Advanced Finite Element Method Research Articles

Probabilistically modelled geometrical imperfections for reliability analysis of vertically loaded steel frames

The article explores the stochastic modelling of 3D steel frames under static vertical load, with a main focus on random initial geometrical imperfections. The random input parameters for initial geometrical imperfections are derived from the tolerance criteria in accordance with European standard. In order to derive statistical parameters from the corresponding standard tolerances, two methods noted as #RSS (random storey sway) and #RSP (random storey position) have been utilized and compared. Both of these methods are used along with the first-order reliability method (FORM) and the advanced finite element method (FEM) – geometrically and materially nonlinear imperfect analysis (GMNIA) to numerically analyse several geometries of steel frame structures. Ultimate resistances of these structures are monitored and basic sensitivity studies are conducted. The results are also compared with the deterministic approach of the European standard. The stochastic approach of the FORM to estimate the ultimate resistance of steel frame structures serves as a verification tool of the classic, in engineering praxis widely used, deterministic approach. This study provides useful provisions for the advanced numerical analyses of steel frames of various geometries. Additionally, the estimations of ultimate resistance by the deterministic European standard approach is verified for selected frame geometries.

Two-field mixed hp-finite elements for time-dependent problems in the refined theories of thermodynamics

AbstractModern manufacturing technologies allow heterogeneous materials with complex inner structures (e.g., foams) to be easily produced. However, their utilization is not straightforward, as the classical constitutive laws are not necessarily valid. According to various experimental observations, the Guyer–Krumhansl equation is a promising candidate for modeling such complex structures. However, practical applications need a reliable and efficient algorithm capable of handling both complex geometries and advanced heat equations. In the present paper, we derive new two-field variational formulations which treat the temperature and the heat flux as independent field variables, and we develop new, advanced hp-type mixed finite element methods, which can be reliably applied. We investigate their convergence properties for various situations, challenging in relation to stability and the treatment of fast propagation speeds. That algorithm is also proved to be outstandingly efficient, providing solutions four magnitudes faster than commercial algorithms.

On the use of mechanics-informed models to structural engineering systems: Application of graph neural networks for structural analysis

This paper investigates the application of mechanics-informed artificial intelligence to civil structural systems. Structural analysis is a traditional practice that involves engineers to solve different real-life problems. Several approaches can be used for this task, going from “by hand” computation to the recent advanced finite element method. However, when structures become complex, the success of the analysis can be complicated, often requiring high computational efforts and time. To tackle this challenge, traditional high-demanding methods can be supported by new technologies, such as machine-learning tools. This new paradigm aims to solve structural problems by defining the desired output after directly elaborating input data. One of the current limitations is that often the physics behind the problem is ignored. To solve this issue, resolution models can combine empirical data and available mechanics prior knowledge to improve the predictive performance involving physical mechanisms. In this paper, a method to develop a Mechanics-Informed Surrogate Model (MISM) on structural systems is proposed, for which input structured data are used to enrich the informative content of mechanics systems. Then, Graph Neural Networks (GNNs) are explored, as a method capable of properly representing and embedding knowledge about a structural system, such as truss structures. The main advantage of the proposed approach is to provide an alternative way to the usual black-box machine-learning-based models. In fact, in the proposed MISM, the mechanics of the structural system plays the key role in the surrogate model definition, in order to obtain physically based outputs for the investigated problem. For the case at hand, MISMs are developed and employed to learn the deformations map of the system, starting from the knowledge of the structural features. The proposed approach is applied to bi-dimensional and tri-dimensional truss structures and the results indicate that the proposed solution performs better than standard surrogate models.

Enhancing medium voltage underground circuit design: Assessing limitations, thermal influence, and accurate modelling

The research article conducted a study aimed at elucidating the limitations present in existing international standards related to the permissible quantity of medium voltage circuits that can be placed within a single trench. The study also explored important considerations for underground circuits in the context of renewable energy projects, particularly focusing on the crucial roles of capacity and load requirements in cable design. The research employed advanced finite element methods with Composition, Environmental, Structure, and Mechanism (CESM) and mathematical modeling to enhance existing procedures defined by international standards like IEC 60287, 60502, and 60228. The primary parameter of interest was the thermal influence of subterranean XLPE (cross-linked polyethylene) current capacity, considering various factors such as circuit quantities, distances, and depths. Notably, the study made several key findings, including a notable reduction in the current capacity of the underground circuits. This reduction in current capacity was found to vary, ranging from 100 % to 25.75 %. The reduction was attributed to factors such as native soil conditions, circuit separation. The findings furnish valuable insights into the challenges pertinent to medium voltage underground circuit design. Moreover, the paper establishes the accuracy of the proposed process, achieving a precision of 99.4850 ± 0.5150 % for 240 mm2 and 99.3698 ± 0.6301 % for 630 mm2.

