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In this paper, infrared thermography is applied to the quantitative characterization of optically semi-transparent media by using a newly introduced mathematical model. The method is specifically aimed to the detection and evaluations in graphic features buried beneath the surface of some particular kind of cultural heritage artefacts, such as books and documents. A numerical approach based on the finite element method, is proposed for solving the model equations. The computed thermographic signal depends on different inspected material physical properties, which have been selectively evaluated by comparing the theoretical results with the experimental ones in specifically designed test samples. Thereafter, the model is applied to the analysis of the results obtained in the case of graphic elements buried within samples constituted by the same previously characterized materials.

This paper combines the Theory of Critical Distances (TCD) and Finite Element Analysis (FEA) to provide estimations of fracture loads in Polyvinyl chloride (PVC) tubular beams containing notch-type defects. The methodology is, however, theoretically applicable to any kind of material and component developing a predominant linear-elastic behavior. FEA is used to determine the stress field at the notch tip, which is then combined with one of the TCD failure criteria (the Point Method, PM) to derive the corresponding critical load. The results prove that this methodology provides reasonable predictions of fracture loads. The authors of this work would like to express their gratitude to the Spanish Ministry of Science and Innovation for the financial support of the project PGC2018-095400-B-I00 “Comportamiento en fractura de materiales compuestos nano-reforzados con defectos tipo entalla”, on the results of which this paper is based.

WOS:000537776600002 Engineering structures commonly have arbitrarily-shaped geometry and contain irregularly-shaped cutouts. The integrity of these structures is significantly influenced by the boundary stresses associated with these cutouts. This paper focuses on the evaluation of the stress of a complicated-shaped structure with an irregularly-shaped hole using a single measured displacement component. Digital Image Correlation (DIC) was utilized herein to record the in-plane displacements of the loaded structure. Considering the complications in providing solely analytical solutions for finite structures or numerical solutions in case of insufficient knowledge of the boundary and loading conditions, this paper demonstrates an effective hybrid technique of experimentally stress analyzing in such situations. Processing only one component of the in-plane displacement information with a stress function provides the full-field stresses, including the edges of the plate. Without the knowledge of the external loading conditions nor the need of physically differentiating the measured displacement to obtain strains, and hence stresses, the proposed hybrid technique simultaneously smoothes the recorded displacement information and evaluates the individual stresses full-field in a strong mechanics foundation (equilibrium and compatibility). To validate and support the proposed hybrid technique based on Airy stress function, the obtained results were compared with the those obtained through thermoelastic stress analysis, finite element analysis, and strain gauges. TUBITAK, Ankara, TurkeyTurkiye Bilimsel ve Teknolojik Arastirma Kurumu (TUBITAK); Kirikkale University, Kirikkale, TurkeyKirikkale University The author is grateful for the financial support from TUBITAK, Ankara, Turkey and Kirikkale University, Kirikkale, Turkey. The author thanks Prof. Robert Rowlands at UW-Madison, Wisconsin, USA.

This paper presents a comparison of two present meshfree approaches for modelling brittle material in case of ballistic impact, where extensive cracking and fragmentation is present. These phenomena are very unfeasible to simulate with a standard Lagrangian technique thus alternative methods have been considered in the last years. A comparison between two methods is the main aim of the present article. Smoothed Particle Hydrodynamics (SPH) is an almost consolidated method that exploit the description of a continuum by means of discrete elements whose properties are “smoothed” by a Kernel Function. In this paper a procedure that exploits the transition from finite elements (FE) to SPH particles, following the onset of an erosion criterion is used. This approach and its results are then compared to the recent state-based Peridynamics. Peridynamics method is based on integral equation and allow a direct application to discontinuities and fractures. The results from both methods are critically compared with experimental data and show that the damage morphology is reproduced similarly by both approaches; however less computation efforts are required when peridynamics are used.

Steel grade 14MoV6 3 is used for manufacturing of boilers and steam pipelines designed for steam temperatures up to 560 °C. This paper presents the numerical simulation of a CT-specimen, using the finite element method. The analysis was performed using Ansys Workbench R21, and represents the initial stage of extensive research involving the behaviour of 14MoV6 3 steel. The goal was to simulate the real experimental conditions, including boundary conditions and loads, which were defined in accordance with relevant standards, and to obtain representative results. The temperature dependent mechanical properties needed for the simulation of plastic behaviour of such specimens under tensile loads were obtained from the experimental data and the literature.

The aim of this paper is to present the implementation of 3D fractional viscoelastic constitutive theory presented in Alotta et al., 2016 [1]. Fractional viscoelastic models exactly reproduce the time dependent behaviour of real viscoelastic materials which exhibit a long “fading memory”. From an implementation point of view, this feature implies storing the stress/strain history throughout the simulations which may require a large amount of memory. We propose here a number of strategies to effectively limit the memory required. The form of the constitutive equations are summarized and the finite element implementation in a Newton-Raphson integration scheme is described in detail. The expressions that are needed to be coded in user-defined material subroutines for quasi static and dynamic implicit and explicit analysis (UMAT and VUMAT) in the commercial finite element software ABAQUS are readily provided. In order to demonstrate the accuracy of the numerical implementation we report a number of benchmark problems validated against analytical results. We have also analysed the behaviour of a viscoelastic plate with a hole in order to show the efficiency of these types of models. The source codes for the UMAT and VUMAT are provided as online supplements to this paper.

