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A major difficulty in finite element analysis is the preparation of an effective mesh leading to a good response solution. In engineering analyses of complex components, oftentimes, much more time is spent to arrive at an adequate mesh than to obtain the solution of the established finite element model. The difficulty in meshing is due to the fact that finite elements need to abut each other and cannot overlap. This can lead to highly distorted elements, e.g. sliver elements, reducing the accuracy of solution. In practice, to establish an effective mesh, frequently, significant expertise in building meshes is needed, because great care must be taken in cleaning up the CAD geometry and preparing an effective mesh. The objective in this paper is to present a new finite element solution scheme including meshing in which the elements can overlap. The property that finite elements can overlap removes many of the meshing difficulties, leads to an effective meshing procedure and an overall easy-to-use solution scheme for an analyst or a designer. We first present the meshing scheme that we propose, which combines the use of traditional finite elements and overlapping finite elements. A particular feature is that the meshing procedure can be directly embedded in CAD driven solutions. We then present the theory used for the formulation of the overlapping finite elements and the coupling with traditional finite elements. We consider spherical and brick-shaped overlapping finite elements for which the theory is largely based on the formulation of the method of finite spheres. Finally, we illustrate the complete solution scheme in the analysis of some two-dimensional problems using the CAD geometry as the starting point. While the paper presents a new paradigm for analysis in CAD environments, with much potential, we realize that much further study and research is needed on some of the important ingredients of the method to render the complete procedure effective for general practical engineering analyses of static and dynamic problems. [ABSTRACT FROM AUTHOR]

As is well-known to all, the conventional finite element method (FEM) is constrained by the “numerical dispersion error” issue for solving acoustic problems at high frequencies. In this paper, the gradient smoothing technique (GST) which is based on the edges of the elements is combined with the conventional FEM to construct a novel edge-based smoothed FEM (ES-FEM) for two dimensional exterior structural–acoustic problems. The smoothed gradient field is obtained by performing the GST over the obtained smoothing domains (SDs). The present ES-FEM is able to provide a relatively appropriate stiffness of the real system owing to the “softening effects” from the GST. Therefore, the accuracy of the numerical solutions can be significantly improved. To effectively handle the exterior Helmholtz equation in unbounded domains, a predefined artificial boundary B is employed to obtain a bounded computational domain and the well-known Dirichlet-to-Neumann (DtN) map is used to prevent the possible reflections from the far-field. Several supporting numerical examples indicated that the ES-FEM with DtN map was very effective for exterior structural–acoustic problems and could produce more accurate numerical results than the conventional FEM. [ABSTRACT FROM AUTHOR]

In this paper an efficient numerical tool is proposed to investigate delamination type failure in multi-layered composite shells. In the current contribution the extended finite element method (XFEM), the mixed-mode cohesive zone model, the contact formulation, and the damage criterion are incorporated into a new algorithm to study the interfacial delamination initiation and growth with less computational effort. A flat-shell formulation is developed in the geometrically non-linear regime to study the response of shells in small strains and moderate rotations. In addition, the equivalent single layer theory (ESLT) is applied to simulate the multi-layered laminates. This formulation is enhanced through the XFEM topology to be able to model discontinuous domains and a mixed-mode bilinear cohesive formulation to track the delamination growth. In the current study, the simulation can be initiated in an intact laminate. Thus, unlike formulations in existing finite element models, incorporating cohesive zone model at all available interfaces is not necessary. The interlaminar stresses are calculated during post-processing and they are being used in the delamination onset criterion. As soon as the criterion is satisfied at a specific layer and location, the formulation of that corresponding element is locally changed to XFEM and the cohesive behaviour. Consequently, the possibility to track delamination growth is locally provided; and hence, the computational cost is reduced. [ABSTRACT FROM AUTHOR]

Local fatigue strength assessment based on threshold values obtained by linear-elastic notch stress calculation is commonly utilized due to its applicability to complex geometries with an acceptable effort. As the result of a finite element computation is affected by the element type and mesh refinement, this paper investigates the numerical influence on the notch stress based fatigue strength assessment of non-welded and welded components. Based on extensive finite element studies employing the software package Abaqus it is concluded that quadratic shape functions with a number of sixteen for non-welded parts and twelve elements over a semicircle for welded joints should be at least applied to minimize the numerical impact. [ABSTRACT FROM AUTHOR]

