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This paper presents the findings of a large‐scale experimental study that focus on assessing structural behavior of reinforced concrete (RC) cantilever slabs with carbon/epoxy fiber‐reinforced polymer (CFRP) composite strips using a near‐surface‐mounted (NSM) approach. The NSM/CFRP system evaluated in this study was implemented in strengthening the shoulders of the Slide Canyon Bridge in California, USA. The experimental phase is divided into two main parts: (i) determining the design parameters for NSM, including the bondline strength through pull‐out tests, and (ii) conducting a practical evaluation of the bending behavior of original and retrofitted RC cantilever slabs, each with varying NSM reinforcement and three different development lengths. Results of this study indicated that the use of NSM‐CFRP has a considerable benefit in that it significantly improves ductility and changes the failure mode of the unstrengthened RC slab from the typical brittle shear‐based failure mode to a more ductile flexural‐based failure mode. The large‐scale slab specimens' performances, which had different development lengths, showed little variance, except for the slab specimen with a development length of 457.0 mm that exhibited an appreciable flexural stiffness as compared to other specimens evaluated in this study. In order to simulate the serviceability and ultimate behavior of the RC slab specimens, linear and nonlinear finite element analyses were performed. A satisfactory agreement between numerical and experimental results was achieved especially at load level prior the initiation of large‐size cracks. [ABSTRACT FROM AUTHOR]

Liquid sodium hybrid bearing is mechanical pump shaft bottom key support components, that play a balanced radial force of the impeller by fluid effect, in order to improve the bearing performance, based on the calculation model, simulation analysis, structure improvement and other aspects of analysis, this paper based on the theory of fluid mechanics of bearing finite element model for numerical calculation and analysis of flow field. Under different eccentricities and vibration velocities, the influence of structure improvement on bearing capacity is analysed. The results show that the bearing capacity of the liquid sodium hybrid bearing is mainly the hydrostatic bearing capacity, and the hydrodynamic pressure only plays an auxiliary role. After the improvement of the load‐bearing structure, the load‐bearing capacity is increased by 4%–7.3%. And the leakage is reduced by 27%–38% when the depth of the annular groove is 0.6 mm. [ABSTRACT FROM AUTHOR]

The focus of this paper is on the solution of Maxwell's equations for time-harmonic fields on triangular, possibly non-orthogonal meshes. The method described was first introduced in References 1 and 2 for eigenvalue problems arising in the design of accelerator components and dielectric loaded waveguides. It is based on the well-known Finite Integration Technique (FIT) which is a proven consistent discretization method for the computation of electromagnetic fields. The FIT-discretization on non-orthogonal 2D grids has close relations to the Nédélec elements or edge elements in the Finite Element Method. Revisiting FIT on triangular grids this paper intends to stimulate thorough studies of the latter subject which is well worth further investigations. Copyright © 1999 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

For the simulation of acoustic-structure interaction problems, the coupled field equations must be solved. The structure is commonly discretized using finite elements, whereas for the acoustic field the boundary element method (BEM) is favorable. A mortar BEM-FEM coupling algorithm is developed that allows the combination of non-conforming meshes. The high flexibility for the choice of discretizations offers a high efficiency, since specialized shape functions and adaptive mesh refinement can be used in the subdomains. The mortar coupling algorithm yields a saddle point problem that is solved using a preconditioned inexact Uzawa algorithm. The iterative solver enables the use of the fast multipole BEM and thus coupled simulations on large boundary element models. [ABSTRACT FROM AUTHOR]

The linear elasticity problem has important applications in structural analysis and engineering design. It is shown that the classical Crouzeix–Raviart finite element method is unstable to solve the linear elasticity eigenvalue problem with the pure traction boundary condition. In this paper, first we propose a new scheme with the stabilization terms. Then we prove the a priori error estimates for approximate eigenpairs. Finally, we carry out numerical experiments using the stabilized scheme. Theoretical analysis and numerical results show that this scheme is locking free and efficient. [ABSTRACT FROM AUTHOR]

In recent years, the propagation of ultrasonic guided waves (UGW) along the structure to inspect has amply proven to be an excellent strategy for the health monitoring of isotropic and composite structures (SHM—structural health monitoring). For the proper development of the SHM system, the finite element method (FEM) must be mentioned, since the possibility to study the UGW in very complex structures, even characterized by different materials. Successfully locating any possible damage and identifying its severity are key factors in SHM, thus allowing to reduce the design costs. Numerically, the damage can be modeled with several approaches but it is still not clear which is the best solution to accurately reproduce the UGW mechanisms in a faulty structure. The objective of this paper is to study the various effects that different severities of damage can have on UGW propagation. For the scope, various numerical approaches are considered and the results are compared. [ABSTRACT FROM AUTHOR]

