Two-dimensional Finite Element Model Research Articles

Geometrically nonlinear transient analyses of rotating structures through high-fidelity models

This work presents geometrically nonlinear transient analyses of various rotating blades. The structures are discretized through refined beams or multi-dimensional finite element models, which are generated using the Carrera Unified Formulation (CUF). The CUF offers a procedure to develop low- and high-fidelity one-dimensional, two-dimensional, and three-dimensional finite element models hierarchically and automatically. Various beam models were developed using different kinematics models based on Taylor or Lagrange expansion functions. Multi-dimensional models were obtained by merging beam and solid elements, exploiting the unique feature of Lagrange polynomials to have only pure displacements as unknowns. This property allows beam and solid elements to be coupled at the node level without requiring complicated mathematical formulations. By utilizing the Finite Element Method in conjunction with the CUF, the governing equations are written by including all rotation effects, namely the Coriolis term, spin-softening, and geometrical stiffening. In a total Lagrangian scenario, the Hilbert-Hughes-Taylor-α method and the iterative Newton-Raphson scheme are employed to solve the equations of motion. The proposed methodology has been applied to evaluate different blade configurations, comparing the solution obtained using linear, linearized, and nonlinear approaches. The results have been verified and validated by comparing them with existing solutions present in the literature.

Investigating the effect of anatomical variations in the response of the neonatal brachial plexus to applied force: Use of a two-dimensional finite element model.

The brachial plexus is a set of nerves that innervate the upper extremity and may become injured during the birthing process through an injury known as Neonatal Brachial Plexus Palsy. Studying the mechanisms of these injuries on infant cadavers is challenging due to the justifiable sensitivity surrounding testing. Thus, these specimens are generally unavailable to be used to investigate variations in brachial plexus injury mechanisms. Finite Element Models are an alternative way to investigate the response of the neonatal brachial plexus to loading. Finite Element Models allow a virtual representation of the neonatal brachial plexus to be developed and analyzed with dimensions and mechanical properties determined from experimental studies. Using ABAQUS software, a two-dimensional brachial plexus model was created to analyze how stresses and strains develop within the brachial plexus. The main objectives of this study were (1) to develop a model of the brachial plexus and validate it against previous literature, and (2) to analyze the effect of stress on the nerve roots based on variations in the angles between the nerve roots and the spinal cord. The predicted stress for C5 and C6 was calculated as 0.246 MPa and 0.250 MPa, respectively. C5 and C6 nerve roots experience the highest stress and the largest displacement in comparison to the lower nerve roots, which correlates with clinical patterns of injury. Even small (+/- 3 and 6 degrees) variations in nerve root angle significantly impacted the stress at the proximal nerve root. This model is the first step towards developing a complete three-dimensional model of the neonatal brachial plexus to provide the opportunity to more accurately assess the effect of the birth process on the stretch within the brachial plexus and the impact of biological variations in structure and properties on the risk of Neonatal Brachial Plexus Palsy.

A Gaussian process approach for rapid evaluation of skin tension

Skin tension plays a pivotal role in clinical settings, it affects scarring, wound healing and skin necrosis. Despite its importance, there is no widely accepted method for assessing in vivo skin tension or its natural pre-stretch. This study aims to utilise modern machine learning (ML) methods to develop a model that uses non-invasive measurements of surface wave speed to predict clinically useful skin properties such as stress and natural pre-stretch. A large dataset consisting of simulated wave propagation experiments was created using a simplified two-dimensional finite element (FE) model. Using this dataset, a sensitivity analysis was performed, highlighting the effect of the material parameters and material model on the Rayleigh and supersonic shear wave speeds. Then, a Gaussian process regression model was trained to solve the ill-posed inverse problem of predicting stress and pre-stretch of skin using measurements of surface wave speed. This model had good predictive performance (R2 = 0.9570) and it was possible to interpolate simplified parametric equations to calculate the stress and pre-stretch. To demonstrate that wave speed measurements could be obtained cheaply and easily, a simple experiment was devised to obtain wave speed measurements from synthetic skin at different values of pre-stretch. These experimental wave speeds agree well with the FE simulations, and a model trained solely on the FE data provided accurate predictions of synthetic skin stiffness. Both the simulated and experimental results provide further evidence that elastic wave measurements coupled with ML models are a viable non-invasive method to determine in vivo skin tension. Statement of significanceTo prevent unfavourable patient outcomes from reconstructive surgery, it is necessary to determine relevant subject-specific skin properties. For example, during a skin graft, it is necessary to estimate the pre-stretch of the skin to account for shrinkage upon excision. Existing methods are invasive or rely on the experience of the clinician. Our work aims to present an innovative framework to non-invasively determine in vivo material properties using the speed of a surface wave travelling through the skin. Our findings have implications for the planning of surgical procedures and provides further motivation for the use of elastic wave measurements to determine in vivo material properties.