Concrete is an heterogeneous structural material whose constitutive behaviour is strictly depending on the mechanical properties of the aggregates and the cement paste. A large number of methods have been devoted to the prediction of the mechanical properties of this material by means of meso-scale analysis. The paper concerns a new meso-scale model of concrete, that considers the composite as a multi-phase material. The numerical description of the meso-scale structure is attained using a random method that allocates at each Gauss point of the finite element discretisation of the Representative Volume Element (RVE) a specific phase of the mixture: aggregate, cement paste, void. Each phase is characterised by a specific non linear constitutive model, whose parameters have been determined by means of experimental tests on the components. More experimental tests have been performed on concrete samples, and they have been numerically reproduced by means of the proposed procedure. Numerical simulations of cyclic uniaxial compression tests have shown the ability of the meso-model to correctly predict the peak strength, the tangent and secant elastic stiffness of the mixture for strains above the peak strain, even adopting a relatively coarse finite element discretisation of the RVE. [ABSTRACT FROM AUTHOR]

Abstract: This work deals with the numerical evaluation of the structural response of simply supported (transversally loaded at mid-span) and cantilever (subjected to tip point loads) beams built from a commercial pultruded I-section GFRP profile. In particular, the paper addresses the beam (i) geometrically linear behaviour in service conditions, (ii) local and lateral-torsional buckling behaviour, and (iii) lateral-torsional post-buckling behaviour, including the effect of the load point of application location. The numerical results are obtained by means of (i) novel Generalised Beam Theory (GBT) beam finite element formulations, able to capture the influence of the load point of application, and (ii) shell finite element analyses carried out in the code Abaqus. These numerical results are compared with (i) the experimental values reported and discussed in the companion paper (Part 1) and (ii) values provided by analytical formulae available in the literature. [Copyright &y& Elsevier]

The objective in this paper is to improve the performance of the 4-node MITC quadrilateral shell finite element, referred to as the MITC4 element (Dvorkin and Bathe, 1984). We propose a new MITC4 shell element, the MITC4+ element, in which the mid-surface membrane strain components are assumed using the concept of the MITC method. The tying membrane strains are obtained from four triangular domains which subdivide the mid-surface of the 4-node quadrilateral shell element. This approach alleviates locking that can happen when the MITC4 shell elements are geometrically distorted in curved geometries. Several basic tests including the isotropy, zero energy mode, and patch tests are performed. Through the solution of various shell problems, the convergence behavior of the MITC4+ shell element is studied to show the improvements reached. [ABSTRACT FROM AUTHOR]

The extended scaled boundary finite element method (X-SBFEM) based on the level set method (LSM) is proposed in this paper to combine the advantages of the scaled boundary finite element method (SBFEM) and the extended finite element method (XFEM). The level set method (LSM) algorithm is applied to further develop the X-SBFEM, especially for the crack propagation problem. The Heaviside enrichment function is used to represent a jump across a discontinuity surface in a split element, and the non-smooth behavior around the crack tip is described using the semi-analytical SBFEM. The stiffness of the region containing the crack tip is computed directly, and the generalized stress intensity factors of many types of singularities are obtained directly from their definitions using consistent formulas. In the numerical simulations, a square plate with an edge crack under tension, a three-point bending beam, a four-point shear beam and a dam (the Koyna dam) with a single propagating crack are modeled. The results show that the proposed X-SBFEM is capable of calculating the stress intensity factors of cracks and predicting crack trajectories and load–displacement relations accurately. An analysis of the sensitivity of the parameters is employed to demonstrate that various mesh densities and crack propagation step lengths led to consistent results. [ABSTRACT FROM AUTHOR]

The paper presents numerical simulations of punching shear in a reinforced concrete slab-column configuration formerly tested in the laboratory. A brief description of the test program at the University of Waterloo is reported. For the simulation, a symmetric quarter of the test configuration is employed. Full three-dimensional finite element discretized geometry is considered together with elastic–plastic reinforcement embedded as truss elements in concrete. Two regularized numerical models of concrete, formulated within elastic–plastic-damage theories, are applied. The first one, called gradient damage, is refined by an additional averaging equation where gradient enhancement involves an internal length scale. In the second one, called rate-dependent damaged plasticity model, a viscoplastic strain rate is introduced. The results for the first model implemented in FEAP and the second model from ABAQUS are discussed in detail. Different issues of numerical simulation to properly predict punching shear behaviour in the slab-column configuration are presented. [ABSTRACT FROM AUTHOR]

Abstract: In this paper we present thermo-plasticity model for dealing with localized failure with softening, which is capable of accounting for mechanical loading and heat transfer simultaneously. The main point concerns the localized failure of the structure which results with heterogeneity of stress and strain field for temperature dependent properties. We discuss how to employ structured mesh for such case, and construct the appropriate enhancements of the displacement and temperature fields by using the finite element method with embedded discontinuities (ED-FEM). For clarity, we first consider 1D case, and provide several illustrative numerical simulations. We then provide the corresponding generalization of the proposed model to 2D case and its numerical implementation based upon structured ED-FEM mesh. [Copyright &y& Elsevier]