"Available online 28 December 2020", Hybrid-Trefftz finite elements are well suited for modeling the response of materials under highly transient loading. Their approximation bases are built using functions that satisfy exactly the differential equations governing the problem. This option embeds relevant physical information into the approximation basis and removes the well-known sensitivity of the conventional finite elements to high solution gradients and short wavelength excitations. Despite such advantages, no public software using hybrid-Trefftz finite elements to model wave propagation through solid and porous media exists to date. This paper covers the formulation and implementation of hybrid-Trefftz finite elements for single-phase, biphasic and triphasic media, subjected to dynamic loads. The formulation is cast in a unified framework, valid for the three types of materials alike, and independent of the nature (harmonic, periodic or transient) of the applied load. Displacement, traction, elastic and absorbing boundary conditions are accommodated. The implementation is made in three novel, open-source and user-friendly computational modules which are freely distributed online., This work was partly funded by Fundação para a Ciência e a Tecnologia (MCTES) through national funds (PIDDAC) under the R&D Units “Institute for Sustainability and Innovation in Structural Engineering (ISISE)” and “Civil Engineering Research and Innovation for Sustainability (CERIS)”, references UIDB/04029/2020 and UIDB/04625/2020, respectively, and through research project CEN-DynaGEO, reference PTDC/EAM-GTC/29923/2017.

This paper proposes a 4-degree-of-freedom (DOF) actuator for a fast steer mirror (FSM) compensation system in order to compensate for 4-DOF laser errors. The mathematic system modeling was built to design and predict the performance of the proposed 4-DOF FSM. Finite element analysis was performed by using a commercial software to analyze the characteristics of the electromagnetic structure and mechanical structure for the proposed 4-DOF FSM. This study further verifies the properties of the proposed 4-DOF FSM by using a laboratory-built prototype. The proposed 4-DOF FSM has the travel range of ±5 mrad and ±0.04 mm along X and Y axes with accuracy of 0.025 mrad and 0.0012 mm and the bandwidth of rotational part and translational part are 10 Hz and 39 Hz, respectively.

Aluminosilicate glass possesses excellent mechanical and functional properties. It combines relatively low density, high hardness and strength in compression. However, the very low tensile strength and inherent brittleness are main concerns to its application. Due to the presence of microheterogeneity and randomly distributed surface flaws, the mechanical strength and failure mechanisms of silicate glasses varies considerably, even for the same glass products. In the present work, inhomogeneous FEM models were proposed and utilized to simulate the discrete failure strength and replicate the multiple crack patterns of aluminosilicate glass. Special attention was paid to the quasi-static three-point bending and ballistic impact loading conditions in this paper. The results from experiments and simulations were compared in detail and show that both the failure strength and fracture modes can be reproduced properly via the proposed numerical models both for three-point bending tests and for ballistic impact conditions. In the latter both the predicted residual velocity of projectile and the fragmentation behavior of glass tiles from the inhomogeneous FEM method show better matching than the homogeneous models.

Functionally Graded Materials (FGM) are a class of advanced composites with a gradual and continuously varying microstructural composition. This paper presents MicroFEA 1.0, which is a software package developed to help overcoming the challenges of designing and analyzing FGM structures. It provides capabilities to fit FGM experimental data to B-Spline curves and to analyze composite materials using mean-field micromechanics homogenization techniques. The package is composed of MATLAB scripts and Fortran subroutines intended for Finite Element Analysis (FEA) using Abaqus. The Abaqus user-material subroutines (UMATs) are designed to work with heterogeneous materials at the integration points level, discarding the need for custom-designed elements. Thermomechanical analyses can also be carried out with the help of UTEMPs. This software will provide valuable help for scientists and engineers facing the development of new FGM structural components.

Prediction of multi-hazard slope stability events requires an informed and judicious choice of the possible scenarios. An incorrect definition of landslide conditions in terms of expected failure volume, material behavior, or boundary conditions can lead to inaccurate predictions and, in turn, to wrong engineering and risk management decisions. Reduced-scale experiments carried out two years before the Vajont disaster were carried out with a material not representative of the actual rockslide behavior and failed in not considering the simultaneous failure of the whole landslide body. Based on these inappropriate assumptions, the physical models led to wrong estimates of the safety operational level for the Vajont reservoir. This work uses the Particle Finite Element Method (PFEM) to analyze the implications of the wrong hypotheses considered in the pre-event experiments, simulating numerically the Vajont disaster for different sliding volumes and material properties. The use of the PFEM for the accurate assessment of the consequences of landslides impinging in water reservoirs has been already validated in a companion paper. In this work, we demonstrate the capabilities of a robust and reliable numerical modeling approach for the simulation of different scenarios, assessing what could have been a safe operational reservoir level in the case of a landslide generated impulse wave. The three-dimensional analyses were run with a high mesh resolution and demonstrate the suitability and robustness of the PFEM model for large-scale landslide and multi-hazard events simulation. This research was supported by the Spanish Ministry of Economy and Competitiveness (Ministerio de Economia y Competitividad, MINECO) through the Severo Ochoa Programme for Centres of Excellence in R&D (CEX2018-000797-S) and the project PRECISE (BIA2017- 83805-R), the CARIPLO Project2016-0769 - DARFLIS-Distributed quantitative risk Analysis for Rapid Flow-like Landslides induced by high Intensity Storms, the Project MIUR – Dipartimenti di Eccellenza 2018–2022, and the PRIN2017 project XFAST-SIMS: Extra fast and accurate simulation of complex structural systems (D41F19000080001).

