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This work deals with fracture mechanisms in quasi-brittle materials, focusing on the characterization of the Fracture Process Zone (FPZ) of specimens under tensile load. Particularly, paper was used as model material. Experiments were conducted on notched and unnotched specimens. Based on an image analysis of these observations, a stochastic finite element model was developed, using both a nonlocal stress-based approach and a discretized random field modeling of the Young's modulus. The proposed methodology allowed characterizing the damage zone and the size of the FPZ, analyzing the influence of the mesostructure, composed of flocs (fiber aggregates where the basis weight is larger than the average one) and antiflocs (complement of flocs). The area of the active FPZ and the normalized stress drop were linked using a surface energy dissipated in the active FPZ. The stress drop, until limiting value, increased with the width of the active FPZ. Finally, a relationship between the surface energy and the nonlocal internal length was established. [ABSTRACT FROM AUTHOR]

Thin-walled tubular deployable composite boom (DCB) has gained significant attention due to its lightweight, simple structure and high packaging efficiency. The experimental and numerical simulation methods were employed in this paper to investigate the folding behavior of the DCB. Using T700/epoxy unidirectional reinforced prepreg as raw material, DCB specimens were prepared by the vacuum bag method. To complete the folding experiments of DCB specimens, a folding mechanism was designed and manufactured. Folding experiments of DCB specimens were conducted and folding moment versus rotational displacement curves were measured. In addition, a Finite Element Model (FEM) was established to predict the folding behavior of the DCB. Different failure criteria were considered in the numerical analysis, including the Tsai‐Hill criterion and maximum stress criterion. Prediction results using the FEM were compared with experimental results, and both sets of results were in good agreement. It is shown that the DCB can achieve the folding function without failure. The research results in this paper are of great significance to the practical engineering application of the DCB. [Display omitted] • Six tubular deployable composite boom specimens and a precise folding mechanism were designed and prepared. • Folding experiments were conducted to measure the folding moment and rotational displacement curves. • A finite element model for predicting the folding behavior of the tubular deployable composite boom was established. [ABSTRACT FROM AUTHOR]

This article describes a new method for evaluation of radial crush strength of paper cores. Based on the theory of multilayered composites, a mathematical model has been developed to calculate the value of destructive force during radial crushing of spirally shaped paper cores whose layers are made of different materials. To start calculations, it is necessary to have geometry parameters of the cores, Young's modulus and SCT of an individual component layers. [ABSTRACT FROM AUTHOR]

This paper delves into the numerical analysis of the extended Fisher-Kolmogorov (EFK) equation within open bounded convex domains R ⊂ R d , where d ≤ 3. Two distinct finite element schemes are introduced, namely the semi-discrete and fully-discrete finite element approximations. The existence and uniqueness of solutions are established for both the semi-discrete and fully-discrete finite element approximations. Error bounds are investigated across different scenarios, including comparisons between the semi-discrete and exact solutions, as well as between the semi-discrete and fully-discrete solutions, along with the fully-discrete and exact solutions. An effective algorithm has been proposed to solve the nonlinear system resulting from the fully-discrete finite element approximation at each time step. The paper also provides computed numerical error results and showcases a variety of numerical experiments to further illustrate and support the findings. [ABSTRACT FROM AUTHOR]

A new cable-damper stopper equipped for Coal-Fired Thermal Power Plants (CFTPPs) was proposed in our previous paper, where a series of shaking table tests were carried out to investigate its seismic performance, so this paper aims to reveal the working mechanism of the stopper from the theoretical and numerical simulation aspects. The stopper is composed of three main components, i.e. a steel cable, a steel block and a viscous damper. First, the nonlinear restraint stiffness of the steel cable to the boiler was derived; second, the critical damping of the stopper, which makes the vibration of the boiler decay exponentially with no oscillation, was derived; third, an iterative method was proposed to globally tune the CFTPP structure, which makes it possible to obtain the optimal parameters of the cable-damper stopper, including the diameter of the steel cable and damping coefficient of the damper. Finally, finite element models were built and time history analyses were conducted to verify the proposed optimization approach. Firstly, the finite element models were proved valid through the comparison between the results of the simulations and the experiments. Then, based on the results of the simulations, the theoretical procedure was validated. The results revealed that the proposed cable-damper stopper reduced the seismic responses of displacements of the top floor and the boiler significantly, about 30.18% and 60.01% respectively compared with their counterparts of CFTPPs without stoppers. [ABSTRACT FROM AUTHOR]

Abstract: Coating blades are used in the paper industry to meter off the excess coating applied to the paper. They are essential in attaining high-quality coating films with minimum operating cost. During the coating process, the blades are worn down at the tip and are replaced when the coating quality degrades. The objectives of this study are to predict the wear rate of the blades and examine the hypothesis that the blades wear into a quasi-steady-state wear profile, despite both low- and high-angle particle impact. Experimental data and results from finite element simulations are presented for a series of blade materials and suspensions. The approach taken differs considerably from earlier studies, in that it treats blade wear as erosion from the action of the impacting slurry particles rather than abrasion, thus explaining the enhanced wear around the heel. The current approach relies on computer experiments to solve the equations for the liquid flow field, the individual particle motion, the substrate deformation and the eroded volume of the blade, rather than employing empirical relations between wear rates and average fluid velocity. The shear thinning behavior of the coating suspension was properly taken into account. To validate the calculations, blade samples from both a pilot and an off-machine coater were collected at a variety of time intervals. The blade samples aided not only in the establishment of the wear rates and the identification of the wear patterns, but also in the confirmation of the steady-state wear hypothesis that is correctly predicted by the simulations. [Copyright &y& Elsevier]