• The node-scheme method is firstly introduced into the XFEM to solve the frictional contact crack problems. • The stress redistribution is considered in the local part of the crack surface in the proposed method. • The proposed method has the ability to solve locking problems in the numerical simulation of the frictional contact crack. In this paper, based on the nodal displacement of the crack surface element, a novel node-scheme method is proposed to model the frictional contact problem in the framework of extended finite element method (XFEM). The paper systematically illustrates the novel node-scheme including the fundamentals of the proposed method, the coupled Coulomb's friction model. The novelty of the proposed method is that the node-scheme method is first introduced into the XFEM, it can consider the stress redistribution in the local part of the crack surface, and it has the advantage of solving the locking phenomenon in the numerical simulation of the frictional contact problem. The numerical results show that the proposed method is accurate and applicable to efficiently solve the frictional contact crack problem. [ABSTRACT FROM AUTHOR]

Abstract: Coupled electro-mechanical problems are frequently encountered when dealing with micro electro-mechanical systems (MEMS) with capacitive actuation and/or readout systems; their numerical solution can be extremely time consuming, due to the nonlinearity of the coupling terms. Coupled electrostatic – structural dynamic simulations are carried out in this paper through an innovative numerical procedure, based on the combined use of a domain decomposition technique and of a proper orthogonal decomposition methodology. The approach is assessed through the analysis of the dynamic response of a doubly clamped beam and of a plane resonator subjected to an electrostatic actuation, showing computational gains up to 98%. [Copyright &y& Elsevier]

Abstract: This paper treats the blast response of a pile foundation in saturated sand using explicit nonlinear finite element analysis, considering complex material behavior of soil and soil–pile interaction. Blast wave propagation in the soil is studied and the horizontal deformation of pile and effective stresses in the pile are presented. Results indicate that the upper part of the pile to be vulnerable and the pile response decays with distance from the explosive. The findings of this research provide valuable information on the effects of underground explosions on pile foundation and will guide future development, validation and application of computer models. [Copyright &y& Elsevier]

Abstract: This paper introduces an original model to simulate the bond failure between concrete and reinforcing steel bars. The model was developed to be used in threedimensional analyses within the framework of the Finite Element Method and for general loading cases. It was designed using a hierarchical approach by combining what is called the base model, which acts as the skeleton of the model and introduces the basic response under monotonic and reversed loading, and four independent and optional sub-models used to enhance the simulation when needed, by considering the cyclic resistance degradation, the peak stress slip evolution, the reload slip evolution and the radial stress effect. The model implementation within the framework of the Finite Element Method is described and its accuracy is assessed using a series of validation tests. At the end, the main conclusions extracted from this work are presented. [Copyright &y& Elsevier]

Abstract: Mid-frequency response analysis often faces computational difficulties when a conventional modal approach is used for a finite element linear system. In this paper, the computational burden is relieved by frequency sweep algorithm or mode acceleration method for a reduced-order system constructed by algebraic substructuring, a variant of model order reduction. The two methods are compared with the help of numerical experiments and their computational complexity. As demonstrated by the finite element simulations, in which proportional damping is assumed, of a turbo-prop aircraft and a ring resonator, the frequency sweep algorithm for reduced-order systems shows the best performance among all considered numerical solutions, including the conventional approach. [Copyright &y& Elsevier]

Abstract: This paper addresses accuracy issues of nodal stresses in both finite elements and finite volumes. Strategies to evaluate nodal stresses for finite elements are also briefly discussed. Emphasis is placed on the application of finite volumes to solid mechanics and an overview of recent advancements is presented. Numerical simulation of test problems shows that accuracy of nodal stresses evaluated using finite elements is strongly dependent on the recovery strategy. In all cases, stress recovery at boundary nodal points renders large errors for all non-patch schemes. Contrastingly, finite volumes provide an accurate computation of nodal stresses, including at domain boundaries. [Copyright &y& Elsevier]

Abstract: In this paper, sloshing waves have been analyzed for baffled and un-baffled tanks. Numerical simulations were carried out based on volume of fluid (VOF) techniques with arbitrary-Lagrangian–Eulerian (ALE) formulation which adopts the displacement of solid, the pressure and displacement in the fluid as variables to model the coupled system. The response of the coupled system is obtained by using the well-known software ADINA, which offers efficient fully coupled fluid–structure interaction capabilities by finite element method. The results obtained are compared with the available experimental data to demonstrate the reduction of sloshing effects in fluid model. [Copyright &y& Elsevier]