In this paper a sensitivity study of a FEM model representing a carbon/epoxy composite material tested in Combined Loading Compression (CLC) is presented and the results are compared to experimental results. The present study aims to simulate the failure of composite materials when subjected to compression and crush loading conditions. This is required as a first step of a Building-Block Approach towards full-scale modelling of complex structures. In the experimental part of the work, a laminate panel was manufactured with carbon unidirectional prepreg (Deltapreg UTS-300-DT120-37EF) in a cross-ply, balanced and symmetric stacking sequence, cured in autoclave at 120°C and 5 bar for 90 min. A number of six samples, extracted from the panel, were tested in compression following ASTM D6641/D6641M-16. Numerical simulations have been implemented by means of the commercial software, ESI-VPS PAM CRASH. Boundary conditions, specimens’ dimensions and material properties emulated real test conditions. A sensitivity study was performed on critical simulation parameters: the effect of mesh size and number of shell surfaces representing the composite stacking sequence was initially investigated. Furthermore, the specimen failure mode was inspected by the application of TIED links between the composite plies. Numerical results have been compared with experimental data and the comparison provided references for testing scale-up in the Building-Block Approach.

In this paper we introduce and analyze a mixed virtual element method (mixed-VEM) for a pseudostress-displacement formulation of the linear elasticity problem with non homogeneous Dirichlet boundary conditions. We follow a previous work by some of the authors, and employ a mixed formulation that does not require symmetric tensor spaces in the finite element discretization. More precisely, the main unknowns here are given by the pseudostress and the displacement, whereas other physical quantities such as the stress, the strain tensor of small deformations, and the rotation, are computed through simple postprocessing formulae in terms of the pseudostress variable. We first recall the corresponding variational formulation, and then summarize the main mixed-VEM ingredients that are required for our discrete analysis. In particular, we utilize a well known local projector onto a suitable polynomial subspace to define a calculable version of our discrete bilinear form, whose continuous version requires information of the variables on the interior of each element. Next, we show that the global discrete bilinear form satisfies the hypotheses required by the Babuška–Brezzi theory. In this way, we conclude the well-posedness of our mixed-VEM scheme and derive the associated a priori error estimates for the virtual solutions as well as for the fully computable projections of them. Furthermore, we also introduce a second element-by-element postprocessing formula for the pseudostress, which yields an optimally convergent approximation of this unknown with respect to the broken H(div)-norm. In addition, this postprocessing formula can also be applied to the postprocessed stress tensor. Finally, several numerical results illustrating the good performance of the method and confirming the theoretical rates of convergence are presented. En este artículo presentamos y analizamos un método de elementos virtuales mixtos (VEM mixto) para una formulación de pseudoesfuerzo-desplazamiento del problema de elasticidad lineal con condiciones de frontera de Dirichlet no homogéneas. Seguimos un trabajo previo de algunos de los autores y empleamos una formulación mixta que no requiere espacios tensoriales simétricos en la discretización de elementos finitos. Más precisamente, las principales incógnitas aquí vienen dadas por la pseudoesfuerzo y el desplazamiento, mientras que otras magnitudes físicas como la tensión, el tensor de deformación de pequeñas deformaciones y la rotación, se calculan mediante fórmulas simples de posprocesamiento en términos de la variable de pseudoesfuerzo. Primero recordamos la formulación variacional correspondiente y luego resumimos los principales ingredientes mixtos de VEM que se requieren para nuestro análisis discreto. En particular, utilizamos un proyector local bien conocido en un subespacio polinómico adecuado para definir una versión calculable de nuestra forma bilineal discreta, cuya versión continua requiere información de las variables en el interior de cada elemento. A continuación, mostramos que la forma bilineal discreta global satisface las hipótesis requeridas por la teoría de Babuška-Brezzi. De esta manera, concluimos la buena posición de nuestro esquema VEM mixto y derivamos las estimaciones de error a priori asociadas para las soluciones virtuales, así como para las proyecciones totalmente computables de las mismas. Además, también introducimos una segunda fórmula de posprocesamiento elemento por elemento para el pseudoesfuerzo, que produce una aproximación óptimamente convergente de esta incógnita con respecto a la norma H (div) rota. Además, esta fórmula de posprocesamiento también se puede aplicar al tensor de tensión posprocesado. Finalmente, se presentan varios resultados numéricos que ilustran el buen desempeño del método y que confirman las tasas teóricas de convergencia. Universidad de Concepción, Chile Universidad Nacional, Costa Rica Escuela de Matemática

Die life estimation in hot forging processes is a compelling challenge, due to the number of factors, mainly wear and plastic deformation induced by thermal effects (tempering). The extent of the heating-cooling cycle and the steady state die temperature are known only after hundredth of work cycles. In the paper a realistic work sequence of repeated forging is simulated by the Finite Elements Method on a symmetrical workpiece geometry, for ease of calculation. Tool wear and tempering-induced deformation are estimated along the complete die life cycle, with the help of Neural Network Regression.

