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The purpose of this paper is to propose a hybrid mesh-free method based on generalized finite difference (GFD) and Newmark finite difference methods to study the elastic wave propagation in functionally graded nanocomposite reinforced by carbon nanotubes (FGNRCN). The presented hybrid mesh-free method is applied for a thick hollow cylinder, which is made of FGNRCN and excited by various mechanical shock loadings.

The FG nanocomposite cylinder is assumed to be under shock loading. The elastic wave propagation is obtained and studied for various nonlinear grading patterns and distributions of the aligned carbon nanotubes. The distribution of carbon naotubes in FG nanocomposite are considered to vary as nonlinear function of radius, which varies with various nonlinear grading patterns continuously through radial direction. The effective material properties of functionally graded carbon nanotube are estimated using a micro-mechanical model.

The mechanical shock analysis of FGNRCN thick hollow cylinder is carried out and the dynamic behavior of displacement field and the time history of radial displacement are obtained for various grading patterns. An effective hybrid mesh-free method based on GFD and Newmark finite difference methods is presented to calculate the average velocity of elastic wave propagation in FGNRCN. The average velocity of elastic wave propagation is obtained for various grading patterns and various kinds of volume fraction. The effects of some parameters on average velocity of elastic wave propagation are obtained and studied in detail.

The calculation of elastic radial wave propagation in a FGNRCN thick hollow cylinder is presented using a hybrid mesh-free method. The effects of some parameters on wave propagation such as various grading patterns of distribution of carbon nanotubes are studied in details.

The purpose of this paper is to study using thermoelectric module to harvest the waste heat from spindle units of machine tools and drive wireless sensors stable, thermal structure design and optimization of the thermoelectric module.

In this paper, mesh-free-based method, rather than the standard finite element method, is used to analyze the thermal behavior of the thermoelectric modules with different structure. After that, experiments are done to obtain the real power output performance of those modules and evaluate the performance of driving a wireless sensor with those modules.

The paper provides that the difference in geometry structure can cause apparent change in surface temperature of heat-conducting plate, and the optimized thermoelectric module could increase the output voltage by about 7 per cent compared with the one without optimization.

It is found that the structure changing of the thermoelectric module is not the only way to increase the harvesting power, so a high efficiency power manage system is needed to be studied in the future.

The paper includes implications for the development of self-powered wireless sensors in the spindle unit for machine tool monitoring.

The paper develops models of thermoelectric modules with different structures on a rotating spindle, and tests the performance of driving wireless sensors with those thermoelectric modules.

This paper describes the solution of a steady‐state natural convection problem in porous media by the radial basis function collocation method (RBFCM). This mesh‐free (polygon‐free) numerical method is for a coupled set of mass, momentum, and energy equations in two dimensions structured by the Hardy's multiquadrics with different shape parameter and different order of polynomial augmentation. The solution is formulated in primitive variables and involves iterative treatment of coupled pressure, velocity, pressure correction, velocity correction, and energy equations. Numerical examples include convergence studies with different collocation point density and arrangements for a two‐dimensional differentially heated rectangular cavity problem at filtration Rayleigh numbers Ra*=25, 50 and 100, and aspect ratios A=1/2, 1, and 2. The solution is assessed by comparison with reference results of the fine‐mesh finite volume method in terms of mid‐plane velocity components, mid‐plane and insulated surface temperatures, streamfunction minimum, and Nusselt number.

This study aims to propose a new numerical method for solving non-linear partial differential equations on irregular domains.

The main aim of the current paper is to propose a local meshless collocation method to solve the two-dimensional Klein-Kramers equation with a fractional derivative in the Riemann-Liouville sense, in the time term. This equation describes the sub-diffusion in the presence of an external force field in phase space.

First, the authors use two finite difference schemes to discrete temporal variables and then the radial basis function-differential quadrature method has been used to estimate the spatial direction. To discrete the time-variable, the authors use two different strategies with convergence orders O(τ1+γ) and O(τ2−γ) for 0 < γ < 1. Finally, some numerical examples have been presented to show the high accuracy and acceptable results of the proposed technique.

The proposed numerical technique is flexible for different computational domains.

Although high-order smooth reproducing kernel mesh-free approximation enables the analysis of structural vibrations in an efficient collocation formulation, there is still a lack of systematic theoretical accuracy assessment for such approach. The purpose of this paper is to present a detailed accuracy analysis for the reproducing kernel mesh-free collocation method regarding structural vibrations.

Both second-order problems such as one-dimensional (1D) rod and two-dimensional (2D) membrane and fourth-order problems such as Euler–Bernoulli beam and Kirchhoff plate are considered. Staring from a generic equation of motion deduced from the reproducing kernel mesh-free collocation method, a frequency error measure is rationally attained through properly introducing the consistency conditions of reproducing kernel mesh-free shape functions.

This paper reveals that for the second-order structural vibration problems, the frequency accuracy orders are p and (p − 1) for even and odd degree basis functions; for the fourth-order structural vibration problems, the frequency accuracy orders are (p − 2) and (p − 3) for even and odd degree basis functions, respectively, where p denotes the degree of the basis function used in mesh-free approximation.

A frequency accuracy estimation is achieved for the reproducing kernel mesh-free collocation analysis of structural vibrations, which can effectively underpin the practical applications of this method.

Traditional adaptive analysis based on a coarse mesh, using finite element method (FEM) analysis, produces the original solution. Then post-processing the result and figuring out the regions should be refined and these regions refined once. Finally, this new mesh is used to get the solution of first refinement. After several iterations of above procedures, we can achieve the last result that is closer to the true solution, which takes time, making adaptive scheme inpractical to engineering application. The paper aims to discuss these issues.