A new shell element has been proposed for geometrically non-linear, finite element analyses of axially moving paper web. Web instability problems of paper travelling in a printing system, such as wrinkling and fluttering, pose special challenges in the numerical analyses. For examples, these are finite bending stiffness (as opposed to membrane), orthotropy, and non-uniform distributions of mechanical and hygro-properties (in different length scales). The new formulation has accounted for paper transport velocity and paper bending stiffness based on a mixed Lagrangian–Eulerian description of the motion. A natural coordinate system has been employed in the analytical and finite element formulations. Benchmarking with different finite elements in various tests showed that the proposed element is indeed more stable and reliable for the chosen application than existing elements. The usability of the shell element has been successfully demonstrated by two example problems: wrinkling of stretched isotropic and orthotropic membranes, and the vibration of a web showing a speed-tensioning effect above a critical web transport velocity. [Copyright &y& Elsevier]

The mechanical response of three different structural core sandwich panels in out-of-plane compression and shear has been analyzed. Specific core shapes examined are arc-tangent, wavy trapezoidal and hemispherical. Unit cells consisting of representative elements of the core attached to face sheets were selected for analysis. Both face sheets and core were assumed made from paper. Finite element analysis employing large deformation and rotations and orthotropic elastic–plastic behavior was used. The results show that the arc-tangent and trapezoidal cores are prone to collapse by extensive bending and buckling, whereas the hemispherical core behaved more stably in compression and shear. Core sheets with a hemispherical shape were prepared from copy paper sheets in a specially designed forming machine. Sandwich test specimens were prepared from this core and tested in out-of-plane compression, and the load-displacement response was compared to predictions from finite element simulations. The experimental and finite element results were consistent. [ABSTRACT FROM AUTHOR]

This paper is devoted to a study of a history-dependent mixed hemivariational-variational inequality arising in contact mechanics. The contact problem concerns the deformation of a viscoelastic body with long memory, subject to a general friction law on one part of the boundary and a frictionless Signorini condition on another part of the boundary. The solution existence and uniqueness of the history-dependent mixed hemivariational-variational inequality based on a Lagrange multiplier approach are proved. Then, a fully discrete scheme is introduced and studied. The trapezoidal rule is used to approximate the integral in the history-dependent operator. For the spatial discretization, the linear finite elements are used to discretize the displacement field, and dual basis functions are used in the approximation of the Lagrange multiplier. Optimal order error estimates are derived for the displacement and the Lagrange multiplier under appropriate solution regularity assumptions. Numerical results are presented to illustrate the theoretical prediction of the convergence orders. [ABSTRACT FROM AUTHOR]

In the present study, the fracture analysis of functionally graded materials (FGMs) of various material distributions with discontinuities (crack and inclusion) under localized loadings is carried out by the extended finite element method (XFEM). In the present work, the effect of discontinuities and material distributions like exponential, power law, Mori–Tanaka, and sigmoidal in FGMs is also presented, where the different material distributions are compared for the fracture analysis of FGM plates and beams. This present work will be helpful for the researchers to understand the effect of different material distributions on FGMs under localized ladings. The XFEM-based numerical analysis is carried out to find stress intensity factors (SIFs) and stress distributions. The MATLAB code is developed for this analysis and is validated with a previously published research paper. [ABSTRACT FROM AUTHOR]

In this paper, we first investigate the well-posedness and regularity of mild solution to a stochastic active fluids model driven by the additive noise. A fully-discrete scheme is proposed for solving the given model, which is based on the finite element method for spatial discretization and the backward Euler method for temporal discretization. By overcoming the difficulty of error analysis caused by the discrete Laplacian operator, we obtain the convergence results of the developed scheme. Finally, some numerical examples are provided to validate the theoretical results and we also simulate the motion states of the active fluids. [ABSTRACT FROM AUTHOR]

The paper presents a static analysis of the buckling and post-buckling state of thin-walled cold-formed steel (TWCFS) lipped channel section beam-columns subjected to eccentric compression. Eccentricity is taken into consideration relative to both major and minor principal axes. An analytical–numerical solution to the buckling and post-buckling problems is described. The solution is based on the theory of thin plates. Equations of equilibrium of section walls are derived from the principle of stationary energy. Then, to solve the problem, the finite difference (FDM) and Newton–Raphson methods are applied. Linear (buckling) and nonlinear (post-buckling) analyses are performed. As a result, pre- and post-buckling equilibrium paths are determined. Comparisons of the obtained numerical results, FE simulation results, and experimental test results are carried out and presented in comparative load-shortening diagrams. Additionally, a comparison of the buckling forces and buckling modes obtained from theoretical analysis and experiments is presented. [ABSTRACT FROM AUTHOR]

The increasing demand for deep excavations in construction projects emphasizes the necessity of robust support structures to ensure safety and stability. Support structures are critical in stabilizing excavation pits, with a primary focus on enhancing their bearing capacity. This paper employs finite element modeling techniques to conduct a numerical analysis of nails and helical anchors' bearing capacity. To reinforce the stability of pit walls, selecting an appropriate method for guard structure construction is imperative. The chosen method should efficiently redistribute forces induced by soil mass weight, displacements, and potential loads in the pit vicinity to the ground. Various techniques, including trusses, piles, cross-bracing systems, nailing, and anchorage systems, are utilized for this purpose. The study evaluates numerical models for two guard structure configurations: nailing systems and helical anchorage. It examines the impact of parameters such as displacement, helical helix count, helix diameter variations, and the integration of nailing systems with helices. Comparative analyses are conducted, including displacement comparisons between different nailing systems and helical anchor systems, along with laboratory-sampled data. The research yields significant insights, with a notable finding highlighting the superior performance of helical bracings compared to nailing systems. The conclusions drawn from this study provide specific outcomes that contribute valuable knowledge to the field of deep excavation support structures, guiding future design and implementation practices. [ABSTRACT FROM AUTHOR]