The paper investigates the penetration mechanics of thick-section composites. For this purpose, a series of quasi-static penetration tests on Kevlar 29 (plane wave) /epoxy panels with a nominal thickness of 6.5 mm (14 layers) were designed and conducted. The experiments were performed at different support spans using a blunt geometry for the punch. During the tests, the punch displacements and the applied force on the punch were measured. Finite element (FE) models were created to replicate the quasi - static punch test using the LS-DYNA solver and exploiting a material damage model that allows the reproduction of all the different types of failure occurring during the tests (fibre failure, matrix failure, delamination). The focus is placed on the capability of the model to mimic the experimental damage in order to have a reliable virtual tool able to provide, with high accuracy, the penetration mechanisms and the trend of the absorbed energy during the different phases of penetration. The comparison between experimental data and numerical results is discussed.

In this paper, a new method based on the use of infrared thermography is proposed for the characterization of repairs and inserted parts on ancient bronzes. In particular, the quality of the contact between different kind of insertions and the main body of bronze statues is investigated by analysing the heat conduction process occurring across the interface between them. The thermographic results have been used to establish the nature of these inserted elements and the way they have been coupled to the main body of the statue during and after the manufacturing process. A model for the heat conduction based on the numerical finite elements method has been applied to compare the obtained results to the theoretical predictions. Measurements have been first carried out on test samples and then in the field on the Boxer at Rest (Museo Nazionale Romano in Rome), a masterpiece of the Greek Statuary, which contains a large variety of inserted items and repairs which are typical of the manufacturing process of bronze artefacts in general.

Lamb waves based Structural Health Monitoring (SHM) systems, thanks to their high sensitivity to damage detection and the ability to travel over a long distance with low power consumption, are founding increasing industrial applications, especially in the aerospace field, where airworthiness authorities require that composite materials in primary structures must remain undamaged during the in-service life. In order to tolerate damage and monitor its severity and, consequently, to repair the structure only when strictly needed, the use of SHM systems appears to be an efficient solution providing benefits for the current design practice. The continuous assessment of the structural integrity, which can be accomplished by SHM systems, can play a key-role to achieve a less-conservative design as well as to facilitate maintenance operations. This paper deals with a sensitivity analysis, based on the Finite Element (FE) theory, aimed to investigate numerically the influence of the damage orientation on the damage detection capability of a Lamb waves based SHM system arranged on a damaged Glass Fiber Reinforced Polymer composite winglet. Damage detection sensitivity has been measured by analyzing the interaction between the modelled damages and guided waves under a specific central frequency. Signals recorded at different locations by piezoelectric sensors have been compared with the baseline signals achieved under a pristine configuration of the winglet by means of a damage index. A specific trend of the considered damage index has been found out as function of the damage orientation.

This paper aims to present a new grid composite structure obtained by stacking hemp fabric layers impregnated by resin using a new continuous process. Both the process feasibility and the mechanical properties of the obtained specimens were investigated in terms of tensile and flexural response. In addition, the effect of the superimposition error of the layers, that can affect the density and the mechanical properties of the produced bio-composites, was studied both experimentally and numerically by finite element models (FEM). The results showed that the process is able to produce low density composites possessing interesting specific mechanical properties with a good level of repeatability.

Made available in DSpace on 2018-11-28T04:46:16Z (GMT). No. of bitstreams: 0 Previous issue date: 2017-05-01 This paper presents a study on the dynamic analysis of rotors mounted on composite shafts. The dynamic analysis of these rotors differs from conventional analysis due to the existence of internal damping in the shaft. The shafts are made of composite materials, which exhibit viscoelastic behavior. The equations of motion for these rotors represent the influence of internal damping on the dynamic behavior of the rotor system. Composite materials can be manufactured using different layups. This study reviews the methodology that can be used to predict the equivalent mechanical properties of composite shafts. Several finite element simulations are presented to show the influence of the composite shaft layup on the dynamic behavior of the rotor. The simulation results are used to present the influence of the layup on Campbell diagrams, critical speeds, instability thresholds and frequency response functions. (C) 2017 Elsevier Ltd. All rights reserved. Univ Estadual Paulista Julio de Mesquista Filho, Campus Guaratingueta, BR-12516410 Guaratingueta, SP, Brazil Univ Estadual Paulista Julio de Mesquista Filho, Campus Guaratingueta, BR-12516410 Guaratingueta, SP, Brazil

The Theory of Critical Distances (TCD) is a method for predicting fatigue and fracture at stress concentration features. It is extensively used in the design of engineering components, being a relatively simple approach based on post processing of finite element analysis (FEA). It requires only one additional material parameter, the so-called critical distance, L . However its implementation for engineering components of complex shape can be difficult because of the need to use a fine mesh and the requirement to obtain stress/distance path information for the feature being investigated. In this paper we propose a new approach by which predictions can be made more easily through control of the size and type of mesh used. We found that by setting the element size to be a simple multiple of L and by using certain other mesh controls which are generally available in commercial software such as ANSYS, fatigue behaviour could be predicted by simply using the “hot spot stress”, i.e. the maximum stress at the notch root. With this approach the user avoids excessive mesh refinement and does not need to obtain the stress at the critical distance in order to make the prediction. We tested eight different stress concentration features including cracks, sharp notches, blunt notches and V-shaped notches, along with an example component (a welded joint). We found that the error in using this approach, compared with that of the usual implementation of the TCD (Point Method) was acceptably small (less than 20%) in the great majority of cases. A few cases in which larger errors arose were found to be due to particular combinations of mesh element size, feature size and component size which caused difficulties for the automatic mesh generation software. This new approach will allow the TCD to be used more easily, for a wider range of industrial components, structures and materials.