Design approach against failure of the earth support using the finite element method The application of the finite element method (FEM) in geotechnical engineering has been established in the last decades for the prediction of deformations in the serviceability limit state (SLS). In practice, stability analyses in the ultimate limit state (ULS) are only partially performed using the FEM and are currently still state of the art. The next generation of Eurocode 7 is intended to regulate numerical methods with regard to their application in the ULS. However, the handling of the additionally required analysis of the German National Annex and DIN 1054 is still unsolved. In this paper, an approach for the numerical analysis of the earth support is presented. Following the well‐established strength reduction method, the weight of the soil γ and the cohesion c' ${{c}^{{ {\prime}}}}$ on the earth resistance side are reduced until failure occurs. On the basis of this, the analysis in ULS is carried out by defining a safety factor for the existing embedment depth of the retaining wall. This is followed by a comparison with the analytical free earth support method, identifying system reserves using the FEM. [ABSTRACT FROM AUTHOR]

In this paper, we propose and analyze the numerical algorithms for fast solution of periodic elliptic problems in random media in ℝd$$ {\mathbb{R}}^d $$, d=2,3$$ d=2,3 $$. Both the two‐dimensional (2D) and three‐dimensional (3D) elliptic problems are considered for the jumping equation coefficients built as a checkerboard type configuration of bumps randomly distributed on a large L×L$$ L\times L $$, or L×L×L$$ L\times L\times L $$ lattice, respectively. The finite element method discretization procedure on a 3D n×n×n$$ n\times n\times n $$ uniform tensor grid is described in detail, and the Kronecker tensor product approach is proposed for fast generation of the stiffness matrix. We introduce tensor techniques for the construction of the low Kronecker rank spectrally equivalent preconditioner in a periodic setting to be used in the framework of the preconditioned conjugate gradient iteration. The discrete 3D periodic Laplacian pseudo‐inverse is first diagonalized in the Fourier basis, and then the diagonal matrix is reshaped into a fully populated third‐order tensor of size n×n×n$$ n\times n\times n $$. The latter is approximated by a low‐rank canonical tensor by using the multigrid Tucker‐to‐canonical tensor transform. As an example, we apply the presented solver in numerical analysis of stochastic homogenization method where the 3D elliptic equation should be solved many hundred times, and where for every random sampling of the equation coefficient one has to construct the new stiffness matrix and the right‐hand side. The computational characteristics of the presented solver in terms of a lattice parameter L$$ L $$ and the grid‐size, nd$$ {n}^d $$, in both 2D and 3D cases are illustrated in numerical tests. Our solver can be used in various applications where the elliptic problem should be solved for a number of different coefficients for example, in many‐particle dynamics, protein docking problems or stochastic modeling. [ABSTRACT FROM AUTHOR]

In this paper, we adopt the discontinuous Galerkin finite element method and the enriched Crouzeix‐Raviart finite element method to study the magnetohydrodynamic (MHD) Stokes eigenvalue problem describing the flow of a viscous and electrically conducting fluid in a duct under the influence of a uniform magnetic field. We give the convergence and error analysis for the approximations, and the theoretical analysis and numerical experiments show that the methods are effective and can be applied to general domains. We also explore the influence of the Hartmann number on the eigenpairs and the consequential variation of the eigenstructure with the magnetic field by numerical experiments. [ABSTRACT FROM AUTHOR]

It is difficult to separate Luer lock adapters during the external ventricular drainage (EVD) since they are often connected by a threaded connection, and the infusion needle put into the patient's body gets pulled out when extubation occurs unexpectedly. The paper described a new magnetic connection assembly made up of ring magnetic permanents and a Hall sensor that could be used to replace Luer lock adapters for quicker disconnection and reconnection of the drainage catheter. For the design and analysis of the device, the finite element method magnetics (FEMM) was used to estimate the size of magnetic permanents and the best detection site of the Hall sensor for detecting whether the magnetic permanents were closely attracted and/or pulled apart. Then an experiment was conducted to confirm our findings. Both simulation and experiment revealed that a pair of hollow cylindrical magnetic permanents, each with height 10 mm, outer diameter 8 mm, and inner diameter 4 mm, could achieve the same force as the Luer lock adapters held, and that the best Hall sensor detection position was in the middle of the permanent magnets, with a radial distance of about 2 mm. [ABSTRACT FROM AUTHOR]

The effect of openings left in reinforced concrete shear walls due to functional requirements or architectural reasons is an important issue that should not be underestimated mainly since shear walls are considered as one of the most critical load‐carrying members in a structure owing to playing an active role against seismic forces. In this paper, a parametric study was carried out by creating a nonlinear finite element model to determine the effects of openings in reinforced concrete shear walls on the maximum shear force bearing capacities, initial stiffness, displacement ductility ratios, and energy dissipation capacities of the shear walls. The variables examined in the study were the size of the openings left in the reinforced concrete shear walls, opening location, the number of openings, and the concrete compressive strength used in the production of the shear walls. In the first part of the study, nonlinear finite element models of three experimental shear wall test elements: one with no opening (solid), and two with openings: were created using ABAQUS finite element software package, then verified by comparing the numerical analysis results with the experimental results. In the second part of the study, a nonlinear finite element model of 44 reinforced concrete shear walls, including the parameters planned to be investigated, was created by using the verified model, and finite element model (FEM) analyses were performed. As a result of numerical analyses, a capacity reduction coefficient proposal has been developed to calculate the shear force capacities of reinforced concrete shear walls with openings. [ABSTRACT FROM AUTHOR]

