Element Nodes Research Articles

Nonlinear Behavior of Fgm Skew Plates Under In-Plane Load

Nonlinear behavior of Functionally Graded Material (FGM) skew plates under in-plane load is investigated here using a shear deformable eight noded iso-parametric plate bending finite element. The material is graded in the thickness direction according to a power-law distribution in terms of volume fractions of the constituents. The effective material properties are estimated using Mori-Tanaka homogenization method. The nonlinear governing equations for the FGM plate under in-plane load are solved by Newton-Raphson technique to obtain the out-of-plane central deflection and in-plane displacement of the loaded edge. The existence of bifurcation-type of buckling for FGM plates is examined for different boundary conditions, constituent gradient index, and skew angle.

Novel Quadrature-Element Analysis of Plane Stress Elastoplasticity

A novel quadrature element for performing plane stress elastoplastic analysis is introduced in this paper. Differing from the popular finite-element method, the quadrature-element method (QEM) first evaluates the integration in the weak-form statement of the problem by an integral quadrature scheme, and then approximates the differentiation at the discrete integration points by the differential quadrature analog. As a result, the QEM avoids construction of shape functions and obtains higher-order elements easily by just increasing the order of integration. The usage of higher-order elements leads to more accurate solutions and coarser geometric meshes without detriment to the computational scale because the number of degrees of freedom is maintained. In addition, the element nodes in the QEM are the same as the integration points that possess physical meanings such as strains and stresses, which is crucial in the elastoplastic analysis for determining the elastic/plastic state of the nodes. A straightforward elastoplastic quadrature-element formulation is developed. Incremental-iterative and return mapping solution schemes are adopted to implement the quadrature element for the elastoplastic analysis. Numerical examples are presented to demonstrate the effectiveness and high accuracy of the proposed approach.

Node projection strategy for FEM simulating cross-scale crack propagation in massive concrete structures

The irregular cross-scale cracks in massive concrete structures threat the safety. Due to huge difference in scale between structures and cracks, the stability of the irregular cross-scale cracks (millimeter level) cannot be accurately analyzed in the massive concrete structures (hundred-meter level). The imprecision of the mesh model is incompatible with existing advanced cracking methods. To address the problem, this paper presents a novel numerical simulation method for irregular cross-scale cracks in massive concrete structures with node projection strategy. The elements that the crack passes through are identified on the original mesh model without cracks, and the numerical simulation model with irregular cracks is generated by projecting the corresponding nodes of elements that the crack passes through onto the crack point cloud. The primary advantage of this method is that it does not require modifying the original element types or meshing the geometric model with cracks. To verify the present method, the three-point bending beams of concrete with regular cracks and irregular cracks are examined with experiment and numerical simulation. It demonstrates that the shape characteristics of an irregular crack can result in distinct tension damage patterns compared to a regular crack. In addition, the crack propagation during dam construction and earthquake loading is investigated to demonstrate the applicability of the present method for simulating crack propagation in massive concrete structures.

An isoparametric element permutation method for railway tunnel–soil interaction modeling in train–track–tunnel–soil dynamic analysis

For evaluating the ground vibration involving metro tunnel operation, it is of necessity to extend the train-track-tunnel near-filed vibration to the train-track-tunnel-soil far-filed vibration in viewpoint of numerical analysis. It therefore becomes a key technology to achieve the tunnel-soil coupling simulation. In this work, a isoparametric element permutation method is proposed, where the 6-node triangular prismatic elements and 8-node spatial isoperimetric elements have been effectively integrated to achieve the finite elemental modelling of the soil system with the tunnel penetrating. The tunnel and soil subsystems are coupled by the spring-dashpot elements. Once the tunnel satisfies symmetrical property in geometry, the proposed method can be applied to build the tunnel-soil interaction by parametric finite element modelling. Through a combination of this proposed tunnel-soil interaction model and the train-track-tunnel dynamic model, a unified model for characterizing the train–track–tunnel–soil dynamic interaction analysis is constructed within the finite element framework. By comparing the simulation results to the measurements in site, the effectiveness of this model is validated, through which track, tunnel, and ground vibrations can be assessed in an entirely coupled way. Through the numerical studies, it is known that both the number of tunnel lines and the number of trains in operation and their running modes hold significant influence and show different vibration attenuation law on ground vibrations, and quantitative analysis can be achieved through this present work.