An exploration into surface wrinkling in 3D printing inspired orthotropic bilayer systems

Surface instability, termed wrinkling, might occur in compressed bilayer systems constituted by an external rigid skin resting on an internal soft substrate, where wrinkling is favored by the rigidity contrast between the two layers. In this paper, the same instability mechanism is explored by considering a substrate characterized by an orthotropic elastic response. By varying the orientation of the principal axes of the substrate’s material, the critical strain of wrinkling and the wrinkles’ wavelength can be tuned during compression. Theoretical formulations for wrinkling are discussed along with the results obtained by linear bifurcation and geometrically nonlinear analyses carried out with two-dimensional finite element models. To experimentally validate the results, the intrinsic properties of Fused Deposition Modeling (FDM) 3D printing technology are leveraged: bilayer objects are manufactured by printing continuous outer shells (corresponding to the rigid skin) along the borders, while the inner raster is shaped with a porous infill pattern, forming a substrate with an orthotropic elastic response.

Obliquely incident seismic response of subway stations following urban soil internal erosion

Urban groundwater infiltration resulting from tropical storm rainfall can lead to internal soil erosion and ground subsidence. The long-term effects of these phenomena may result in uneven settlement of the subway system, posing risks to its safety and operational integrity. Suffusion poses a significant hazard to long-term subway operation. It is a type of soil internal erosion characterized by the migration of fine particles from the pore channels between coarse particles. This study focused on the performance degradation of different gap-graded sands caused by internal erosion, observed through triaxial compression tests. Using the cap plasticity model and considering mechanical parameters before and after soil erosion, a refined two-dimensional finite element model of a soil subway station structure based on ABAQUS was developed to analyze the deformation and damage pattern of the subway structure resulting from soil internal erosion and earthquake. The results of this study demonstrated that localized internal soil erosion significantly contributes to uneven settlement in subway stations, potentially compromising their seismic performance during oblique seismic excitations.

Effects of crustal rheology and fault strength on the formation of the Qaidam Basin: Results from 2-D mechanical modeling

The Cenozoic Qaidam Basin on the northern Tibetan Plateau is bounded by the foreland thrust belts of the East Kunlun Mountains to the south and Qilian Mountains to the north. In this basin, the maximum thickness of the accumulated sedimentary strata is ∼17 km near the geographic center of the basin. Such a basin architecture challenges the classic foreland-basin deformation model, wherein substantial sediments should be localized near the basin margins owing to thrust loads on a bending plate. Based on the available geological and geophysical constraints, we built a two-dimensional viscoelastoplastic finite element model to investigate whether the unique pattern of the Qaidam Basin was mechanically related to the rheological structure of the crust and frictional strength of the basin-bounding thrust fault. By testing reasonable bounds on the viscosity of the ductile crust and effective frictional coefficient of the thrust faults, we modeled a basin framework that fits well with that of Qaidam Basin. The model parameters include a layered rheological structure, with the viscosity of the ductile crust of the basin being two orders of magnitude greater than that of the adjacent mountain belts and an effective frictional coefficient of >0.2. Furthermore, the initial width of the basin significantly affected its deformation style. Therefore, the layered rheological structure of the crust and frictional strength of the basin-bounding thrust faults played important roles in the formation of the Qaidam Basin. Our findings suggest that the inelastic behavior of the crust affects foreland deformation, highlighting that the classic foreland basin model must be revised for some tectonic settings.