Unlocking the biomechanical effects of cervical spine positioning rotation manipulation in the treatment of patients with neck pain. In this paper, the safety of the cervical positioning rotation manipulation is analyzed by experimentally obtaining head kinematic data, importing them into a finite element model that has been developed and validated, and calculating and analyzing the angular displacements, disc pressures, and articular surface contact forces in the normal and pathological models. The results show that the cervical spine positioning rotation technique is more effective in adjusting the position and applying force to the cervical spine C5–C6 "tendon out of the groove and bone misalignment" pathological model. Also, the cervical positioning rotation manipulation is applied with less variation in disc nucleus pulposus pressure than in the non‐positioning situation. Thus, in patients with disc degeneration, cervical positioning rotational manipulation has a more direct mechanical effect and is safer than non‐positioning rotational manipulation. The cervical spine positioning rotation manipulation is a safe method that can effectively treat patients with neck pain. It has been well demonstrated in the computational analysis of the pathological model. [ABSTRACT FROM AUTHOR]

This paper analyses the performance of the experimental setups to assess the punching strength of slab‐column connections in continuous flat slabs under vertical and horizontal loading. In the last years, several experimental campaigns have been performed to investigate the punching strength of slab‐column connections, but most of the experimental tests concerned isolated slab‐column connections. Among the few setups aimed at reproducing the eccentric punching failure in continuous flat slabs, the setup developed at the NOVA School of Science and Technology in Lisbon is considered in this paper. The performance of the Lisbon setup is assessed through nonlinear finite element analyses, calibrated on experimental data, by comparison with numerical results of a theoretical continuous setup. Then, the performance of the isolated setups, used in many researches and at the base of some international codes, is also evaluated through the same finite element model. Numerical analyses highlight that the setup developed in Lisbon could provide reliable ultimate rotations of continuous flat slab connections, but it underestimates the punching strength. Despite isolated setups lead to similar results when compared with the Lisbon setup, the latter seems to provide a better representation of a continuous slab‐column connection. The numerical analyses presented in this paper have been performed assuming monotonic lateral loading. [ABSTRACT FROM AUTHOR]

The paper presents the tridimensional numeric model of an inner slab‐column connection of reinforced concrete, which was previously tested against the punching shear in the lab of the University of Brasília. The numerical analysis has been carried out by the finite element method, using the software ABAQUS. To evaluate the sensitivity of the main factors that influence the responses of the model, a parametric investigation was conducted as per the finite element mesh, mechanical properties of the concrete and plastic parameters of the assumed model for the concrete, named by concrete damaged plasticity model (CDPM). The results of the resistance capacity, displacements, strains, cracking pattern, and failure mode were compared with those obtained experimentally. From this comparison, it was concluded that the numerical model was able to reproduce the punching shear phenomenon with a high level of precision. [ABSTRACT FROM AUTHOR]

As one kind of jacketed vessels, half‐pipe jacketed vessels are widely used in engineering owing to the structural and heat transfer advantages. But for the design of half‐pipe jacketed vessels, there are limitations in codes ASME VIII‐1 and ASME VIII‐2. In this paper, a new design method based on numerical limit‐load analysis is proposed to design half‐pipe jacketed vessels. The scheme and advantages of the method are presented through a design of half‐pipe jacketed vessel. It is found that by performing limit‐load analysis, problems of the codes ASME VIII‐1 and ASME VIII‐2 about the structural limitation of the half‐pipe jacketed vessels and loading limitation are solved. In addition, by performing limit‐load and parametric analysis, the strength weakness areas on the vessels can be found, and the rational strength design of a structure can be achieved. [ABSTRACT FROM AUTHOR]

Intrinsic localized mode (ILM) can be generated in multiple mass‐spring systems using nonlinear springs, and ILM has attracted a lot of attention due to its special vibration modes that are not found in linear systems. However, the difficulty of creating nonlinearity remains a barrier to ILM research. In this paper, we propose a rotating magnetic spring based on magnetic nonlinearity. The nonlinear restoring properties of the proposed magnetic spring are confirmed by finite element method (FEA). Finally, using the restoring properties obtained from FEA, it is shown that ILM can be excited by MATLAB numerical analysis. © 2021 Institute of Electrical Engineers of Japan. Published by Wiley Periodicals LLC. [ABSTRACT FROM AUTHOR]