Identification of key thermal couplings affecting the bentonite behaviour in a deep geological nuclear waste repository

Deep geological nuclear waste repositories use the multi-layer Engineered Barrier System (EBS) to isolate nuclear waste from the environment. The key component of the barrier is densely compacted bentonite, closely resembling claystone. Therefore, to ensure safety, we need a numerical model for the bentonite and the barrier that predicts EBS behaviour during transient thermal, hydraulic, mechanical and chemical conditions. The paper identifies key mechanisms and processes affecting the bentonite in the barrier due to temperature changes (thermal couplings) based on advanced fully-coupled Finite Element Method simulations. The paper investigates 1) non-isothermal infiltration experiment on FEBEX bentonite (Villar and Gomez-Espina, 2009) and, 2) Centro de Investigaciones Energeticas Medioambientales y Tecnologicas (Ciemat) test (Martin et al., 2006), presenting 10 simulation configurations that are set up by inactivating one thermal coupling/variable at a time. The difference between these simulations and the baseline model results, examined in terms of the net mean stress (swelling pressure), suction and fluid flow, give insights into the significance of investigated coupling. Results suggest that thermal couplings related to vapour density, viscosity, water retention curve, and molecular diffusivity are among the most influential. The study additionally highlights the importance of water transport as liquid and gas, and water evaporation and condensation.

A comparison of countermeasures against landslide on the road No.152, Sapa Town, Lao Cai Province, Vietnam

Landslide hazards are one of the most common geological disasters due to the impacts of natural factors, mainly rainfall, and human activities, such as the construction of transport infrastructure and mining projects. In Vietnam, most of the landslides and slippage frequently occur in mountainous areas, especially in Lao Cai province during the rainy season. In 2021, a slope failure happened near the Mong Hoa valley, on Road No. 152, sections Km 2+728.26–Km 2+827.04 in Cau May ward, Sapa town, Lao Cai province. In this study, topographical features, geomorphological features, hydrological features, geological investigation, and laboratory tests were performed to analyse the slope stability. This study used the Limit Equilibrium Method (LEM) and the Finite Element Method (FEM) to analyse the slope stability, and several countermeasures were proposed for this slope such as the retaining wall, ground anchors, and soil nails. This numerical result showed that the ground anchors and soil nails are the suitable method to prevent the instability of the slope. This study shows that compared with the traditional LEM method and advanced FEM method is that it can capture more results not only safety factor but also horizontal displacement and load anchor result. As a result, this analysis showed that the safety factor value in the finite element method was greater than that in the limit equilibrium method.

Dynamic stability analysis of jointed rock slopes using the combined finite-discrete element method (FDEM)

The combined finite-discrete element method (FDEM) is an advanced finite element and discrete element coupling method, which is commendably suitable for simulating the slope’s entire evolution process from cracking, expansion, penetration, sliding, collision to deposition under seismic load. The original FDEM has apparent shortcomings in simulating the dynamic instability process of earthquake-induced landslides, and some targeted improvements are made to the original program. Numerical tests are carried out to prove the accuracy and robustness of the improved FDEM, and the influence of the structural plane on the dynamic evolution mechanism and process of the slope is studied. The results show that the improved FDEM can accurately reproduce the entire dynamic evolution processes and failure forms of different jointed rock slopes under seismic load and can quantitatively evaluate the dynamic stability of jointed rock slopes (dynamic safety factor and critical failure surface). In addition, the results also emphasize that the slope failure degree significantly affects the dynamic response of the slope and suggest that the combination of the cut-through of the failure surface and the increase of kinetic energy should be used as the criteria for slope dynamic instability simulation by FDEM. This study provides scientific and technological support for revealing the failure mechanism of jointed rock slopes and disaster reduction and prevention.