Abstract: This paper treats the dynamic response and energy absorption of aluminum foam-filled conical tubes under axial impact loading using non-linear finite element techniques. The influence of geometrical, material and loading parameters on the impact response is investigated using validated numerical models. Results are quantified in terms of important impact response parameters and indicate that the foam filler stabilizes the crushing process and thus improves the energy absorption capacity. The superior performance of foam-filled conical tubes as impact energy absorbers is evident from the results. The research information generated will be useful in developing guidance towards the design of these devices in impact applications. [Copyright &y& Elsevier]

Abstract: This paper presents a new simple and efficient two-dimensional frame finite element (FE) able to accurately estimate the load-carrying capacity of reinforced concrete (RC) beams flexurally strengthened with externally bonded fibre reinforced polymer (FRP) strips and plates. The proposed FE, denoted as FRP–FB-beam, considers distributed plasticity with layer-discretization of the cross-sections in the context of a force-based (FB) formulation. The FRP–FB-beam element is able to model collapse due to concrete crushing, reinforcing steel yielding, FRP rupture and FRP debonding. The FRP–FB-beam is used to predict the load-carrying capacity and the applied load-midspan deflection response of RC beams subjected to three- and four-point bending loading. Numerical simulations and experimental measurements are compared based on numerous tests available in the literature and published by different authors. The numerically simulated responses agree remarkably well with the corresponding experimental results. The major features of this frame FE are its simplicity, computational efficiency and weak requirements in terms of FE mesh refinement. These useful features are obtained together with accuracy in the response simulation comparable to more complex, advanced and computationally expensive FEs. Thus, the FRP–FB-beam is suitable for efficient and accurate modelling and analysis of flexural strengthening of RC frame structures with externally bonded FRP sheets/plates and for practical use in design-oriented parametric studies. [Copyright &y& Elsevier]

In the present paper, the process of the formulation of the stiffness and transfer matrices and of the load vectors of Timoshenko beams on Kerr-type three-parameter elastic foundation is presented. These matrices are developed on the basis of the exact solution of the governing differential equations for all potential solution cases. The reliability and precision of the modeling of beams resting on elastic foundation through the use of these matrices is assessed by means of two numerical examples. [Copyright &y& Elsevier]

A moving rail vehicle may cause propagating waves to the surroundings potentially leading to detrimental effects for the track construction, nuisances for the surroundings and interference with delicate electronic equipment. A full computational model should be able to couple a correct simulation of the rigid body motion of the different train parts with accurate prediction of the solid wave propagation in the ground. This paper integrates the dynamics of the vehicle and the elastic soil into one monolithic system. Equations of motion for the train have been merged the system representing the FEM problem for the rest of the structure. Three models of modern high-speed locomotives were run over a solid finite element model of a rail structure. [Copyright &y& Elsevier]

Abstract: In this paper a numerical model is presented for assessing the stress and displacement state of RC structures with textile post-reinforcement. The physical nonlinear computational model is based on layered hybrid finite elements with assumed stress distribution, which are extended by the introduction of an arbitrary number of discrete, coupled parallel reference planes in such a way that deformations perpendicular to the reference planes and shear deformations along the interfaces between the layers may be taken into account on a discrete basis. Besides a verification of the method on the basis of experimental results, practical application possibilities are also demonstrated. [Copyright &y& Elsevier]

Non-linear properties of a generic hydraulic engine mount (HEM) are identified and characterized by experiment and simulation approaches. The experimental methods for obtaining static and dynamic performances of the HEM are presented. The characteristics of two configurations of the take-apart HEMs (one is with an inertia track and a free decoupler and the other one is only with an inertia track) and their rubber springs are studied. The relations between static stiffness of an HEM and its rubber springs in three orthogonal directions are investigated. The influences of preload, excitation amplitudes and frequencies on the dynamic stiffness of an HEM are verified. The effects of the free decoupler on dynamic characteristics of the HEM are studied by comparisons of the test results of the two HEMs. The dynamic fluid pressure and the temperature in the upper chamber of an HEM are measured under different excitation conditions. A fully coupled fluid–structure interaction (FSI) and finite element analysis (FEA) model for simulation of HEMs is developed in this paper, which can be used to simulate the static and dynamic performances of the HEMs with only stress versus strain relations of the rubber materials, the fluid physical parameters and the HEMs sizes. The simulated results of one HEM with the proposed model are given, and the results match well with the measured data, or in coincidence with the working mechanisms of HEMs. [Copyright &y& Elsevier]