is treated as a single body without dividing it into beam and plate elements. Moreover the equilibrium and compatibility conditions are automatically imposed by the integral equations. In the proposed model the final system of equation is obtained by coupling the bending problem to the stretching problem. Besides, in order to reduce the number of degrees of freedom, both the displacements and tractions are approximated along the beam width, leading to a model where the values are defined on the beams axis. In order to validate the proposed formulation, the numerical results are compared to a well know finite element code.     

Strain–life curves of steels and methods for determining the curve parameters. Part 2. Methods based on the use of artificial neural networks

The authors look into the possibility of using artificial neural networks for predicting the deformation characteristics of steels (the parameters of the Basquin–Manson–Coffin strain–life curve equation) based on static strength and plasticity characteristics, by constructing four independent neural networks with different configurations of input and output data. The prediction of parameters of the Basquin–Manson–Coffin equation and the fatigue life calculations by means of artificial neural networks are demonstrated to provide a better accuracy in comparison to the available conventional methods.     

Influence of ultrasonication energy on the dispersion consistency of Al2O3–glycerol nanofluid based on viscosity data,and model development for the required ultrasonication energy density

Achieving homogenised and stable suspensions has been one of the important research topics in nanofluid investigations. Preparing nanofluids, especially from the two-step method, is often accompanied with varying degrees of agglomerations depending on some parameters. These parameters include the physical structure of the nanoparticle, the prevalent particle charge, the strength of van der Waals forces of attraction and repulsiveness strength. Amongst the methods of deagglomeration, the use of ultrasonic vibration is most popular for achieving uniform dispersion. However, there are very few works related to its effect on the thermo-physical properties of nanofluids, and above all, standardising the minimum required ultrasonication time/energy for nanofluids synthesis. In this work, the optimum energy required for uniform and initially stable nanofluid has been investigated through experimental study on the combined influence of ultrasonication time/energy, nanoparticle size, volume fraction and temperature on the viscosity of alumina–glycerol nanofluids. Three different sizes of alumina nanoparticles were synthesised with glycerol using ultrasonication-assisted two-step approach. The viscosities of the nanofluid samples were measured between temperatures of 20–70?°C for volume fractions up to 5%. Based on the present experimental results, the viscosity characteristics of the nanofluid samples were dependent on particle size, volume fraction and working temperature. Using viscometry, the optimum energy density required for preparing homogenous nanofluid was obtained for all particle sizes and volume fractions. Finally, an energy density model was derived using dimensionless analysis based on the consideration of nanoparticle binding/interaction energy in base fluid, particle size, volume fraction, temperature and other base fluid properties. The model's empirical constants were obtained using nonlinear regression based on the present experimental data.     

Response of dynamic systems to renewal impulse processes: Generating equation for moments based on the integro-differential Chapman–Kolmogorov equations

In the present paper the method is developed for the derivation of differential equations for statistical moments of the state vector (response) of a non-linear dynamic system subjected to a random train of impulses. The arrival times of the impulses are assumed to be driven by a non-Poisson counting process. The state vector of the dynamic system is then a non-Markov process and no method is directly available for the derivation of the equations for response moments. The original non-Markov problem is converted into a Markov one by recasting the excitation process with the aid of an auxiliary, pure-jump stochastic process characterized by a Markov chain. Hence the conversion is carried out at the expense of augmentation of the state space of the dynamic system by auxiliary Markov states. For the augmented problem the sets of forward and backward integro-differential Chapman–Kolmogorov equations are formulated. The general, generating equation for moments is obtained with the aid of the forward and backward integro-differential Chapman–Kolmogorov operators. The developed method is illustrated by the examples of several renewal impulse processes.     

Preparation and characterization of multi-walled carbon nanotube/hydroxyapatite nanocomposite film dip coated on Ti–6Al–4V by sol–gel method for biomedical applications: An in vitro study

In the present research, the introduction of multi-walled carbon nanotubes (MWCNTs) into the hydroxyapatite (HA) matrix and dip coating of nanocomposite on titanium alloy (Ti–6Al–4V) plate was conducted in order to improve the performance of the HA-coated implant via the sol–gel method. The structural characterization and electron microscopy results confirmed well crystallized HA–MWCNT coating and homogenous dispersion of carbon nanotubes in the ceramic matrix at temperatures as low as 500 °C. The evaluation of the mechanical properties of HA and HA/MWCNT composite coatings with different weight percentages of MWCNTs showed that the addition of low concentrations of MWCNTs (0.5 and 1 wt.%) had improved effect on the mechanical properties of nanocomposite coatings. Moreover, this in vitro study ascertained the biocompatibility of the prepared sol–gel-derived HA/MWCNT composite coatings.