A Numerical Model for Pressure Analysis of a Well in Unconventional Fractured Reservoirs

Fractured reservoirs are highly heterogeneous in both matrix and fracture properties, which results in significant variations in well production. Assessing and quantifying the influence of fractures on fluid flow is essential for developing unconventional reservoirs. The complicated effects of fractures in unconventional fractured reservoirs on fluid flow highly depend on fracture geometry, fracture distribution, and fracture properties, which can be reflected in pressure transient testing. The biggest challenge lies in delineating the pre-existing natural fracture distribution pattern, density, azimuth, and connectivity. Using the advanced finite element method, this paper builds a finely characterized near-wellbore model to numerically simulate the pressure transient testing process in naturally fractured reservoirs and further evaluates fracture-related effects to obtain a more accurate solution. First, the numerical program is benchmarked by the analytical solutions and numerical results of Eclipse. Next, different fracture models with single fractures or fracture networks are set up to investigate the effects of fracture parameters numerically (e.g., fracture location, fracture dip angle, fracture spacing, the ratio of fracture permeability to matrix permeability, fracture network orientation, horizontal fracture distribution, etc.) on pressure transient behaviors in naturally fractured reservoirs. Velocity and pressure profiles are presented to visualize and analyze their effects, and new features in the flow regimes of the derivative plots of the bottom-hole pressure are identified and discussed. Finally, based on geological and geophysical data, including image logs, core descriptions, wireline logs, and seismic and well test data, a practical fractured model of the Dalwogan 2 well in the Surat basin is built, analyzed, and compared with homogenous and measured data. The results show significance in characterizing the complex fracture networks in near-wellbore models of unconventional fractured reservoirs.

Analysis of the sound insulation performance of periodic wall structures by a virtual acoustic laboratory

The propagation of acoustic waves in periodic structures, also known as phononic crystals or PCs, is prohibited in certain frequency ranges, which are referred to as the frequency band-gaps. The existence, the location and the width of the frequency band-gaps are mainly determined by the geometrical parameters and the material properties of the PCs. In this work, a virtual acoustic laboratory based on a fully coupled fluid-structure interaction (FSI) model is developed to determine the sound insulation capacity of one-dimensional (1D) and two-dimensional (2D) periodic walls. The FSI model is discretized using the frequency-domain spectral element method (FDSEM), which is an advanced finite element method (FEM) using special high-order shape functions. Following the guidelines of the ISO10140, the setup of the developed FSI model allows us to take into account the essential physical phenomena, especially the interaction of the wall structure with the fluid domains (air). The FSI model based on the FDSEM increases the computational efficiency and accuracy in comparison with the standard FEM. Several numerical examples will be presented and discussed to show that the designed periodic walls in certain frequency ranges within the band-gaps may exhibit much better sound insulation capabilities than monolithic walls.

Brainstorm-DUNEuro: An integrated and user-friendly Finite Element Method for modeling electromagnetic brain activity

Human brain activity generates scalp potentials (electroencephalography – EEG), intracranial potentials (iEEG), and external magnetic fields (magnetoencephalography – MEG). These electrophysiology (e-phys) signals can often be measured simultaneously for research and clinical applications. The forward problem involves modeling these signals at their sensors for a given equivalent current dipole configuration within the brain. While earlier researchers modeled the head as a simple set of isotropic spheres, today's magnetic resonance imaging (MRI) data allow for a detailed anatomic description of brain structures and anisotropic characterization of tissue conductivities. We present a complete pipeline, integrated into the Brainstorm software, that allows users to automatically generate an individual and accurate head model based on the subject's MRI and calculate the electromagnetic forward solution using the finite element method (FEM). The head model generation is performed by integrating the latest tools for MRI segmentation and FEM mesh generation. The final head model comprises the five main compartments: white-matter, gray-matter, CSF, skull, and scalp. The anisotropic brain conductivity model is based on the effective medium approach (EMA), which estimates anisotropic conductivity tensors from diffusion-weighted imaging (DWI) data. The FEM electromagnetic forward solution is obtained through the DUNEuro library, integrated into Brainstorm, and accessible with either a user-friendly graphical interface or scripting. With tutorials and example data sets available in an open-source format on the Brainstorm website, this integrated pipeline provides access to advanced FEM tools for electromagnetic modeling to a broader neuroscience community.

Evaluation on Piezoaeroelastic Energy Harvesting Potential of A Jet Transport Aircraft Wing with Multiphase Composite by means of Iterative Finite Element Method

This paper presents new insight on the potential of piezoaeroelastic energy harvesting on the transport aircraft wing structure. A novel numerical investigation is conducted in the present study. An advanced iterative finite element method (FEM) is applied to estimate the amount of harvested energy. Currently, FEM-based commercial software has a limited application on piezoelectric structures, i.e., actuator and sensor. The iterative FEM algorithm extends the commercial software implementation for the energy harvesting analysis. The multidisciplinary issue of the aeroelastic phenomenon and piezoelectric energy harvesting is evaluated in the present case. Likewise, interestingly, stress and failure analysis of a lifting surface with an active energy harvesting component could be enabled. Implementation of a wing with an embedded piezoelectric layer is concerned. A cruise flight condition and gust disturbance are evaluated. The analysis concerning the occurrence of gust also provides a more realistic insight into the power harvested during a flight operation.