This paper based on FEM proposes a multi-level refinement strategy with a refinement strategy and an indicator. The proposed indicator uses value of the maximum difference of strain energy density among the elements that associated with one node, and divides all nodes into several categories based on the value. A multi-level refinement strategy is proposed according to which category the node belongs to refine different elements to different times rather than whether refine or not.

Multi-level refinement strategy takes full use of the numerical calculation, resulting in the whole adaptive analysis that only need to iterate twice while other schemes must iterate more times. Using much less times of numerical calculation and approaches, more accurate solution, making adaptive analysis more practical to engineering.

Multi-level refinement strategy takes full use of the numerical calculation, resulting in the whole adaptive analysis only need iterate twice while other schemes must iterate more times. using much less times of numerical calculation and approaches more accurate solution, making adaptive analysis more practical to engineering.

The purpose of this study is to analyze the transportation of heat and mass in three-dimensional (3D) shear rate-dependent viscous fluid. Thermal enhancement plays a significant role in industrial and engineering applications. For this, the authors dispersed trihybrid nanoparticles into the fluid to enhance the working fluid’s thermal enhancement.

The finite element method is a numerical scheme and is powerful in achieving convergent and grid-independent solutions compared with other numerical techniques. This method was initially assigned to structural problems. However, it is equally successful for computational fluid dynamics problems.

Wall shear stress has shown an increasing behavior as the intensity of the magnetic field is increased. Simulations have predicted that Ohmic heat in the case of trihybrid nanofluid (MoS₂–Al₂O₃–Cu/C₂H₆O₂) has the greatest value in comparison with mono and hybrid nanofluids. The most significant influence of chemical reaction on the concentration in tri-nanofluid is noted. This observation is pointed out for both types of chemical reaction (destructive or generative) parameters.

Through a literature survey, the authors analyzed that no one has yet to work on a 3D magnetohydrodynamics Carreau–Yasuda trihybrid nanofluid over a stretched sheet for improving heat and mass transfer over hybrid nanofluids. Herein, molybdenum disulfide (MoS₂), aluminum oxide (Al₂O₃) and copper (Cu) nanoparticles are mixed in ethylene glycol (C₂H₆O₂) to study the thermal enhancement and mass transport of their corresponding resultant mono (Cu/C₂H₆O₂), hybrid (Al₂O₃–Cu/C₂H₆O₂) and trihybrid (MoS₂–Al₂O₃–Cu/C₂H₆O₂) nanofluids.

To present an approach to parameterization based shape optimization of statically loaded structures and to propose its practical implementation.

In order to establish a convenient shape parameterization, the design element technique is employed. A rational Bézier body is used to serve as the design element. The design element is used to retrieve the nodal geometrical data of finite elements (FEs). Their field geometrical data are obtained using the FE own internal functions. For practical implementation it is proposed to establish the optimization cycle by two separately running processes. The data exchange is established by using self‐descriptive and platform‐independent XML conforming data files.

The proposed approach offers an unified approach to shape optimization of skeletal, as well as continuous structures. Structural shape may be varied smoothly with a relative small set of design variables. The employment of a gradient‐based optimization algorithm assures computational efficiency.

The aspects of FE mesh deterioration are not considered in this work. This would be necessary if for the actual problem at hand major and excessively non‐uniform shape changes of the FE mesh are expected.

A useful source of information for someone who is planning to develop a general or special‐purpose integrated structural analysis and shape optimization software.

The paper offers a rather simple, but quite powerful approach to structural shape optimization together with practical hints for its computational implementation.

A number of works have been published in the scientific literature proposing the solution of heat diffusion problems by first transforming the relevant partial differential equation to the frequency domain. The purpose of this paper is to present a mesh-free strategy to assess transient heat propagation in the frequency domain, also allowing incorporating initial non-zero conditions.

The strategy followed here is based in Kansa's method, using the MQ RBF as a basis function. The resulting method is truly mesh-free, and does not require any domain or boundary integrals to be evaluated. The definition of good values for the free parameter of the MQ RBF is also addressed.

The strategy was found to be accurate in the calculation of both frequency and time-domain responses. The time evolution of the temperature considering an initial non-uniform distribution of temperatures compared well with a standard time-marching algorithm, based on an implicit Crank-Nicholson implementation. It was possible to calculate frequency-dependent values for the free parameter of the radial basis function.

As far as the authors are aware, previous implementations of the frequency domain heat transfer approach required domain integrals to be evaluated in order to implement non-zero initial conditions. This is totally avoided with the present formulation. Additionally, the method is truly mesh-free, accurate and does not require any element or background mesh to be defined.

This paper aims to investigate the application of adaptive integration in element-free Galerkin methods for solving problems in structural and solid mechanics to obtain accurate reference solutions.

An adaptive quadrature algorithm which allows user control over integration accuracy, previously developed for integrating boundary value problems, is adapted to elasticity problems. The algorithm allows the development of a convergence study procedure that takes into account both integration and discretisation errors. The convergence procedure is demonstrated using an elasticity problem which has an analytical solution and is then applied to accurately solve a soft-tissue extension problem involving large deformations.

The developed convergence procedure, based on the presented adaptive integration scheme, allows the computation of accurate reference solutions for challenging problems which do not have an analytical or finite element solution.

This paper investigates the application of adaptive quadrature to solid mechanics problems in engineering analysis using the element-free Galerkin method to obtain accurate reference solutions. The proposed convergence procedure allows the user to independently examine and control the contribution of integration and discretisation errors to the overall solution error. This allows the computation of reference solutions for very challenging problems which do not have an analytical or even a finite element solution (such as very large deformation problems).