From the literature it is known that orthogonal polynomials as the Jacobi polynomials can be expressed by hypergeometric series. In this paper, the authors derive several contiguous relations for terminating multivariate hypergeometric series. With these contiguous relations one can prove several recursion formulas of those series. This theoretical result allows to compute integrals over products of Jacobi polynomials in a very efficient recursive way. Moreover, the authors present an application to numerical analysis where it can be used in algorithms which compute the approximate solution of boundary value problem of partial differential equations by means of the finite elements method. With the aid of the contiguous relations, the approximate solution can be computed much faster than using numerical integration. A numerical example illustrates this effect. [ABSTRACT FROM AUTHOR]

Surface Stokes and Navier--Stokes equations are used to model fluid flow on surfaces. They have attracted significant recent attention in the numerical analysis literature because approximation of their solutions poses significant challenges not encountered in the Euclidean context. One challenge comes from the need to simultaneously enforce tangentiality and H1 conformity (continuity) of discrete vector fields used to approximate solutions in the velocity-pressure formulation. Existing methods in the literature all enforce one of these two constraints weakly either by penalization or by use of Lagrange multipliers. Missing so far is a robust and systematic construction of surface Stokes finite element spaces which employ nodal degrees of freedom, including MINI, Taylor--Hood, Scott--Vogelius, and other composite elements which can lead to divergence-conforming or pressure-robust discretizations. In this paper we construct surface MINI spaces whose velocity fields are tangential. They are not H1-conforming, but do lie in H(div) and do not require penalization to achieve optimal convergence rates. We prove stability and optimal-order energy-norm convergence of the method and demonstrate optimal-order convergence of the velocity field in L2 via numerical experiments. The core advance in the paper is the construction of nodal degrees of freedom for the velocity field. This technique also may be used to construct surface counterparts to many other standard Euclidean Stokes spaces, and we accordingly present numerical experiments indicating optimal-order convergence of nonconforming tangential surface Taylor--Hood P2 P1 elements. [ABSTRACT FROM AUTHOR]

Introduction/purpose: In recent times, with the tendency to develop new types of armor-piercing ammunition, constant investments in the development of new types of armored obstacles is necessary. Obstacles made of high-alloy steel plates are still the best form of protection against larger caliber ammunition. There are a number of factors to consider when selecting an alloy, including the weight, dimensions, intended use, desired ballistic performance, and costs. According to that, a numerical analysis of penetration of a 30mm armor-piercing fin-stabilized discarding sabot projectile into the steel alloy Weldox 460 plates of different thicknesses at a distance of 1000m with a velocity of 1300m/s is presented in this paper. Methods: The stresses and deformations of the penetration effect were calculated through numerical analysis and finite element modeling. To specify material characteristics, the Johnson-Cook material model and the fracture of materials model have been utilized. In order to define models and carry out numerical calculations, the software packages FEMAP and LS Dyna have been used in this paper. Results: For a numerical analysis of the penetration process of this projectile type against armor obstacle, four different armor plate thicknesses are calculated: 10mm, 50mm, 100mm, and 110mm. For each of them, the results are shown in a form of stress and displacement, so that the interaction phenomena between the sub-projectile and the armor plate can be described. Conclusion: Modeling the impact on armor-piercing obstacles is extremely difficult, time-consuming, and complex, and the resulting models very successfully (or with some deviation) approximate the real problem of projectile penetration. One of the most effective methods for solving problems of this kind and others of a similar nature in recent times is the finite element method analysis. The material and the target dimensions, as well as the ballistic parameters and the material of the projectile have the biggest influence on projectile penetration. The target's resistance to penetration increases when all input parameters are maintained at the same level and its thickness is increased, and vice versa. [ABSTRACT FROM AUTHOR]

Abstract: A finite element procedure, developed in order to account for the effect of high anisotropy at folding of coated papers, is presented. The anisotropic behaviour (with very low stiffness in the thickness direction) is modelled using stiff structural elements (trusses and beams). The numerical results indicate that high elastic anisotropy leads to lower strain levels at folding than reported in previous analyses where this effect was not accounted for. High plastic anisotropy, on the other hand, will contradict this result. [Copyright &y& Elsevier]

Folding of coated paper is examined numerically using the finite element method. Particular emphasis is put on the behaviour of field variables relevant for cracking of the coating layers. In the numerical analysis, the basepaper is modelled as an anisotropic elastic–plastic material (both elastic and plastic anisotropy is accounted for) while the constitutive behaviour of the coating layers are approximated by classical (Mises) elastoplasticity. The numerical results suggest, among other things, that particular forms of plastic anisotropy can substantially reduce the maximum strain levels in the coating. It is also shown that delamination buckling, in the present circumstances, will have a very small influence on the strain levels in the coating layer subjected to high tensile loading. [Copyright &y& Elsevier]

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]