In this paper, we apply the characteristic finite volume method (CFVM) for solving a convection‐diffusion problem on two‐dimensional triangular grids. The finite volume method is used to discretize the equation while the finite element method is applied to estimate the gradient quantities at cell faces. The numerical analysis of the convergence has been implemented for the CFVM in one‐dimension. The approximate L2 norm of the error is derived to determine the errors for the approximate solution. The accuracy of four piecewise linear reconstruction techniques, namely, Frink, Holmes‐Connell, Green‐Gauss, and least‐squares methods are investigated on structured triangular grids. Numerical evidence shows that the least‐squares method is the most accurate of all methods for smooth initial condition problems. For discontinuous initial condition problems, the Frink and the Holmes‐Connell methods give a spurious oscillating solution in the vicinity of the discontinuity upstream of the discontinuity, and the Green‐Gauss and least‐squares methods give a spurious oscillating solution in the vicinity of the discontinuity downstream of the discontinuity. Moreover, the amplitude of the oscillation could be amplified on the finer grid sizes. [ABSTRACT FROM AUTHOR]

Inclusion is one of the main causes for unqualified wire. However, the forming mechanism of drawing fracture due to inclusions is still unclear. Therefore, it is significant to figure out the forming mechanism of wire drawing fracture with inclusions for designing and manufacturing high‐quality wires. In this paper, a physical model of wire with inclusion is established based on experimental observations. Multipass drawing is simulated by using finite element method (FEM) with the developed numerical damage modeling. Numerical results demonstrate that the damage increases with the development of drawing progress, and the damage caused by high elastic modulus of inclusion is greater than that of low elastic modulus. Pen‐tip shaped fracture of wire with inclusions is mainly caused by the superposition of core and external V‐shaped damage. Furthermore, the core V‐shaped crack will propagate along the external V‐shaped damage area. [ABSTRACT FROM AUTHOR]

Summary: This paper concentrates on strong delay‐independent stability of neutral linear time‐invariant delay systems with multiple commensurate time delays. The stability analysis of linear neutral systems is complicated by the need to locate the roots of a transcendental characteristic equation and to take into account the global hyperbolicity of an associated difference system. In this paper, we propose a convex necessary and sufficient condition for testing strong delay‐independent stability. This result mainly follows from Kronecker sum properties and the Kalman‐Yakubovich‐Popov lemma, which allows us to present the main result in terms of a single linear matrix inequality feasibility test. The paper is closed by showing numerical examples that illustrate the applicability and effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

In this paper, we propose a Galerkin finite element method for the Cahn‐Hilliard‐Cook equation involving the Caputo‐type fractional derivative, which can be used to describe the interface phenomena for modeling the phase transitions with the random effects and the properties of shape memory. The regularity properties of mild solution to the given problem are presented, and a result concerning the convergence error estimate of the corresponding semidiscrete scheme is established. Finally, we construct the fully discrete scheme based on the approximations of the Mittag‐Leffler function, and the strong convergence error estimate of the proposed scheme is also studied. [ABSTRACT FROM AUTHOR]

In this paper, numerical limit analysis is applied to evaluate the bearing capacity of a single rigid pile embedded in a ponderable homogeneous cohesive‐frictionless soil subjected to vertical, horizontal, and moment (VHM) loading combinations. All loads act in the same plane. Accurate lower and upper bounds are calculated using finite element limit analysis code OPTUMG3. As the gap between the bounds hardly exceeds 5%, the average limit load provides a good estimate of the exact ultimate load and can be used with confidence for design purposes. By adopting typical values for the dimensionless pile length‐to‐diameter ratio, most cases of practical interest are treated. The numerical results are compared against failure surfaces predicted by theories from the literature. Comparison shows that previously developed methods can be conservative or slightly overestimates the limit loads. New design charts are provided. The safe loads domain is constructed in the VHM space using the average limit load. Closed‐form expressions are proposed to describe the native and the normalized VMH failure envelope as a function of the pile length‐to‐diameter ratio. In the VH plane, the failure surface is described by an eccentric superellipse, whereas in the MH plane, the limit curve is an inclined ellipse. [ABSTRACT FROM AUTHOR]

In this paper, we introduce numerical schemes and their analysis based on weak Galerkin finite element framework for solving 2‐D reaction–diffusion systems. Weak Galerkin finite element method (WGFEM) for partial differential equations relies on the concept of weak functions and weak gradients, in which differential operators are approximated by weak forms through the Green's theorem. This method allows the use of totally discontinuous functions in the approximation space. In the current work, the WGFEM solves reaction–diffusion systems to find unknown concentrations (u, v) in element interiors and boundaries in the weak Galerkin finite element space WG(P0, P0, RT0). The WGFEM is used to approximate the spatial variables and the time discretization is made by the backward Euler method. For reaction–diffusion systems, stability analysis and error bounds for semi‐discrete and fully discrete schemes are proved. Accuracy and efficiency of the proposed method successfully tested on several numerical examples and obtained results satisfy the well‐known result that for small values of diffusion coefficient, the steady state solution converges to equilibrium point. Acquired numerical results asserted the efficiency of the proposed scheme. [ABSTRACT FROM AUTHOR]

In this paper, we consider the effect of adding a coarse mesh correction to the two‐grid algorithm for the mixed Navier–Stokes/Darcy model. The method yields both L2 and H1 optimal velocity and piezometric head approximations and an L2 optimal pressure approximation. The method involves solving one small, coupled, nonlinear coarse mesh problem, two independent subproblems (linear Navier–Stokes equation and Darcy equation) on the fine mesh, and a correction problem on the coarse mesh. Theoretical analysis and numerical tests are done to indicate the significance of this method. [ABSTRACT FROM AUTHOR]