Effects of local fiber discontinuity on the fatigue strength parameter at the fiber inclusion corner in fiber-reinforced composites

Abstract To comprehend the fatigue failure mechanism at the fiber discontinuity in fiber-reinforced composites, it is necessary to evaluate the local mechanical behaviors. The fatigue strength depends on the stress distribution at the fiber inclusion corner. An improved advanced finite element method (IAFEM) is proposed for the stress intensity factor (SIF) analysis at the fiber inclusion corner. In the IAFEM, the element stiffness matrix of singular inclusion corner element (SICE) is obtained, and the singular elastic field at the tip of the fiber inclusion is determined. The effects of load direction, fiber distribution, fiber geometry, and material properties on SIFs are analyzed numerically using the IAFEM. The difference in stress field distribution between two-dimensional and three-dimensional fiber inclusions is discussed. The IAFEIM and calculation results can provide reference for fatigue strength analysis and preparation of composite materials.

Buckling curves of stainless steel CHS members: Current state and proposed provisions

The study objective is to propose the optimal shape of the flexural buckling curves for stainless steel circular hollow cross-section (CHS) members. It has been pointed out by several researchers, that the currently utilized buckling curves do not fulfil the required structural reliability level, and several provisions have already been proposed. Following this research, our proposals are based on a numerical investigation of the ultimate limit state of geometrically imperfect stainless steel CHS columns of three different material grades (Austenitic 1.4307, Ferritic 1.4003 and Duplex 1.4462) using the statistical characteristics of input initial imperfections, material and geometric parameters. The statistical characteristics are considered according to the results of published research. The first-order reliability method (FORM) supported by the advanced finite element method – geometrically and materially nonlinear imperfect analysis (GMNIA) – is used. The values of the ultimate resistance obtained using FORM are compared with the values of the design resistance determined according to the corresponding European standards and are used to determine the optimal shape of flexural buckling curves. Additionally, the influence of linear correlation between the ultimate resistance of CHS stainless steel columns exposed to flexural buckling and input imperfections is discussed. Studies have shown that the maximum effect of initial axial curvature on resistance occurs at higher slenderness compared to carbon steels. The obtained results present provisions to optimize the flexural buckling curves of stainless steel CHS members and could significantly improve the structural efficiency, resulting in material savings, while preserving the required level of structural reliability.

Comparison of a novel finite element method for sucker rod pump downhole dynamometer card determination based on real world dynamometer cards

• Evaluation of the downhole dynamometer card based on the finite elements method. • The novel advanced finite element method overcomes limitation of existing models and is based on physical parameters. • An excellent match with measured downhole dynamometer cards was reached. • The simulation results allow a the evaluation of the performance parameters of the sucker rod pumping system. An advanced dynamic finite element model is presented that diagnoses the downhole pump performance of sucker rod pumping systems, applicable for any pumping conditions and equipment used. The results are compared to downhole measurements and other state of the art evaluation techniques. Existing diagnostic tools exhibit specific limitations that reduce their applicability and output quality. This paper introduces a diagnostic tool, which can predict the rod string's stress field and its movement not only at the pump plunger but all along the rod string. Moreover, this tool can account for the interaction between rod guides and tubing as well as rod string and tubing. To this end, innovative tube-to-tube contact modeling is applied. The high precision results are accomplished by running a dynamic finite element simulation. The basic principle is to evaluate the plunger load incrementally by consecutively applying restarts of each time step, fully automated and computation time optimized. This publication shows that both the plunger load and the rod string's dynamic behavior can be determined for any given wellbore as long as the borehole trajectory and surface dynamometer measurements are known. The dynamic finite element model is evaluated for a deviated system and a vertical system equipped with two different downhole pump types. Comparing the simulation results with the available downhole measurements shows an excellent match. The the proposed solution provides a considerable amount of details about the overall system's behavior. The evaluation has shown that the performance of standard and novel downhole pump types can be successfully diagnosed in detail, which is just possible under limitations with commercial software solutions.. The novelty of the shown technique is the consideration of the full 3D trajectory, the implementation of only physical properties of the equipment used, and a realistic setup. The validation of the model output with measured downhole data indicates an excellent accuracy of the shown model.