This paper presents the results of a numerical study of a planar antenna with a complex form factor. The antenna is based on a combination of two resonators, a disc resonator and a ring resonator. The feeding of the ring resonator is performed using a coplanar structure: pointwise by galvanic contact between the central conductor of the coplanar line and the ring resonator and by distributed electromagnetic coupling of the ring resonator and the aperture of the outer conductor of the coplanar line. The antenna was placed over a metal plane whose geometric dimensions were significantly larger than those of the antenna to exclude the influence of edge diffraction effects. In numerical simulation a complex approach including the method of semi-open resonator and the finite element method (FEM) implemented within the commercial package HFFS was used. The dependences of spectral, energy and polarization characteristics on material constants and frequency parameter have been investigated. It was found that within the framework of single-parameter optimization it is impossible to simultaneously achieve a high level of all important parameters. The values of frequencies of spectral lines in the spectral characteristics of the antenna are found with a relative error not worse than 1200 Hz. Frequency ranges within which there is no degeneration of oscillation types are established. The distributions of surface currents on the metal elements of the antenna, allowing to determine the position of phase centers of excitation, are presented. It is shown that the proposed antenna can provide an acceptable level of matching both at fixed frequencies and in sufficiently wide local frequency bands, reaching 11% with respect to the center frequency of the sub-band. The boundary values of gain coefficients in frequency bands are established. The simulation results allow to predict effective radiation with formation of practically single-lobe radiation pattern and presence of elliptical polarization. [ABSTRACT FROM AUTHOR]

The Double-Yield (D-Y) model is a widely used method for predicting the mechanical properties of caved rock. However, determining the numerical simulation parameters for this model typically requires extensive trial and error. In this paper, a new approach for parameter inversion of the D-Y model is proposed and applied to a real case study involving repeated mining in multiple coal seams. The proposed framework combines FLAC3D, a finite element numerical simulation software, with a new computational tool developed using MATLAB® App Designer. By applying this framework to the case study, the accuracy and efficiency of parameter determination in the mining area are improved. In addition, a 3D finite element model of multiple coal seams is generated based on the geological information of the case study, and the stress evolution is analyzed. The simulation results are then validated through field measurements, providing valuable reference information for safe and efficient production. Overall, this improved method for parameter inversion of the D-Y model, along with the combined numerical simulation and field measurement approach, enhances the understanding of stress evolution in multiple coal seams and contributes to safer and more efficient mining operations. Highlights: An in-depth analysis was conducted to examine how variations in Double-Yield parameters impact the numerical simulation curve. A breakthrough approach for parameter inversion of the Double-Yield (D-Y) model is introduced, and the computational tool is developed. A 3D finite element model is crafted to analyse the dynamic stress evolution during repeated mining of multiple coal seams. The accuracy of simulation outcomes is bolstered by validation against field measurements of mining-induced stress. [ABSTRACT FROM AUTHOR]

In this work, a study on a cap and pin insulator (1512L) is proposed to evaluate the distribution of the electric field and the potential along the insulator under different conditions. A computational and experimental study for the examination of a real insulators model is assessed. Tests on contaminated insulators in the laboratory under the suggested conditions have been carried out. Finite element methods (FEM) have been employed in the numerical analysis to assess the electrical properties of the insulator under the suggested contamination profiles, including potential and electric field. The study proposed in this paper provides an effective and practical tool for analysis and enhance the dielectric properties of the studied insulator. [ABSTRACT FROM AUTHOR]

This paper investigates the effect of an open hole on the stability of a compressed laminated composite plate. The study was carried out in two ways: using experimental tests and numerical analysis. As a result of the experiment, the buckling form and path of the plate were recorded. The form of buckling was determined using the ARAMIS non-contact measurement system. The critical load value was determined from the working path using the approximation method. The experimental results were verified by numerical analysis based on the finite element method. FEM investigations were carried out in terms of a linear eigenproblem analysis. This allowed the bifurcation load and the corresponding buckling form of the numerical model of the plate to be determined. Investigating the effect of the hole in the compressed plate at a critical state showed high agreement between the proposed test methods. No clear effect of the hole size on the buckling of the plate was observed. In contrast, a clear effect of the hole on the critical load value was determined. The maximum decrease in the critical load value was 14%. The same decrease was observed for the stiffness of the post-critical characteristics. It was shown that the [45|−45|90|0]s composite plate had more than three times lower strength compared to [0|−45|45|90]s and [0|90|0|90]s. The novelty of this article is the development of a research methodology based on new interdisciplinary research methods for describing the influence of the central hole on the stability of compressed composite plates. The ABAQUS system was used for the numerical analysis. [ABSTRACT FROM AUTHOR]

The aim of this paper is twofold. First, we prove L p estimates for a regularized Green's function in three dimensions. We then establish new estimates for the discrete Green's function and obtain some positivity results. In particular, we prove that the discrete Green's functions with singularity in the interior of the domain cannot be bounded uniformly with respect of the mesh parameter h. Actually, we show that at the singularity the discrete Green's function is of order h - 1 , which is consistent with the behavior of the continuous Green's function. In addition, we also show that the discrete Green's function is positive and decays exponentially away from the singularity. We also provide numerically persistent negative values of the discrete Green's function on Delaunay meshes which then implies a discrete Harnack inequality cannot be established for unstructured finite element discretizations. [ABSTRACT FROM AUTHOR]