In this paper we provide key estimates used in the stability and error analysis of discontinuous Galerkin finite element methods (DGFEMs) on domains with curved boundaries. In particular, we review trace estimates, inverse estimates, discrete Poincaré–Friedrichs' inequalities, and optimal interpolation estimates in noninteger Hilbert–Sobolev norms, that are well known in the case of polytopal domains. We also prove curvature bounds for curved simplices, which does not seem to be present in the existing literature, even in the polytopal setting, since polytopal domains have piecewise zero curvature. We demonstrate the value of these estimates, by analyzing the IPDG method for the Poisson problem, introduced by Douglas and Dupont, and by analyzing a variant of the hp‐DGFEM for the biharmonic problem introduced by Mozolevski and Süli. In both cases we prove stability estimates and optimal a priori error estimates. Numerical results are provided, validating the proven error estimates. [ABSTRACT FROM AUTHOR]

In this paper, we present the numerical analysis on high order dual parametric finite element methods for the cavitation computation problems in nonlinear elasticity, which leads to a meshing strategy assuring high efficiency on numerical approximations to cavity deformations. Furthermore, to cope with the high order approximation of the finite element methods, properly chosen weighted Gaussian type numerical quadrature is applied to the singular part of the elastic energy. Our numerical experiments show that the high order dual parametric finite element methods work well when coupled with properly designed weighted Gaussian type numerical quadratures for the singular part of the elastic energy, and the convergence rates of the numerical cavity solutions are shown to be significantly improved as expected. [ABSTRACT FROM AUTHOR]

This paper presents a numerical solution of the coupled system of the time‐dependent Stokes and fully dynamic Biot equations. The numerical scheme is based on standard inf‐sup stable finite elements in space and the Backward Euler scheme in time. We establish stability of the scheme and derive error estimates for the fully discrete coupled scheme. To handle realistic parameters which may cause nonphysical oscillations in the pore fluid pressure, a heuristic stabilization technique is considered. Numerical errors and convergence rates for smooth problems as well as tests on realistic material parameters are presented. [ABSTRACT FROM AUTHOR]

In this paper, we numerically analyse a phase‐lag model with two temperatures which arises in the heat conduction theory. The model is written as a linear partial differential equation of third order in time. The variational formulation, written in terms of the thermal acceleration, leads to a linear variational equation, for which we recall an existence and uniqueness result and an energy decay property. Then, using the finite element method to approximate the spatial variable and the implicit Euler scheme to discretize the time derivatives, fully discrete approximations are introduced. A discrete stability property is proved, and a priori error estimates are obtained, from which the linear convergence of the approximation is derived. Finally, some one‐dimensional numerical simulations are described to demonstrate the accuracy of the approximation and the behaviour of the solution. [ABSTRACT FROM AUTHOR]

In this paper, the advantages of numerical simulation to improve the process of copper electroforming are demonstrated. In this regard, the finite element model of copper electroforming for a rotating cone electrode was first prepared and then, the effect of the key parameters, such as applied current density, solution conductivity, electrode spacing, and anode height, on the uniformity of the thickness was investigated. The model combines tertiary current distribution with Bulter–Volmer electrode kinetics and computational fluid dynamics at the turbulent condition. In order to validate the model, a cone‐shaped shell was produced by electroforming method in the laboratory. The obtained results illustrate that the tertiary current distribution model on the rotating cone cell cathode is accurate and efficient for the electroforming process simulation and it can be used for parametric studies. Moreover, the effect of the current density on the morphology and properties of the electroformed layer was investigated. [ABSTRACT FROM AUTHOR]

In this paper, we will investigate a two grid finite element discretization method for the semi‐linear hyperbolic integro‐differential equations by piecewise continuous finite element method. In order to deal with the semi‐linearity of the model, we use the two grid technique and derive that once the coarse and fine mesh sizes H, h satisfy the relation h = H2 for the two‐step two grid discretization method, the two grid method achieves the same convergence accuracy as the ordinary finite element method. Both theoretical analysis and numerical experiments are given to verify the results. [ABSTRACT FROM AUTHOR]

Cracking is an important phenomenon in the failure of geomaterials. The prediction of crack paths is difficult and challenging because of the randomness and uncertainty in the cracking behaviors of geomaterials. In this paper, to predict crack paths based on 2D X‐ray computed tomography (CT) images, a digital energy grade‐based approach is proposed, and the corresponding energy principle is established. Excellent consistency of crack paths is found between the predicted crack path and the real crack path of the specimen. The numerical results indicate that the proposed approach provides a useful way to predict cracking paths in geomaterials. Meanwhile, the stress and displacement fields before and after the specimen fails can be obtained by combining the proposed method with finite element (FE) analysis. In total, this proposed method can be applied not only to monitoring the health of but also to the stability analysis of engineering structures during engineering activities. [ABSTRACT FROM AUTHOR]