This paper presents the prediction of the contours of plastic work for an AZ31 magnesium alloy sheet in the first quadrant of the stress space using a rate-dependent crystal plasticity finite-element method. The contour of plastic work was initially rather flat in the vicinity of equi-biaxial tension, but bulged severely thereafter. Evidently, the shapes of the contours changed as the plastic work increased, exhibiting a differential work-hardening behavior. The variation of the relative activity of each family of slip systems was examined to investigate the mechanism of the differential work-hardening behavior. During uniaxial tension, the work-hardening was determined mainly by the basal slip in the very beginning, whereas it was determined by both the prismatic and the basal slip in the subsequent deformation. On the other hand, during equi-biaxial tension, the relative activity of the prismatic slip systems was much smaller than that under uniaxial tension, whereas the relative activity of the basal slip systems played a dominant role in the work-hardening throughout the deformation. A simple analysis revealed that it was more difficult to activate the prismatic slip systems for equi-biaxial tension than uniaxial tension in rolled magnesium alloy sheets because the two biaxial stresses tended to cancel each other thus decreasing the relative activity as the biaxial stress ratio approached unity. On the other hand, the basal slip systems were much easily activated than the prismatic slip systems although their Schmid factors were small because the shear stress required for the activation of the basal slip systems was much lower than that of the prismatic slip systems. We concluded that such differences in the activities of the slip systems eventually resulted in the differential work-hardening behavior of the contour of plastic work.

This paper proposes a topology optimization for a linear elasticity design problem subjected to an uncertain load. The design problem is formulated to minimize a robust compliance that is defined as the maximum compliance induced by the worst load case of an uncertain load set. Since the robust compliance can be formulated as the scalar product of the uncertain input load and output displacement vectors, the idea of “aggregation” used in the field of control is introduced to assess the value of the robust compliance. The aggregation solution technique provides the direct relationship between the uncertain input load and output displacement, as a small linear system composed of these vectors and the reduced size of a symmetric matrix, in the context of a discretized linear elasticity problem, using the finite element method. Introducing the constraint that the Euclidean norm of the uncertain load set is fixed, the robust compliance minimization problem is formulated as the minimization of the maximum eigenvalue of the aggregated symmetric matrix according to the Rayleigh–Ritz theorem for symmetric matrices. Moreover, the worst load case is easily established as the eigenvector corresponding to the maximum eigenvalue of the matrix. The proposed structural optimization method is implemented using topology optimization and the method of moving asymptotes (MMA). The numerical examples provided illustrate mechanically reasonable structures and establish the worst load cases corresponding to these optimal structures.

This paper proposes a new topology optimization method, which can adjust the geometrical complexity of optimal configurations, using the level set method and incorporating a fictitious interface energy derived from the phase field method. First, a topology optimization problem is formulated based on the level set method, and the method of regularizing the optimization problem by introducing fictitious interface energy is explained. Next, the reaction–diffusion equation that updates the level set function is derived and an optimization algorithm is then constructed, which uses the finite element method to solve the equilibrium equations and the reaction–diffusion equation when updating the level set function. Finally, several optimum design examples are shown to confirm the validity and utility of the proposed topology optimization method.

The theory of Chester and Anand (2011) for fluid diffusion and large deformations of elastomeric gels is implemented as a user-defined element (UEL) subroutine in the commercial finite element software package ABAQUS. A specialized form of the constitutive equations and the governing partial differential equations of the theory are summarized, and the numerical implementation is described in detail. To demonstrate the robustness of the numerical implementation a few illustrative numerical simulation examples for axisymmetric, plane strain, and three-dimensional geometries are shown. For educational purposes, and also to facilitate the numerical implementation of other coupled multiphysics theories, the source code for the UEL is provided as an online supplement to this paper., National Science Foundation (U.S.) (NSF CMMI-1063626)

The objective of this paper is to investigate the stress update algorithm and the tangent operator for an enhanced generalized plasticity model developed recently for partially saturated soils, where on top of the hydrostatic and deviatoric components of the (effective) stress tensor suction has to be considered as an independent variable. The soil model used for the applications can be derived from a potential energy function and is thermodynamically consistent. The Galerkin method is used to obtain a weak form of the governing equations and a “stress–suction coupling matrix” is derived in the discretization in space by finite element method. The implicit integration algorithm is incorporated in a code for partially saturated soil dynamics. The framework of generalized plasticity is presented and examples are shown including subsidence above a model gas reservoir.