Finite element models with node-dependent kinematics based on Legendre polynomials for the global–local analysis of compact and thin walled beams

In the present work, enhanced one-dimensional finite elements with node-dependent kinematics are proposed for the static analysis. Finite element governing equations are derived by applying the Carrera Unified Formulation. This framework subdivides the three-dimensional displacement field into a cross-section domain and an axis domain. The dimension along the beam is discretized by using Lagrange-based shape functions. At each node of the element, an independent structural theory can be imposed, thus obtaining a node-dependent kinematic model. This method permits to focus on the finite element node. In this way, several combinations of kinematics can be used together. In particular, Taylor-based and Legendre-based expansions have been adopted in this paper to create global–local models without using special coupling methods. The results have been compared with well-established benchmarks from the literature. Compact section and thin-walled beams have been taken into account. Results have been given in terms of displacements and stresses. It is shown that the present model provides high accuracy with a reduced number of degrees of freedom.

A temporally piecewise adaptive multiscale scaled boundary finite element method to solve two-dimensional heterogeneous viscoelastic problems

By combining the Multiscale Scale Boundary Finite Element Method (MsSBFEM) and the Temporally Piecewise Adaptive Algorithm (TPAA), a new numerical model is presented to reduce the solution scale of the two-dimensional heterogeneous viscoelastic problems. Utilizing TPAA, a spatially and temporally related problem is transformed into a series of recursive spatial problems, which are solved by MsSBFEM. The solution scale can be effectively reduced by recourse of a bridge between small-scale and large-scale via Scaled Boundary Finite Element Method (SBFEM) based numerical base functions, and the solution accuracy can be improved only by increasing nodes of coarse elements without increasing any new node inside. By virtue of singular, polygon and Quadtree elements, SBFEM renders the proposed algorithm more efficient and convenient to tackle with the stress singularity, and to generate SBFE mesh. TPAA provides a measure to secure the temporal computational accuracy via an adaptive process when the step size varies. Numerical examples are provided to elucidate the effectiveness of proposed approaches, and satisfactory results are achieved at both the large and small scales.

On the Anti-Aliasing Properties of Entropy Filtering for Discontinuous Spectral Element Approximations of Under-Resolved Turbulent Flows

For large Reynolds number flows, it is typically necessary to perform simulations that are under-resolved with respect to the underlying flow physics. For nodal discontinuous spectral element approximations of these under-resolved flows, the collocation projection of the nonlinear flux can introduce aliasing errors which can result in numerical instabilities. In Dzanic and Witherden (J. Comput. Phys., 468, 2022), an entropy-based adaptive filtering approach was introduced as a robust, parameter-free shock-capturing method for discontinuous spectral element methods. This work explores the ability of entropy filtering for mitigating aliasing-driven instabilities in the simulation of under-resolved turbulent flows through high-order implicit large eddy simulations of a NACA0021 airfoil in deep stall at a Reynolds number of 270,000. It was observed that entropy filtering can adequately mitigate aliasing-driven instabilities without degrading the accuracy of the underlying high-order scheme on par with standard anti-aliasing methods such as over-integration, albeit with marginally worse performance at higher approximation orders.

Experimental Testing of a Tensegrity Simplex: Self-Stress Implementation and Static Loading

A physical model of the simplest three-dimensional tensegrity unit was built at human scale out of aluminum. Self-stress implementation and static loading tests were performed on this model. At each step, accurate measurements were obtained for all nodal positions and element forces. For the prestressing phase, elongations were imposed, via mechanical devices, in different combinations of elements, called prestress scenarios. Experimental results are compared to the theoretical self-stress state obtained by singular value decomposition of the equilibrium matrix and to numerical simulations using the dynamic relaxation method. It is shown that internal forces follow the same linear trend for all prestress scenarios even if the geometry is significantly impacted. Compressive tests were conducted by hanging masses from the top nodes. It is shown that there exists a unique load-displacement relation that follows the infinitesimal mechanism direction for a finite distance, which depends on the self-stress level. The paper provides a detailed overview of the simplex’s structural behavior using both experimental and numerical results while discussing the limitations of the analysis methods explored.