This paper presents a better understanding of the use of finite integration techniques (FIT) and finite element method (FEM) in different types of microstrip antennas in order to determine which numerical method gives relatively more accurate results. Although the theoretical formulation based on Maxwell's equations of both FEM and FIT are approached from different aspects in the literature, there is still a lack of comparison of the same antenna type using different numerical methods employing FEM and FIT. Therefore, in this study, FEM and FIT were applied to two different types of microstrip antennas, and their simulation and experimental results was compared. For the first antenna demonstration, a multilayer structure was chosen to achieve one of the significant parameters. Then, a microstrip antenna with a compact structure was used in the second demonstration. Using these two antennas, the accuracy of FEM and FIT in different structures were compared and all simulated return loss and gain results were verified by the measured results. The experimental demonstrations show that FEM performs better for both types of microstrip antennas while FIT provides an adequate result for two‐layer microstrip antennas. [ABSTRACT FROM AUTHOR]

Summary: In this paper, a finite‐time stability results of linear delay fractional‐order systems is investigated based on the generalized Gronwall inequality and the Caputo fractional derivative. Sufficient conditions are proposed to the finite‐time stability of the system with the fractional order. Numerical results are given and compared with other published data in the literature to demonstrate the validity of the proposed theoretical results. [ABSTRACT FROM AUTHOR]

Summary: This paper discusses the formulation and the numerical performance of a fully implicit algorithm used to integrate a rate‐dependent model defined within a breakage mechanics framework. For this purpose, a Generalized Backward Euler (GBE) algorithm has been implemented according to two different linearization strategies: The former is derived by a direct linearization of the constitutive equations, while the latter introduces rate effects through a consistency parameter. The accuracy and efficiency of the GBE algorithm have been investigated by (1) performing material point analyses and (2) solving initial boundary value problems. In both cases, the overall performance of the underlying algorithm is inspected for a range of loading rates, thus simulating comminution from slow to fast dynamic problems. As the viscous response of the breakage model can be recast through a viscous nucleus function, the presented algorithm can be considered as a general framework to integrate constitutive equations relying on the overstress approach typical of Perzyna‐like viscoplastic models. [ABSTRACT FROM AUTHOR]

Summary: This paper aims to develop a multiscale approach that has the ability to characterise the influence of microstructural instabilities on global failures in granular materials. For this purpose, the Chang‐Hicher multiscale constitutive relation has been implemented into a finite element code, and the expression of the second‐order work, as an indicator of the material instability, has been computed at the interparticle contact scale, at the representative element volume scale, and at the boundary value problem scale. At the global scale, the second‐order work can be obtained through the integration of that obtained at interparticle contacts. Hence, it becomes possible to analyse the range of instability from the microstructure to the macrostructure. Drained and undrained triaxial tests were numerically simulated. With this method, it was demonstrated that the grain‐scale origin of the specimen instability was well captured. Additionally, biaxial tests were conducted and the onsets of localised and diffuse failure in granular assemblies were successfully predicted. The transition from diffuse to localised failure was demonstrated at different scales, whereby the coincidence between the direction of local instabilities and the direction of the shear band became evident. The influence of the boundary conditions and of the heterogeneity of the initial porosity on the failure mode of granular materials was also analysed. All these examples demonstrate that the developed multiscale approach can characterise in a satisfactory manner the influence of instability at the inter‐grain contacts upon the global failure of granular assemblies. [ABSTRACT FROM AUTHOR]

Summary: In this paper, collaborative distributed dynamic output‐feedback control problem is investigated for a class of wireless control systems with Markovian‐type control network and distributed network‐induced delays. The network consists of a set of interconnected nodes characterized by a directed graph with an adjacency matrix that specifies space distribution (ie, interconnection topology). Each node of wireless control systems not only routes information but also performs its local control. We assume measurements and distributed network‐induced delays are subject to two independent Markovian chains. It is shown that the collaborative distributed dynamic output‐feedback approach offers better performances compared with noncollaborative distributed control approach. An irrigation canal system is used to demonstrate practical potentials of the developed control strategy. [ABSTRACT FROM AUTHOR]

Summary: In this paper, we present the vibration control design for a string with the boundary time‐varying output constraint. The dynamics of the string is a distributed parameter system described by a partial differential equation and two ordinary differential equations. A barrier Lyapunov function with a logarithmic function is adopted to prevent the time‐varying constraint violations. Adaptive control is designed to handle the system parametric uncertainties. Stability analysis and the solvability of the inequality equations are provided. Numerical simulations are provided to illustrate the effectiveness of the proposed control design. [ABSTRACT FROM AUTHOR]

Abstract: We have been studying on measuring capacitance and potential using long‐distance electrode for estimating a permittivity distribution. The estimating method of permittivity distribution was proposed using finite element method (FEM) and genetic algorithm. However, the measurement accuracy was not reviewed. In this paper, we carried out numerical analysis using FEM in case of change of diameter, position, and permittivity of a rod of dielectric and discussed the measurement accuracy of capacitance and potential. [ABSTRACT FROM AUTHOR]