The description as well as the prediction of the behavior of concrete under severe high temperature–pressure loading such as those typical of a loss-of-coolant accidental scenario considered for PWR containment buildings, matter in the study of such engineering applications and are also of interest in other fields such as safety evaluations during fire. The purpose of this paper is to present a flexible staggered finite element thermo-hygral model and then to use it as a numerical tool to determine the temperature and gas pressure fields that develop in concrete when heated.

A comprehensive computational study is undertaken to identify the influence of friction in material characterization by indentation measurement based on elasto- plastic solids. The impacts of friction on load versus indentation depth curve, and the values of calculated hardness and Young’s modulus in conical and spherical indentations are shown in this paper. The results clearly demonstrate that, for some elasto-plastic materials, the curves of load versus indentation depth obtained either by spherical or conical indenters with different friction coefficients, cannot be distinguished. However, if utilizing the parameter β (see text for details), to quantify the deformation of piling-up or sinking-in, it is easy to find that the influence of friction on piling-up or sinking-in in indentation is significant. Therefore, the material parameters which are related to the projected area will also have a large error caused by the influence of friction. The maximum differences on hardness and Young’s modulus can reach 14.59% and 6.78%, respectively, for some elastic materials shown in this paper. These results do not agree with those from researchers who stated that the instrumented indentation experiments are not significantly affected by friction.

In this paper, the discontinuous Galerkin method for the positive and symmetric, linear hyperbolic systems is constructed and analyzed by using bilinear finite elements on a rectangular domain, and an O(h2)-order superconvergence error estimate is established under the conditions of almost uniform partition and the H3-regularity for the exact solutions. The convergence analysis is based on some superclose estimates derived in this paper. Finally, as an application, the numerical treatment of Maxwell equation is discussed and computational results are presented.

In this paper, we consider the elastomechanical problems of a honeycomb structure of composite materials. A multiscale finite element method and the postprocessing technique with high accuracy are presented. We will derive the proofs of all theoretical results. Finally, some numerical tests validate the theoretical results of this paper.

Monolithic components are commonly used in the aeronautical industry due to their homogeneity and excellent strength-to- weight-ratio: ribs, stringers, spars, and bulkheads can be mentioned as examples. In order to assure enough stiffness to the whole component, monolithic parts are often made of thin walls, and webs, obtained usually starting from a raw block of material and removing up to 95% of the weight of the initial block. Therefore, increasing the removal rate as much as possible is the main condition to reach high productivity. The drawback is that, at high removal rate conditions (high feed, large depth of cut), the low stiffness of the thin walls causes dynamic problems, due to the forced vibrations induced by the milling process: even in case of a stable cutting process, vibrations appear as the result of the combination between the tool and workpiece natural frequencies, excited by the tooth-passing frequency harmonics. This paper presents an overview of a comprehensive milling process plan approach, based on finite element method (FEM), which by considering the effects of fixturing, tooltip dynamics, and material removal, allows to define the optimized cutting velocity in order to reduce deflections and vibrations during machining. The advantages of the proposed model over previous works are: (i) it provides a seamless interface to import the G-code generated by a CAM packages; (ii) it performs a computationally efficient modal superposition frequency response analysis of complex workpieces, considering the tooltip position provided by CAM; (iii) it predicts the workpiece non-linear behaviour during machining due to its changing geometry; (iv) it automatically tunes spindle speed continuously along the toolpath, taking into account both the tooltip dynamics and the local workpiece modal behaviour. The effectiveness of the proposed approach has been experimentally validated.

This paper is devoted to analyze a splitting method for solving incompressible inviscid rotational flows. The problem is first recast into the velocity–vorticity–pressure formulation by introducing the additional vorticity variable, and then split into three consecutive subsystems. For each subsystem, the L2 least-squares finite element approach is applied to attain accurate numerical solutions. We show that for each time step this splitting least-squares approach exhibits an optimal rate of convergence in the H1 norm for velocity and pressure, and a suboptimal rate in the L2 norm for vorticity. A numerical example in two dimensions is presented, which confirms the theoretical error estimates.

This paper deals with a posteriori error estimates for advection–reaction–diffusion equations. In particular, error estimators based on the solution of local problems are derived for a stabilized finite element method. These estimators are proved to be equivalent to the error, with equivalence constants eventually depending on the physical parameters. Numerical experiments illustrating the performance of this approach are reported.

Recently, a new suite of twelve benchmark problems for adaptive finite element methods (FEM) was published at the US National Institute for Standards and Technology (NIST). These benchmark problems come with exact solutions, and they exhibit all typical difficulties associated with elliptic problems including singularities, steep internal layers, anisotropy, and oscillations. In this paper we solve these benchmark problems using the open source library Hermes (http://hpfem.org). All these results are reproducible—they are part of the Git repository of the open source Hermes project, and the reader can experiment with them by himself/herself. Instructions for this are provided. We hope that authors of other adaptive FEM codes will make their results for these test problems available in a reproducible fashion as well.