Finite Element Based Static and Dynamic Vibration Analysis of a Beam with Axial Variation of Material Properties

Abstract: The study examines the vibration analysis of a damped cantilever beam with nonuniform variation in material properties using finite element methods. With power modification of material parameters in the axial direction, the static and dynamic response of a prismatic rectangular beam with damping has been examined. For the finite element approach, two noded beam elements with two degrees of freedom at each node were evaluated. The power law variation of material properties was used throughout the investigation. This research investigated the effects of proportional damping on displacement, velocity, and acceleration responses. The proposed beam's mass, stiffness, and damping matrices were calculated using Hamilton's concept. In the temporal domain, the Newmark Method has been utilized

Fatigue Analysis of an Inclined Crack Propagation Problem by the X-FEM Method

The extended finite element method (X-FEM) has been used to solve fracture mechanics, problems in materials with various behavior laws (for example, isotropic, orthotropic or piezoelectric materials... For each type of material, it is necessary to obtain “enrichment functions” which model the behavior of the fields of displacement and stresses in the vicinity of the front of crack. In this paper, fatigue crack propagation analysis was modeled, by the extended finite element method X-FEM to evaluate the total energy and strain energy at the angled crack length, and to have the development of the increment time concerning the different values of α which is equal to 15°, 30° and 45, this development has been studied numerically by solving the problem of finite elements by the computer code ABAQUS. Quadratic 4-node elements (CPS4R) were used.

Advanced numerical modelling of the nonlinear mechanical behaviour of a laterally loaded pile embedded in stiff unsaturated clay

Capturing and understanding the ultimate limit state behaviour of reinforced concrete piles embedded in soil requires the use of advanced tools or the performance of expensive tests. An experiment was performed where reinforced concrete piles embedded in a stiff unsaturated clay profile were load-tested on-site. However, even though in-situ experiments can provide engineers with valuable insight, their cost and time limitations come with restrictions, especially when dealing with a parametric investigation on the soil's material properties, the size of the piles, or the piles' material properties. The objective of this research work was to numerically model the nonlinear mechanical behaviour of laterally loaded full-scale piles through detailed 3D modelling, and perform an in-depth parametric investigation to provide answers to unknown factors that the actual physical experiment could not answer. Furthermore, this work serves as a pilot project that will be used to pave the way in developing multiple soil-structure interaction models that will be used to generate a dataset that helps the creation of predictive models through machine learning algorithms. For the needs of this research work, the reinforced concrete piles were discretised with 8-noded isoparametric hexahedral elements that accounted for cracking through the smeared crack approach. Steel reinforcement bars and stirrups were simulated as embedded rebar elements, while the soil domain was also discretised through 8-noded hexahedral elements. Most of the required material properties assumed during the nonlinear analyses were defined according to relevant laboratory experiments. According to the numerical investigation, it was found that the proposed numerical model has the ability to reproduce the experimental results with high accuracy, while providing in-depth insight on the failure mechanisms for both the soil and reinforced concrete domains.

Numerical analysis of a FEM based on a time-primitive of the electric field for solving a nonlinear transient eddy current problem

The aim of this paper is to analyze from a mathematical and a numerical point of view a formulation of a transient eddy current problem in terms of a time-primitive of the electric field in a bounded domain with ferromagnetic conductors. To this aim, we introduce a Lagrange multiplier to impose the free-divergence condition in the isolated domain. Thus, we obtain a nonlinear degenerate parabolic problem in mixed form and prove its well-posedness. Then, we propose a fully-discrete scheme by using an implicit Euler scheme for time-discretization and a finite element method based on edge and nodal elements for the spatial discretization. We prove quasi-optimal error estimates for the approximation and include some numerical examples to confirm the obtained theoretical results.