In this paper, we propose a new numerical method to find the ground state energy of a given physical system within the Kohn–Sham density functional theory. The h‐adaptive finite element method is adopted for spatial discretization and implemented with matrix‐free operator evaluation. The ground state energy is found by performing unconstrained minimization with non‐orthogonal orbitals using the limited memory Broyden–Fletcher–Goldfarb–Shanno (BFGS) method. A geometric multigrid preconditioner is applied to improve the convergence. The clear advantage of the proposed approach is demonstrated on selected examples by comparing the performance to other methods such as preconditioned steepest descent minimization. The proposed method provides a solid framework toward O(N) complexity for the locally adaptive real‐space solution of density functional theory with finite elements. [ABSTRACT FROM AUTHOR]

The numerical solution for the time fractional advection‐diffusion problem in one‐dimension with the initial‐boundary condition is proposed in this paper by B‐spline finite volume element method. The fractional derivative is Caputo in the proposed scheme. The stability of the proposed numerical method is studied, and the numerical results presented support the theoretical results. [ABSTRACT FROM AUTHOR]

Dynamic two-phase interaction of soil can be modelled by a displacement-based, two-phase formulation. The finite element method together with a semi-implicit Euler-Cromer time-stepping scheme renders a discrete equation that can be solved by recursion. By experience, it is found that the CFL stability condition for undrained wave propagation is not sufficient for the considered two-phase formulation to be numerically stable at low values of permeability. Because the stability analysis of the two-phase formulation is onerous, an analysis is performed on a simplified two-phase formulation that is derived by assuming an incompressible pore fluid. The deformation of saturated porous media is now captured in a single, second-order partial differential equation, where the energy dissipation associated with the flow of the fluid relative to the soil skeleton is represented by a damping term. The paper focuses on the different options to discretize the damping term and its effect on the stability criterion. Based on the eigenvalue analyses of a single element, it is observed that in addition to the CFL stability condition, the influence of the permeability must be included. This paper introduces a permeability-dependent stability criterion. The findings are illustrated and validated with an example for the dynamic response of a sand deposit. Copyright © 2015 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, we develop a simple expression to evaluate the electric force acting on a carbon nanotube–(CNT) based nanoactuator assuming a nonparallel actuating plates (out‐of‐plane) arrangement. The actuating force is initiated by the asymmetry of the resultant electric fringing fields caused mainly due to the nonparallel electrodes arrangement. The nanoactuator is designed based on a CNT flexible electrode (nonstationary) and 2 symmetrically located actuating stationary rectangular shaped out‐of‐plane plates. The resultant electric force is mathematically approximated from the outcomes of a planar (2‐D) numerical solution of the electric problem via a finite element–based numerical analysis. The influence of the design geometrical parameters on the resultant electric force are examined. Several key design parameters were inspected: the width and thickness of the stationary actuating electrodes, the radius of the flexible electrode (the CNT), and the lateral and vertical separation distances between the movable and grounded electrodes. Through several simulations, we show the effect of the lateral and vertical offsets as well as the electrodes thickness in the optimization of the performance of the nanoactuator assuming such nonparallel plates actuating configuration. We also simulate the effect on the resultant actuating force level with the electrode thickness as well as the electrodes lateral separation distance. [ABSTRACT FROM AUTHOR]

Abstract: This paper focuses on calculating and analysing the thickness and load level influence on the stress intensity factor distribution along the thickness, both individually and together. The main objective is improving the knowledge about the small region existing near the surface where the stress intensity factor results remain independent of external factor as load level or thickness. It is found that this phenomenon occurs around a pivot node within the crack front (PI) that presents advantages for the correlation of numerical and experimental studies. The work evaluates the finite element model of an Al 2024‐T35 compact tension specimen with no plastic wake effect introduced. The three‐dimensional behaviour near the crack front is simulated through numerical analysis with ANSYS code, and J‐integral method is used to determinate the curves of K evolution along the thickness. The results are studied according to a series of parameters that characterize the curves. Conclusions are presented on the areas of influence of each factor involved. [ABSTRACT FROM AUTHOR]

This paper presents a novel data assimilation method for patient-specific blood flow analysis based on feedback control theory called the physically consistent feedback control-based data assimilation (PFC-DA) method. In the PFC-DA method, the signal, which is the residual error term of the velocity when comparing the numerical and reference measurement data, is cast as a source term in a Poisson equation for the scalar potential field that induces flow in a closed system. The pressure values at the inlet and outlet boundaries are recursively calculated by this scalar potential field. Hence, the flow field is physically consistent because it is driven by the calculated inlet and outlet pressures, without any artificial body forces. As compared with existing variational approaches, although this PFC-DA method does not guarantee the optimal solution, only one additional Poisson equation for the scalar potential field is required, providing a remarkable improvement for such a small additional computational cost at every iteration. Through numerical examples for 2D and 3D exact flow fields, with both noise-free and noisy reference data as well as a blood flow analysis on a cerebral aneurysm using actual patient data, the robustness and accuracy of this approach is shown. Moreover, the feasibility of a patient-specific practical blood flow analysis is demonstrated. [ABSTRACT FROM AUTHOR]