In this paper, finite element method is used to calculate the static performance of gas journal bearing, in which rotation speed term is introduced into the stiffness matrix of linear triangular element to realize the performance calculation of the bearing with rotation speed. The results indicate that the average gas film thicknesses corresponding to the maximum load capacity and stiffness, and the minimum attitude angle increase with the growth of orifice diameter. Load capacity and stiffness significantly improved with the increase of rotation speed, eccentricity ratio and supply pressure when the bearing has thin average gas film thickness. Attitude angle increases with the growth of rotation speed, while the growth rate slows down or even decreases at high speed. The most effective way of reducing attitude angle is to increase supply pressure. It can be found that rotation speed affects attitude angle through changing gas pressure difference between two orifices, while other parameters have the same effect by changing gas pressure at orifice outlet. Article Highlights: Analyzing performances of gas journal bearings by solving Reynolds equation with FEM. Solving Reynolds equation with speed term using FEM. Investigating the effect of bearing parameters on attitude angle, stiffness, and load capacity. [ABSTRACT FROM AUTHOR]

Convection-diffusion-reaction equations model the conservation of scalar quantities. From the analytic point of view, solutions of these equations satisfy, under certain conditions, maximum principles, which represent physical bounds of the solution. That the same bounds are respected by numerical approximations of the solution is often of utmost importance in practice. The mathematical formulation of this property, which contributes to the physical consistency of a method, is called the discrete maximum principle (DMP). In many applications, convection dominates diffusion by several orders of magnitude. It is well known that standard discretizations typically do not satisfy the DMP in this convectiondominated regime. In fact, in this case it turns out to be a challenging problem to construct discretizations that, on the one hand, respect the DMP and, on the other hand, compute accurate solutions. This paper presents a survey on finite element methods, with the main focus on the convection-dominated regime, that satisfy a local or a global DMP. The concepts of the underlying numerical analysis are discussed. The survey reveals that for the steady-state problem there are only a few discretizations, all of them nonlinear, that at the same time both satisfy the DMP and compute reasonably accurate solutions, e.g., algebraically stabilized schemes. Moreover, most of these discretizations have been developed in recent years, showing the enormous progress that has been achieved lately. Similarly, methods based on algebraic stabilization, both nonlinear and linear, are currently the only finite element methods that combine the satisfaction of the global DMP and accurate numerical results for the evolutionary equations in the convection-dominated scenario. [ABSTRACT FROM AUTHOR]

The powder mixed electrical discharge machining (PMEDM) process was simulated via finite element analysis in the current study to assess heat behavior and material removal rate. The goal of this paper is to conduct a thorough experimental and thermal examination of electrical discharge machining (EDM) in order to forecast its cutting characteristics and subsequently optimize the output variables using a response surface methodology for simulations and choosing the most suitable set of process variables related to the PMEDM process. This study's objective is to design a 2D axisymmetrical transient thermal model that might also describe the physics of material removal in a single spark PMEDM operation on a Titanium Zirconium Molybdenum (TZM) superalloy. ANSYS (version 9.1) software is used to perform transient heat transfer simulations to determine the temperature profile with the amount of material removal at different current, pulse on and off times, gap voltages, and fraction of heat that enters the specimen. The PMEDM process produced craters with a lower diameter and depth, which increased the material removal rate and enhanced the surfacing quality. Compared to the conventional EDM process, the inclusion of powder raised the heat flux given to the work material by 10%–12%. It has been determined that with the single spark modeling technique, the temperature significantly dropped in both the radial and depth directions. The computational results are compared with experimental observations for similar machining conditions, and both results agree satisfactorily. [ABSTRACT FROM AUTHOR]

In laboratory practice, several standards for testing the bending stiffness of corrugated board are used. There are often cases of tests where the results depend on the way the sample is placed on the supports. The problem arises when the board is five-ply (with two corrugated layers with different corrugation heights) or when the board has asymmetrically selected papers on the flat layers. This article focuses on the problem related to boundary conditions, with particular attention to the local effects of the support of the sample. Because the cardboard layers, both flat and corrugated, have a small thickness, a slight deformation of the papers can always be observed at the point of contact between the sample and the support, which affects the readings of the measured stiffness. The paper presents theoretical and numerical analyses showing how much the method of supporting the sample affects the measured bending stiffness of various samples. Numerical observations were compared with the results of analyses presented by other scientists as well as with experimental results. [ABSTRACT FROM AUTHOR]

Abstract: Strains, computed by the finite element method, are evaluated and compared to an experimentally determined strain field. The analyzed low-density paper has been designed to ensure bond–breakage as the dominating damage mechanism and the paper material is approximately in-plane isotropic. An optical non-contact displacement measuring system has been used in fracture tests to determine the strain field in the crack-tip region of a pre-fabricated crack. Additionally, acoustic emission monitored tensile tests have been conducted to determine onset and evolution of damage processes and thereby enabling calibration of required constitutive parameters. The results suggest that the investigated paper material can tolerate significantly higher strains than what is predicted by a classic elastic–plastic J 2-flow theory. Immediately before onset of the final fracture (i.e., localization), the experimental measured normal strain in the near-tip region is around 60% higher than the computed strain when using exclusively an elastic–plastic theory for the corresponding load while the strain computed utilizing a non-local damage theory is of the same order of magnitude as the experimentally measured strain. Hence, it seems essential to include a non-local continuum theory to describe strains in the near-tip region quantitatively correct for paper materials. It is demonstrated that path independence of the well-known J-integral does not prevail for this class of material models. Only for the special situation of a homogenous damage field in the crack-tip region may the stress and strain fields be described by the well-known HRR-solutions. [Copyright &y& Elsevier]