A general interaction integral for dynamically propagating cracks in anisotropic materials

In this paper, some relevant tools for numerical analysis of dynamically propagating cracks in anisotropic materials are discussed within the framework of the eXtended Finite Element Method (XFEM). A general interaction integral that is domain-independent is proposed to determine the Stress Intensity Factors (SIFs) for both stationary and dynamically propagating cracks in anisotropic materials. Besides, a set of functions for enriching the nodes of the tip element, which are applicable for modeling both quasi-stationary and dynamically propagating cracks in anisotropic materials, are also proposed. In addition, a modified form of the Maximum Tangential Stress (MTS) criterion is manipulated for estimating the direction of the propagating crack which takes into account the asymptotic stress field near a propagating crack tip in anisotropic materials under mixed mode plane loading. Finally, the accuracy of the suggested method is then confirmed using some numerical examples that involve both stationary and dynamically propagating cracks. Additionally, a thorough investigation is done into the impacts of material anisotropy and material orientation on the path of dynamically propagating cracks in orthotropic structures.

Spatial Coupling of Mass Transit Networks and Business Centers in China's Megacities: A Complex Network Theory Approach

As fundamental nodal elements in urban spatial structures, the coupling and coordinated development of urban business centers and urban rail transit contributes to the optimization of these structures. Utilizing complex network theory, a model for the urban rail transit network was constructed. The importance and hub nature of urban rail transit stations were evaluated from different angles, including degree centrality, closeness centrality, betweenness centrality, and eigenvector centrality. These metrics examined the station's degree, closeness to other nodes, number of shortest paths, and centrality of neighboring nodes. The coupling relationship between urban rail transit and urban business centers was taken into account, leading to the creation of a coupling and coordination degree model for urban rail transit stations and urban business centers. An analysis of the spatio-temporal evolution of the coupling relationship between urban rail transit and business centers in Beijing, Shanghai, and Guangzhou from 2000 to 2020 was conducted. The findings indicated an interactive and mutually influencing coupling relationship between the urban rail transit network and urban business centers. Over time, the coupling and coordination degree of urban rail transit stations and urban business centers trended from being uncoordinated towards preliminary, moderate, and good coordination. Spatial heterogeneity existed in the coupling and coordination status of different circles, with the best coupling and coordination conditions being in the core area. There was a degree of variance in the coupling and coordination development situation of rail transit stations and business centers in the core areas of different cities. Among them, Shanghai's core area had the best spatial coupling and coordination development situation, Beijing's core area lagged in business center development compared to the construction of the urban rail transit network, while Guangzhou's core area saw urban rail transit network development lag behind its mature business centers. The application of these research findings aids in promoting sustainable urban development. While this study primarily measured the importance of urban rail transit network stations from the node centrality perspective, future studies could further examine the spatial coupling of urban rail transit and business centers from the viewpoints of accessibility and passenger flow.

Nodal integration-based particle finite element method (N-PFEM) for poro-elastoplastic modelling of saturated soils under large deformation

This paper presents the nodal integration-based particle finite element method (N-PFEM) for poro-elastoplastic analysis of saturated soils subject to large deformation, utilising the generalised Hellinger-Reissner variational principle to reformulate the governing equations for saturated soil dynamics into a min–max optimisation problem. With finite element discretisation and nodal integration over cells, the problem is transformed into a standard second-order cone programming problem, efficiently resolved using the advanced primal–dual interior point method. The N-PFEM method has several advantages, including the use of linear triangular elements without volumetric locking issues, the avoidance of regularisation techniques, and the elimination of tedious variable mapping after remeshing. The numerical model is validated for large deformation analysis of saturated soils with a series of benchmarks against available analytical and numerical solutions, with a case study of the deformation of an embankment considering stone column reinforcement also carried out. This N-PFEM framework offers an effective and efficient simulation approach for the evolutionary behaviour of saturated soils with large deformation in complex geotechnical configurations of practical relevance.

Models and Algorithms of Abstract Flows in Evacuation Planning

Flows over time generalize classical network flows by introducing a notion of time. Each arc is equipped with a transit time that specifies how long flow takes to traverse it, while flow rates may vary over time within the given edge capacities. Ford and Fulkerson’s original 1956 max flow/min cut paper formulated max flow in terms of flows on paths. In 1974, Hoffman pointed out that Ford and Fulkerson’s original proof was quite abstract, and applied to a wide range of max flow-like problems. In this abstract model we have capacitated elements and linearly ordered subsets of elements called paths that satisfy switching property. When two paths P and Q cross at an element (node) then there must be a path that is a subset of the first path up to the crossing element and a subset of the second path after the crossing element. Contraflow is a widely accepted solution approach that increases the flow and decreases the evacuation time making the traffic smooth during evacuation by reversing the required road directions from the risk areas to the safe places. In this paper, we integrate the abstract flow with contraflow, give mathematical formulations of these models and present efficient polynomial time algorithms for solving the abstract contraflow problems.