Computer experiments often have inputs that are proportions/fractions of components in a mixture. In these mixture computer experiments, it can be of interest to perform robust and tolerance design on the mixture proportions since the proportions are subjected to noise variations. Traditionally, manufacturing of mixture products is controlled via interval tolerances for mixture amounts. In this paper, an optimal tolerance region for proportions, which gives optimal quality cost among all possible tolerance regions for mixture proportions with the same acceptance probability, is proposed for integrated parameter and tolerance design in mixture computer experiments. Real examples are given to demonstrate the improvements that can be achieved with the optimal tolerance region. [ABSTRACT FROM AUTHOR]

This paper develops a method to analyze the piled raft foundation under vertical harmonic load. This method takes into account the interactions among the piles, soil, and raft. The responses of the piles and raft are formulated as a series of equations in a suitable way and that of layered soils is simulated with the use of the analytical layer-element method. Then, according to the equilibrium and continuity conditions at the piles-soil-raft interface, solutions for the piled raft systems are obtained and further demonstrated to be correct through comparing with the existing results. Finally, some examples are given to investigate the influence of the raft, pile length-diameter ratio, and layering on the response of the piled raft foundations. Copyright © 2017 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

In this paper, we present the approximate solution of damped Boussinesq equation using extended Raviart-Thomas mixed finite element method. In this method, the numerical solution of this equation is obtained using triangular meshes. Also, for discretization in time direction, we use an implicit finite difference scheme. In addition, error estimation and stability analysis of both methods are shown. Finally, some numerical examples are considered to confirm the theoretical results. Copyright © 2017 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

In the paper, an equilibrium problem for elastic bodies with a thin elastic Timoshenko inclusion and a thin semirigid inclusion is analyzed. The inclusions are assumed to be delaminated from elastic bodies, thus forming a crack between the inclusions and the elastic matrix. Nonlinear boundary conditions are imposed at the crack faces to prevent a mutual penetration between the crack faces. The inclusions have a joint point. A passage to a limit is investigated as a rigidity parameter of the elastic inclusion goes to infinity. The limit model is investigated. Junction boundary conditions are found at the joint point for the problem analyzed as well as for the limit problem. [ABSTRACT FROM AUTHOR]

SUMMARY To realize fast electromagnetic field analysis, the parallelization technique has been often introduced into the preconditioned Krylov subspace method. When the multicolor ordering is applied to parallelization of forward and backward substitution, the elapsed time of matrix calculation might increase owning to the increment of bandwidth. Therefore, the block-multicolor ordering based on the level structure arising in reverse Cuthill-McKee ordering has been developed. The validity of developed method was demonstrated on the parallelized incomplete-Cholesky-preconditioned conjugate gradient method. In this paper, the parallelization performance of preconditioned minimized residual method based on the three-term recurrence formula of the CG-type (MRTR) method supported by developed ordering is investigated. Furthermore, the affinity of developed ordering or cache-cache elements technique for parallelized forward and backward substitution in Eisenstat's technique is particularly examined. [ABSTRACT FROM AUTHOR]

This paper is focused on the methodological aspects of the numerical study of stress intensity factor (SIF) evolution through thickness. The work evaluates the modelling of an Al-alloy 2024-T351 CT specimen under mode I nominal loading in fracture. No plastic wake effect is introduced to separate the influence of plasticity-induced crack closure near the surface. Numerical models have shown the complexity 3-D behaviour in the vicinity of the crack front and finite element methods (FEM) are widely used in these problems with interesting results. However, there is a lack of literature support in many simplifying assumptions. In previous studies, authors have analysed some issues as the evolution of the plastic zone, the crack closure stress or the SIF. The current work attempts to describe and justify the key aspects of the methodology developed to address these problems by the FEM. A huge effort has been made to study main parameters involved and their influence in the results, especially in order to properly capture the SIF distribution along the thickness. Recommendations about mesh density are provided, and the main procedures to obtain K are discussed. [ABSTRACT FROM AUTHOR]

Heat transfer of a power-law non-Newtonian incompressible fluid in channels with porous walls has not been carefully studied using a proper numerical method despite a few constructions of approximate analytic solutions through the similarity transformation and perturbation method for Newtonian fluids (i.e. power-law index being one). In this paper, we propose a finite element method for the thermal incompressible flow equations. The incompressible condition is treated by a penalty formulation. Numerical solutions are validated by comparing them with an approximate analytic solution of the Navier-Stokes equation in the Newtonian fluid case. Then, the method is used to simulate the heat transfer of various power-law fluids. Additionally, unlike previous studies, we allow the thermal diffusivity to be a function of temperature gradient. The effect of different values of the parameters on the temperature and velocity is also discussed in this paper. Copyright © 2013 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]