Virtual Prototyping of the Cement Transporter Including Strength Criterion Based on Geotechnical Boundary Conditions

Regarding the vehicles used in civil engineering, some are manufactured in large quantities and some (especially innovative ones) are still prototypes manufactured for tests or rare use. The latter describes the case of equipment for mass mixing (mass stabilization) technology which is not widely used compared to other types of geotechnical equipment. The purpose of this paper is to present a research and development project on an innovative cement transporter designed for mass mixing. Three-dimensional models and advanced finite element method (FEM) calculations are used to validate the design of the most important part of the cement transporter—the frame connecting the undercarriage and the upper carriage. The results presented in the paper confirm that the design based on the strength criterion and boundary conditions from geotechnical safety requirements can be used for designing the parts of the prototype vehicle. It is concluded that in innovative vehicle design for geotechnical purposes, the analyses may extend beyond the standard static analyses.

An advanced mixed Lagrangian-Eulerian and finite element method to simulate 3-D subsurface variably saturated flows

An advanced mixed Lagrangian-Eulerian and finite element method to simulate 3-D subsurface variably saturated flows

Digital Twins for Wind Energy Conversion Systems: A Literature Review of Potential Modelling Techniques Focused on Model Fidelity and Computational Load

The Industry 4.0 concept of a Digital Twin will bring many advantages for wind energy conversion systems, e.g., in condition monitoring, predictive maintenance and the optimisation of control or design parameters. A virtual replica is at the heart of a digital twin. To construct a virtual replica, appropriate modelling techniques must be selected for the turbine components. These models must be chosen with the intended use case of the digital twin in mind, finding a proper balance between the model fidelity and computational load. This review article presents an overview of the recent literature on modelling techniques for turbine aerodynamics, structure and drivetrain mechanics, the permanent magnet synchronous generator, the power electronic converter and the pitch and yaw systems. For each component, a balanced overview is given of models with varying model fidelity and computational load, ranging from simplified lumped parameter models to advanced numerical Finite Element Method (FEM)-based models. The results of the literature review are presented graphically to aid the reader in the model selection process. Based on this review, a high-level structure of a digital twin is proposed together with a virtual replica with a minimum computational load. The concept of a multi-level hierarchical virtual replica is presented.

Approximate analysis of non-uniform torsion

It is difficult to obtain closed form exact solutions for the non-uniform torsion of beams. Advanced finite element methods easily produce very accurate solutions, but simple programs are not widely available. One simple program is validated by comparing its solutions with closed form solutions.A simple approximate method is proposed which combines the uniform and warping torsion stiffness approximations. The determination of the warping stiffness approximation is simplified by using the moment-area method. The approximate twist rotations are compared with the accurate solutions, are shown to be of generally acceptable accuracy, and in most cases to be conservative.Approximate solutions for the central twist rotations of simply supported beams with off-centre torques can be combined using superposition to find solutions for a wide range of torque loadings. A worked example is given.

FEM/XFEM modeling of the 3D fracturing process in transversely isotropic geomaterials

This paper studies the fracturing process in geomaterials in order to define the mechanical properties of elements belonging to the lithosphere, such as the kaolonite-rich Opalinus Clay (OPA) formation, due to its potential application as host rock for radioactive waste. For the sedimentary genesis, this rock can be considered a transversely isotropic geomaterial, as also documented in the experimental literature. The fracturing problem is here tackled computationally for a Semi-Circular Bending test (SCB), by resorting to a classical Finite Element Method (FEM) combined with a cohesive zone modeling, or a more advanced eXtended Finite Element Method (XFEM). The selected approaches are successfully compared despite the different computational demand and complex nonlinear nature of the problem. A parametric investigation checks, also, for the possible influence of the notch shape on the fracturing behaviour of the specimen, both in terms of peak load and direction of propagation of the crack within the specimen.

Experimentally validated modeling of the optical energy deposition in highly ionized ambient air by strong femtosecond laser pulses

The deposition of femtosecond laser optical energy in gases leads to the emission of secondary electromagnetic and acoustic radiation. These optoacoustic components have a complex nonlinear dependency on the laser beam characteristics, such as the pulse energy, duration, wavelength and the focusing conditions, as well as on the optical and elastic characteristics of the gaseous medium. The initial interaction times are governed by the high electronic excitation and ionization. These phenomena result in a self-modulation of the laser pulse, significantly affecting the optical energy deposition on the medium. Such complex nonlinear phenomena are very difficult to be studied via analytical equations. To address this, a multiphysics Particle-In-Cell model is applied for the evaluation of the optical energy deposition and plasma generation from tightly focused femtosecond pulses in ambient air. The computational domain of the model is built to describe optical energy deposition in its full spatiotemporal scale. The model is validated by experimental results of the absorbed energy. The agreement between the computational and experimental results provides the basis for the future development of an advanced microstructural Finite Element Method model, which, combined with the Particle-In-Cell model, will have the ability of delivering detailed insights for all the sub-domains and timescales varying from nano- to femto-seconds of the laser-induced breakdown phenomenon.Graphic