In this paper the problem of numerical approximation of non-Newtonian fluid flow with free surface is considered. Namely, the flow of fresh concrete is addressed. Industrial mixtures often behaves like non-Newtonian fluids exhibiting a yield stress that needs to be overcome for the flow to take place, cf. [R.B. Bird, R.C. Armstrong, O. Hassager, Dynamics of Polymeric Liquids, vol. 1, Fluid Mechanics, Wiley, New York, 1987; R.P. Chhabra, J.F. Richardson, Non-Newtonian Flow in the Process Industries, Butterworth-Heinemann, London, 1999]. The main interest is paid to the mathematical formulation of the problem and to discretization with the aid of finite element method. The described numerical procedure is applied onto the solution of several problems.

This paper presents a numerical model for the prediction of free field vibrations due to vibratory and impact pile driving. As the focus is on the response in the far field, where deformations are relatively small, a linear elastic constitutive behavior is assumed for the soil. The free field vibrations are calculated by means of a coupled FE–BE model using a subdomain formulation. The results show that, in the near field, the response of the soil is dominated by a vertically polarized shear wave, whereas in the far field, Rayleigh waves dominate the ground vibration and body waves are importantly attenuated. Finally, the computed ground vibrations are compared with the results of field measurements reported in the literature.

This paper deals with convergence analysis and applications of a Zienkiewicz-type (Z-type) triangular element, applied to fourth-order partial differential equations. For the biharmonic problem we prove the order of convergence by comparison to a suitable modified Hermite triangular finite element. This method is more natural and it could be applied to the corresponding fourth-order eigenvalue problem. We also propose a simple postprocessing method which improves the order of convergence of finite element eigenpairs. Thus, an a posteriori analysis is presented by means of different triangular elements. Some computational aspects are discussed and numerical examples are given.

Abrasive water jets (AWJs) are finding growing applications for machining a wide range of difficult-to-machine materials such as titanium alloys, stainless steel, metal matrix and fibre reinforced composites, etc. Current applications of AWJs include machining of Titanium alloys for aircraft components and bio-medical implants to removal of aircraft engine coatings. This paper presents the application of an elasto-plastic model based explicit finite element analysis (FEA) to model the erosion behaviour in abrasive water jet machining (AWJM). The novelty of this work includes FE modelling of the effect of multiple (twenty) particle impact on erosion of Grade 5 Titanium alloy (Ti-6Al-4V). The influence of abrasive particle impact angle and velocity on the crater sphericity and depth, and erosion rate has been investigated. The FE model has been validated for stainless steel and yields largely improved results. Further, the same FEA approach has been extended to model the multi-particle impact erosion behaviour of Titanium alloy.

The paper presents an innovative methodology of coupling the conventional finite element machining simulations with computational fluid dynamic (CFD) model to analyse the temperature distribution at the cutting tool. The conventional finite element machining simulations were conducted using DEFORM 2D to predict the heat generation and tool tip temperature during the cutting action. Machining simulations were conducted using Ti6Al4V and uncoated carbide as a workpiece and tool material respectively. Modified version of Johnson-Cook constitutive model was incorporated in the conventional finite element based machining simulations to predict the behavior of flow stresses for Ti6Al4V titanium alloy. Computational fluid dynamics (CFD) simulations were performed using ANSYS® CFX. CFD model has incorporated air as a cooling media to simulate the dry cutting and temperature distribution at the tool surface was obtained. The coupled numerical modeling methodology showed encouraging potential of predicting precise temperature distribution on the cutting tool. The approach can be further evaluated to predict temperature distribution under flood cooling and minimum quantity lubrication (MQL).

This paper addresses the finite element method for the two-dimensional time-dependent Schrödinger equation on an infinite strip by using artificial boundary conditions. We first reduce the original problem into an initial-boundary value problem in a bounded domain by introducing a transparent boundary condition, then fully discretize this reduced problem by applying the Crank–Nicolson scheme in time and a bilinear or quadratic finite element approximation in space. This scheme, by a rigorous analysis, has been proved to be unconditionally stable and convergent, and its convergence order has also been obtained. Finally, two numerical examples are given to verify the accuracy of the scheme.

This paper considers a stabilized method based on the difference between a consistent and an under-integrated mass matrix of the pressure for the Stokes equations approximated by the lowest equal-order finite element pairs (i.e., the P1–P1 and Q1–Q1 pairs). This method only offsets the discrete pressure space by the residual of the simple and symmetry term at element level in order to circumvent the inf–sup condition. Optimal error estimates are obtained by applying the standard Galerkin technique. Finally, the numerical illustrations agree completely with the theoretical expectations.

In this paper the buckling and post-buckling of elastic structures taking into account large rotations are investigated using an asymptotic-numerical method. The critical points are detected by two different ways: first by a bifurcation indicator, second by analysing the poles of a Padé approximant. The first step of the post-buckling branch is computed starting from the bifurcation point and using an extended system. The remaining bifurcating branch is followed by the same algorithm as for the fundamental path. Several examples are tested to show the effectiveness of the proposed method.

In this paper we present existence of blow-up solutions for elliptic equations with semilinear boundary conditions that can be posed on all domain boundary as well as only on a part of the boundary. Systems of ordinary differential equations are obtained by semidiscretizations, using finite elements in the space variables. The necessary and sufficient conditions for blow-up in these systems are found. It is proved that the numerical blow-up times converge to the corresponding real blow-up times when the mesh size goes to zero.