EU digital communication strategy during the COVID-19 vaccination campaign: Framing, contents and attributed roles at stake

If in recent years the European Union (EU) has had to face complex and multifactorial “poly-crises” (such as Brexit, refugees or the euro), the pandemic caused by COVID-19 has been an unprecedented event on a global scale with important implications at all levels. Indeed, it has reinforced public health issues aimed at protecting the population as nodal elements of the policies implemented by this organization. This research aims to analyze the different organizational communication strategies on Twitter implemented by the main EU institutions during the COVID-19 vaccination campaign, in order to examine the presence of this exceptional milestone. This study has been carried out using an eminently quantitative methodology, based on a content analysis to quantify the different variables and indicators established for the publications of the official profiles of the European Commission, the European Parliament and the European Council. The proposed categories focus on exploring their predominant thematic areas, as well as main purposes/attributed functions. In the light of the results obtained, it is concluded that the vaccination campaign is a milestone with a considerable volume of publications by all profiles. However, among the attributed functions, the distribution of aseptic information has been predominant, which is why it is discussed whether these institutions have sufficiently taken advantage of the possibilities offered by the digital environment of Twitter for the dissemination of the European message.

Control of dimensional accuracy of hollow turbine blades during investment casting

Because of their variable airfoil cross sections and internal hollow cavities with complex serpentine shapes, hollow turbine blades are prone to sectional deformation during investment casting, resulting in dimensional errors. To control the deformation of turbine blades, a novel one-step reverse compensation method based on a variable shrinkage factor is proposed in this study. First, the directional solidification process was simulated to predict the deformation distribution of the turbine blades. The deformation of the airfoil and platform increases further after constraints removal, with the trailing edge of up to 0.4192 mm. Subsequently, the shrinkage rate of each finite element node of the turbine blades was calculated to guide the mold design. Finally, three cross sections of the blade were validated using a coordinate measuring machine. The experimental results show that the optimized deformation using the proposed method is within the design requirement of 0.15 mm, and the maximum deformation of the blade has lowered by 68.2 %, which indicates that the dimensional accuracy of the hollow turbine blades is effectively controlled.

Enrichment of three-dimensional numerical manifold method with cover-based contact theory for static and dynamic mechanical response analysis

Based on the mathematical grid of 4-node tetrahedral finite element form, the dual cover system, weight function and displacement function of three-dimensional numerical manifold method (3D-NMM) are proposed. The derivation process of element stiffness matrix, inertial force matrix, loading point matrix, etc. are systematically demonstrated in the present work. Based on the cover-based contact theory, the contact detection algorithm among discrete 3D blocks is realized, and the 3D manifold framework is programmed. The accuracy of the developed code is firstly calibrated through two continuum deformation analysis: cantilever beam bending model and axial tensile model of thin plate with circular hole. Then it is applied to three complex discontinuous instability simulation (SHPB, brick wall structure and cliff slope) to verify the effectiveness and accuracy of the proposed contact algorithm. The classic Steven low velocity impact process is also simulated, and the deformation and failure of polymer bonded composites (PBC) are predicted, which further verifies the feasibility and robustness of the developed code in dealing with dynamic impact problems.

Enriched Finite Element Method Based on Interpolation Covers for Structural Dynamics Analysis

This work proposes a novel enriched finite element method (E-FEM) for structural dynamics analysis. We developed the enriched 3-node triangular and 4-node tetrahedral displacement-based elements (T-elements). The standard linear shape functions of these T-elements were enriched using interpolation cover functions over each patch of elements. We also introduced and compared different orders of cover functions; higher-order functions obtained higher computational performance. Subsequently, the forced and free vibration analyses were performed on various typical numerical examples. The proposed enriched finite element method generated more precise numerical results and ensured faster convergence than the original linear elements.