Abstract: We present a model for the laminated composite plate problem based on the Reissner–Mindlin model and first-order lamination theory. The weak problem based on this model is solved with the finite element method using stabilized MITC (mixed interpolation of tensorial components) finite elements. Detailed a priori estimates are given for the mixed finite element formulation of the problem. Explicit bounds for the continuity and coercivity constants of the coupling terms are presented, thus refining earlier results. Furthermore, we present an application of the theory to the paper cockling problem and investigate the effect of boundary conditions on the small-scale deformation of the solution numerically. [Copyright &y& Elsevier]

Abstract: A model, using the finite element method (FEM), was developed for the analysis of the time and humidity-dependent stresses of paper webs at offset printing press conditions. The offset press was simplified to a flat thin moving web and its unit process steps were described by combinations of prescribed displacements, tractions and moisture ratios. Based on previous modelling and experimental findings, a convective hygro-viscoelastic model of the paper web was derived. The constitutive law and some of the boundary conditions were implemented as user-defined subroutines into commercial FEM software in a displacement-based framework. Some simulation examples were used to study the applicability of the proposed formulation in the analysis of web-fed offset printing at stationary conditions. The numerical stationary solutions converged rapidly and the model was robust for the investigated conditions. Incorporating effects from moisture, the numerical results show web tension profiles along the analysed model press comparable to those found by others from full-scale newsprint printing press trials. Effects of altered levels of the peripheral velocities of rollers, friction, web velocity, moisture and web properties on in-plane stresses and strains are presented. In order to exemplify the practical use of the model for runnability investigations, different analysed quantities obtained from the numerical solutions were related to web tension, web widening, misregister in multi-colour printing, sheet size analysis, conditions for web stability and traction conditions at drag rollers. [Copyright &y& Elsevier]

Abstract: The fundamentals of a new radiation model are described in this paper. The spatial and angular dependence of the radiation intensity are split in such a way that the radiation intensity is approximated by a linear combination of basis functions dependent only on the angular direction. The coefficients of the approximation are functions of the spatial coordinates. The spatial discretization is performed using the finite volume method and the angular discretization is based on the finite element method. This means that the basis functions are defined according to the criteria used in the finite element method. The step scheme was employed in the spatial discretization and bilinear basis functions were chosen for the angular discretization. The method may be applied to both grey and non-grey media, non-scattering and scattering media, simple and complex geometries. However, it is still in an early stage of development, and therefore it is applied in this paper to simple one-dimensional problems of radiative transfer in enclosures with grey, emitting-absorbing and scattering media. The results obtained show that the method gives good results for several benchmark problems with available analytical solutions, and converges to the exact solution as the grid is refined and the number of terms in the approximation increases. [Copyright &y& Elsevier]

Folding of coated papers is examined numerically using the finite element method. The analysis is focused on the influence from dynamic effects on the folding process. In particular, the behaviour of field variables relevant for cracking of the coating layers are studied in some detail. The results presented indicate that dynamic effects are of little importance as regards maximum strain levels in the coating but will influence the stress and strain distributions. Accordingly, a quasi-static analysis of the problem will be sufficient in order to describe many of the important features related to cracking. [Copyright &y& Elsevier]

This paper focuses on the finite element analysis simulation of the impact properties of composite sandwich structures made of carbon fiber-reinforced polymer lamina. In the existing studies, the composite sandwich structures with A-shaped cores have superior mechanical properties under quasi-static plane compression loads compared to W-shaped, Y-shaped, and X-shaped cores. However, there is limited research on the impact resistance of this structure. This paper studied the resistance of a composite A-shaped core structure to ballistic impact. Using ABAQUS/explicit finite element analysis software, ballistic impact tests for the composite A-shaped core structure were simulated based on the Hashin and Yeh failure criteria with a progressive damage model introduced in the user-defined subroutine VUMAT. First, the composite Y-shaped core sandwich structure was verified via experiments and simulations to determine the accuracy of the method, and then the composite A-shaped sandwich structure was subjected to a series of ballistic impact simulations. With varied impact velocity, the damage to the front and rear face sheet and cores via ballistic loads was simulated to illustrate the overall dynamic response process of the sandwich structure. Subsequently, a curve was fitted using a ballistic limit velocity equation, which was used as the criterion to evaluate the impact resistance of the composite A-shaped core structure. The results showed that, under the same relative density and the same number of component layers, the ballistic limit velocity of the composite A-shaped core sandwich structure was bigger than the composite Y-shaped core sandwich structure. The composite A-shaped core structure had 12.23% higher ballistic limit velocity than the composite Y-shaped core, indicating the impact resistance capabilities of the A-shaped core structure. In addition, the impact location's effect on the impact response was investigated. [ABSTRACT FROM AUTHOR]

The temperature action of long-span cable-stayed bridges is complicated because of the high indeterminacy of their structure. Previous studies on the temperature behavior of bridges were either limited by finite sensors, failing to capture the accurate relation between the temperature field and temperature-induced responses, or constrained to a "divide-and-conquer" strategy, requiring considerable manual intervention and regarded as computationally inefficient. This study develops a unified approach to the investigation of thermal behaviors of cable-stayed bridges by integrating the heat-transfer analysis and structural analysis based on the same refined global 3D finite element model. The companion paper (Part I) investigates the temperature distribution, while this paper (Part II) focuses on temperature-induced responses. The temperature distribution data is automatically converted to thermal loads, and thermal elements are changed to structural elements to calculate the temperature-induced responses of the bridge. Results show that the effect of the temperature variation of cables is nonnegligible and should be taken into account during the structural analysis. The longitudinal displacement of the girder and the longitudinal displacement of the tower top are mainly influenced by the average girder temperature, the mid-span deflection and the cable stress are dominated by the cable temperature and average girder temperature, and the stress of the girder is controlled by the vertical temperature difference. The ratio of the thermal stress to the dead load stress of the girder can reach 96%. The calculated displacement and stress of the bridge agree well with the corresponding measurements, consequently verifying the effectiveness of the proposed unified approach to calculating temperature-induced responses. [ABSTRACT FROM AUTHOR]