In this paper, we derive two stabilized discontinuous finite element formulations, symmetric and nonsymmetric, for the Stokes equations and the equations of the linear elasticity for almost incompressible materials. These methods are derived via stabilization of a saddle point system where the continuity of the normal and tangential components of the velocity/displacements are imposed in a weak sense via Lagrange multipliers. For both methods, almost all reasonable pair of discontinuous finite element spaces can be used to approximate the velocity and the pressure. Optimal error estimate for the approximation of both the velocity of the symmetric formulation and pressure in L2 norm are obtained, as well as one in a mesh-dependent norm for the velocity in both symmetric and nonsymmetric formulations.

In this paper, we develop both semi-discrete and fully discrete mixed finite element methods for modeling wave propagation in three-dimensional double negative metamaterials. Optimal error estimates are proved for Nédélec spaces under the assumption of smooth solutions. To our best knowledge, this is the first error analysis obtained for Maxwell's equations when metamaterials are involved.

The paper provides new expansions of leading eigenvalues for [email protected][email protected]@ru in S with the Dirichlet boundary condition u=0 on @?S by finite elements, with the support of numerical experiments. The theoretical proof of new expansions of leading eigenvalues is given only for the bilinear element Q"1. However, such a new proof technique can be applied to other elements, conforming and nonconforming. The new error expansions are reported for the Q"1 elements and other three nonconforming elements, the rotated bilinear element (denoted by Q"1^r^o^t), the extension of Q"1^r^o^t (denoted by EQ"1^r^o^t) and Wilson's element. The expansions imply that Q"1 and Q"1^r^o^t yield upper bounds of the eigenvalues, and that EQ"1^r^o^t and Wilson's elements yield lower bounds of the eigenvalues. By the extrapolation, the O(h^4) convergence rate can be obtained, where h is the boundary length of uniform rectangles.

This paper is devoted to the numerical simulation of two-dimensional stationary Bingham fluid flow by semismooth Newton methods. We analyze the modeling variational inequality of the second kind, considering both Dirichlet and stress-free boundary conditions. A family of Tikhonov regularized problems is proposed and the convergence of the regularized solutions to the original one is verified. By using Fenchel’s duality, optimality systems which characterize the original and regularized solutions are obtained. The regularized optimality systems are discretized using a finite element method with (cross-grid P1)–Q0 elements for the velocity and pressure, respectively. A semismooth Newton algorithm is proposed in order to solve the discretized optimality systems. Using an additional relaxation, a descent direction is constructed from each semismooth Newton iteration. Local superlinear convergence of the method is also proved. Finally, we perform numerical experiments in order to investigate the behavior and efficiency of the method.

The accuracy of a finite element numerical approximation of the solution of a partial differential equation can be spoiled significantly by singularities. This phenomenon is especially critical for high order methods. In this paper, we show that, if the PDE is linear and the singular basis functions are homogeneous solutions of the PDE, the augmentation of the trial function space for the Finite Volume Element Method (FVEM) can be done significantly simpler than for the Finite Element Method. When the trial function space is augmented for the FVEM, all the entries in the matrix originating from the singular basis functions in the discrete form of the PDE are zero, and the singular basis functions only appear in the boundary conditions. That is to say, there is no need to integrate the singular basis functions over the elements and the sparsity of the matrix is preserved without special care. FVEM numerical convergence studies on two-dimensional triangular grids are presented using basis functions of arbitrary high order, confirming the same order of convergence for singular solutions as for smooth solutions.

We present an adaptive sparse grid algorithm for the solution of the Black–Scholes equation for option pricing, using the finite element method. Sparse grids enable us to deal with higher-dimensional problems better than full grids. In contrast to common approaches that are based on the combination technique, which combines different solutions on anisotropic coarse full grids, the direct sparse grid approach allows for local adaptive refinement. When dealing with non-smooth payoff functions, this reduces the computational effort significantly. In this paper, we introduce the spatially adaptive discretization of the Black–Scholes equation with sparse grids and describe the algorithmic structure of the numerical solver. We present several strategies for adaptive refinement, evaluate them for different dimensionalities, and demonstrate their performance showing numerical results.

In this paper, we consider a discretization method proposed by Wieners and Wohlmuth [The coupling of mixed and conforming finite element discretizations, in: Domain Decomposition Methods, vol. 10, Contemporary Mathematics, vol. 218, American Mathematical Society, Providence RI, 1998, pp. 547–554] (see also [R.D. Lazarov, J. Pasciak, P.S. Vassilevski, Iterative solution of a coupled mixed and standard Galerkin discretization method for elliptic problems, Numer. Linear Algebra Appl. 8 (2001) 13–31]) for second order operators, which is a coupling between a mixed method in a subdomain and a standard Galerkin method in the remaining part of the domain. We perform an a posteriori error analysis of residual type of this method, by combining some arguments from a posteriori error analysis of Galerkin methods and mixed methods. The reliability and efficiency of the estimator are proved. Some numerical tests are presented and confirm the theoretical error bounds.

In this paper we consider a singularly perturbed elliptic model problem with two small parameters posed on the unit square. The problem is solved numerically by the finite element method using piecewise linear or bilinear elements on a layer-adapted Shishkin mesh. We prove that method with bilinear elements is uniformly convergent in an energy norm. Numerical results confirm our theoretical analysis.