Introduction/purpose: Thin plates made of high–strength steel are frequently used both in civil and military ballistic protection systems. In order to choose an appropriate type of alloy, it is necessary to fulfil a number of criteria, such as the condition of use, the desired ballistic performance, weight, dimensions, and price. This paper presents a numerical analysis of the penetration of a 30mm armor-piercing projectile with a velocity of 750m/s into steel alloy Weldox 460 plates of different thicknesses at a distance of 1000m . Methods: The analysis has been performed using numerical methods and finite element modeling to calculate stresses and deformation caused by the penetration effect. For defining material characteristics, the Johnson- Cook material model and the fracture of materials model have been used. In this paper, the software packages FEMAP and LS Dyna have been used for defining models and performing numerical calculations. Results: The results of the performed numerical analysis as well as the obtained stress and displacement values are presented for four different armor plate thicknesses: 30mm, 33mm, 34mm, and 40mm. The results show a penetration effect and an interaction between the projectile and the armor plate. Conclusion: Modeling the impact on armor-piercing obstacles is very complex, extensive, and demanding, and the formed models approximate the real problem of projectile penetration in a very successful way (or with a certain deviation). In recent times, the analysis using the finite element method has proven to be one of effective approaches to solving such and similar problems. The material and the dimensions of the obstacle, as well as the material and the ballistic parameters of the projectile have the greatest influence on projectile penetration. Keeping all the input parameters at the same level and increasing the thickness of the target leads to its increased resistance to penetration. [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]

Imperfect geometry beams with functionally graded carbon nano tubes (CNT) have recently been used in many structural applications, and many numerical analyses have been performed to assess the stiffness property in beams and structures. Where the stiffness enhancement of a beam greatly contributes to its stability by augmenting the geometrically defective beam's deformation withstanding capabilities under loading. However, the stiffness enhancement in terms of imperfect geometrical design characteristics has not been considered in previous research. Hence in this paper, a novel Persuaded Resilient Design is introduced in which the geometric imperfection is induced in the design in the form of a hollow trapezoidal laminate in such a way that the designed imperfect layered laminate enhances the flexural rigidity of the beam. Additionally, by employing a Parametric Stability Analysis, the act of the curved beam is structured by meshing the design with FEA applying UDL, and three-point bending. The peak and trough sustainability of the unique designed geometrically flawed beam incorporating functionally graded CNTs is determined via a finite element model. Thus, the FG-CNT reinforced curved beam behavior of the novel design is efficiently analyzed. [ABSTRACT FROM AUTHOR]

A parametric study employing three-dimensional finite element analysis is used in this paper to examine the improvement of soft clay and silty loose sand under a road embankment using deep soil mixing (DSM) columns. Both soils are designed with three variables namely DSM column diameter (D), DSM column length (L) and centre-to-centre distance of the DSM columns (s). The settlement values under the road embankment constructed with and without DSM columns were obtained by numerical analysis. The analyses were also repeated for the DSM columns which were stiffened by adding I-profiles. The results showed that the improvement effect of the DSM columns on settlement is higher in soft clay. For constant improvement area ratio (ar), the maximum improvement is achieved for D = 80 cm (2.62 ft.) and increasing D did not affect the degree of improvement. In both soil types, settlement decreased with increasing L within the weak soil zone. Increasing L into the comparatively stronger soil did not significantly affect the settlement value. Although the settlement decreased with increasing ar in silty loose sand, it reached at maximum in soft clay at ar of thirty-five percent and was not affected thereafter with increasing ar values. [ABSTRACT FROM AUTHOR]

One of the main difficulties that has to be faced with fictitious domain approximation of incompressible flows with immersed interfaces is related to the potential lack of mass conservation across the interfaces. In this paper, we propose and analyze a low order fictitious domain stabilized finite element method which mitigates this issue with the addition of a single velocity constraint. We provide a complete a priori numerical analysis of the method under minimal regularity assumptions. A comprehensive numerical study illustrates the capabilities of the proposed method, including comparisons with alternative fitted and unfitted mesh methods. [ABSTRACT FROM AUTHOR]

In structural construction practice, the use of reinforced concrete slabs is extremely common due to their structural and economic advantages. An important issue is the study of structural behavior given to horizontal effects. The significance of this is centered not only on the scales caused by wind and construction loads, which are considered to be "normal" i.e., the quasi-static, which is essentially one-way monotonically increasing but also the most researched seismic, i.e., cyclically varying, direction and magnitude effects. The most widespread methods for sizing flat plate slabs to unidirectional, quasi-static horizontal loads are the so-called Equivalent Frame Method and the Effective Beam Width Method. In addition to analytical and basically linear numerical theoretical methods, several laboratory experiments have been performed and published. In this paper, we investigate the behavior of columnsupported flat plate slabs against unidirectional, monotonically increasing horizontal loads using an advanced nonlinear numerical modeling method. Numerical models constructed with different geometric dimensions were created with ATENA 3D three-dimensional nonlinear finite element software. In the numerical studies, in addition to the vertical loads in the global sense, the horizontal loads were also taken into account. In our studies, we analyzed the global behavior of the structure, crack propagation, and internal stresses. The results were illustrated on force - displacement diagrams and compared with the results of the laboratory experiments used, thus showing the accuracy and limitations of the numerical modeling procedure. The numerical results were also compared with the results determined on the basis of the equivalent framework models. [ABSTRACT FROM AUTHOR]

In this paper, we consider mixed finite element approximation of a coupled system of nonlinear parabolic advection-diffusion-reaction variational (in)equalities modeling biofilm growth and nutrient utilization in porous media at pore-scale. We study well-posedness of the discrete system and derive an optimal error estimate of first order. Our theoretical estimates extend the work on a scalar degenerate parabolic problem by Arbogast et al, 1997 [4] to a variational inequality; we also apply it to a system. We also verify our theoretical convergence results with simulations of realistic scenarios. [ABSTRACT FROM AUTHOR]

Iron graphite (FeGr) composite is a potential design material for machine tools to increase vibration damping without additional energy. Previous studies focused on the isolated composite's properties rather than their damping effect as a passive damper to assembled components. There is currently no effective model using real mode superposition (RMS) method for demonstrating the damping behavior of FeGr composites in a multi-material structure. This paper presents a local damping description for a finite element model with RMS assuming constant loss factor for all modes to simulate the damping behavior of FeGr composites and their contribution to system damping and a test rig to identify the model parameters for typical machine tool boundary conditions. The influence of FeGr spacers with 0, 20%, 40%, and 60% graphite content on eigenfrequency and on damping of the test rig was measured, and the results were used to identify the damping model. The agreement of eigenfrequencies and damping ratio between measurement and simulation proves the effectiveness of the parameterized damping model predicting the mode-dependent damping behavior of FeGr in machine tool joints. The material analysis indicates that increasing the graphite content of FeGr composites from 0 to 60% amplifies the system damping from 0.03% to 0.6% at first bending mode. The interface pressure in a tightly fastened FeGr joint affects the system damping significantly. When designing machine tools, the surface condition of FeGr composite cannot be overlooked. FeGr dominates system damping and shows better damping performance at high vibration amplitudes. [ABSTRACT FROM AUTHOR]

This paper is devoted to a study of a new kind of bilateral obstacle problem. The obstacles are made of rigid bodies covered by soft layers which are deformable and allow penetration. A model of an elastic rigid bilateral obstacle problem is established, and three equivalent descriptions are derived: the energy form, the variational inequality form, and the differential equation form. We prove the solution existence and uniqueness of this model and provide an error estimate of the numerical solutions. The optimal order error estimate for the linear finite element method is derived under the proper regularity assumption. A penalty method is introduced to solve the finite element approximation problem, and the convergence results are obtained when the penalty parameter tends to infinity. Several numerical examples are reported, and the results are in good agreement with the theoretical analysis. [ABSTRACT FROM AUTHOR]

The water leakage through segmental joint gaskets has become a major concern that adversely affects the normal serviceability of underwater shield tunnels throughout the construction and operational periods. Therefore, it is of great significance to investigate the sealing performances of the joint gaskets, which directly helps evaluate the waterproof capacity of underwater shield tunnels. To date, the numerical modeling plays an irreplaceable role in the analysis on the waterproof capacity of the joint gaskets. Nevertheless, conventional methods tend to ignore the self-sealing effect induced by the water seepage pressurization, thus failing to reveal the progressive evolution of the water infiltration process through the joint gasket. To remedy this defect, this paper proposed a novel numerical model to simulate the penetration process of the sealing gasket based on the Python language-enabled secondary programming in the ABAQUS software, which could fully consider the superimposed seepage squeezing effect. Based on the proposed model, the waterproof failure process and the dynamic contact stress of the gasket's water seepage path subject to excessive hydraulic pressure were thoroughly investigated. Moreover, indoor tests on the waterproof capacity of the gasket were also performed to validate the proposed model. It is found that the numerical results from the developed model are consistent with the experimental results. This research will contribute to better understanding of the gaskets' hydraulic penetration process and more accurate prediction of the maximum waterproof capacity in underwater shield tunnels. [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]

This paper presents the numerical damage analysis of concrete structures using higher-order beam theories based on Carrera Unified Formulation (CUF). The concrete constitutive relation is modeled using continuum damage mechanics based on a modified Mazars concrete damage model, in which both the tensile and compressive softening behaviors are regularized with classical fracture energy methodology. An expression is proposed to estimate the characteristic length in higher-order beam theories, to prevent mesh dependency. Both softening constitutive laws and fracture energy calculations are obtained according to Model Code 2010. To assess the efficiency of the proposed model, three classical benchmark quasi-static experiments are taken for validation. From the comparison between numerical and experimental results, the proposed CUF model using continuum damage mechanics can present 3D accuracy with low computational costs and reduce the mesh dependency. [ABSTRACT FROM AUTHOR]

The paper aims to develop a finite element methodology to deal with vibrations and buckling of laminated thin plates subjected to thermal and hygroscopic effects, once a second-order strain gradient theory is included to overcome the limitations of conventional elasticity and to capture nonlocal phenomena. The numerical scheme takes advantage of Hermite approximation for both membrane and bending primary variables, since the strain gradient introduces higher-order derivatives of the nodal displacements. Its versatility is proven by dealing with general lamination schemes and arbitrary boundary conditions. The analyzed configurations cannot be solved analytically. [ABSTRACT FROM AUTHOR]