Influence of Failure-Load Prediction in Composite Single-Lap Joints with Brittle and Ductile Adhesives Using Different Progressive-Damage Techniques.

The usage of adhesively bonded joints, such as single-lap and double-lap joints, is increasing rapidly in aerospace composite structures as a popular alternative to bolts and rivets. Compared to the conventional joining methods such as fastening and riveting, adhesive-bonding technology better prevents damage to composite structures due to the smooth configuration and the mitigation of stress concentration around holes. In this work, the built-in progressive-damage-modeling techniques in Abaqus, including the cohesive zone model (CZM) and the virtual crack closure technique (VCCT), are used to predict the strength and progressive failure of composite single-lap joints subjected to tensile loading. Modeling of an adhesive layer by using a zero/non-zero-thickness cohesive element, cohesive surface, and VCCT is investigated, as is the effect of brittle and ductile adhesives. Two-dimensional finite-element models with different damage-modeling strategies are performed in this study. The failure-load predictions are compared with the experimental results obtained from the literature. For the ductile adhesive, the predicted failure loads using a zero/non-zero-thickness cohesive elements and a cohesive surface are all shown to be in good agreement with the experiments. However, the VCCT technique predicts higher failure loads. For a brittle adhesive, on the other hand, the predictions by zero/non-zero-thickness cohesive elements and cohesive surfaces reveal notable deviations compared to the experimental results. In contrast to the ductile adhesive, the VCCT technique is revealed to be accurate in predicting the brittle adhesive.

Study on Damage Inference of Parker Trusses Based on Bayesian Principles

The assessment of the health condition and safety of engineering structures is currently a research focus in the field of civil engineering. The traditional deterministic model for damage recognition is limited by the fine reading of field inspections and the accuracy of experts, resulting in a low recognition rate. Structural damage identification methods that consider uncertainty have been developed due to modelling errors, observation noise, system time variability, and other factors that lead to uncertainty. This study focuses on the Parker truss structure, and a two-dimensional planar finite element model is established by setting various key parameters such as prior distribution, stiffness, modulus of elasticity, node distribution, and external loading. The model is updated using the Bayesian updating principle. This principle is then combined with the finite element model. Opensees software is used for programming, and the Monte Carlo random sampling technique is used for structural damage inference. The study results demonstrate that the method can accurately identify the damage level of Parker truss structures with high robustness. The method can be of reference significance and practical value for identifying damage in truss structures.

Simulation of interfacial debonding in hollow particle reinforced composites with VCFEM

The addition of hollow glass microsphere into composites is a method to improve mechanical properties. However, the interfacial debonding of hollow microsphere inevitably causes a decrease in the mechanical properties of the material, which ultimately leads to the failure of the composites. In the numerical simulation of such hollow particle-reinforced composites, the ordinary displacement finite element requires a large number of meshes, which undoubtedly greatly increases the computational cost. In this paper, a new VCFEM is proposed to solve this problem by establishing a two-dimensional Voronoi cell finite element model, deriving the residual energy generalized function of hollow particle-reinforced composites, and calculating the interface debonding. The simulation results are compared with the commercial software MARC, ABAQUS to verify the effectiveness of this VCFEM. The results show that this VCFEM greatly improves the computational efficiency while ensuring the accuracy. Based on this model, this paper also investigates the effect of the generation of interfacial debonding on the overall structure and the effect of different wall thickness of hollow particles on the damage of element debonding.

Physical and Finite Element Models for Determining the Capacity and Failure Mechanism of Helical Piles Placed in Weak Soil

The foundations of particular engineering structures, including marine and jetty structures, mooring systems for submerged platforms or those on the ocean surface, and transmission towers, are subjected to various external loads including compression, uplift, and lateral loads. In such cases, to improve the soil resistance below foundations, pile foundations such as helical piles, anchored piles, and batter piles are commonly preferred, depending on the in situ conditions. Helical piles, increasingly used as an alternative foundation to conventional piles, are placed in the soil body by rotating with torque. This paper deals with the contribution of a helical pile in improving loose sandy soil, and the main purpose is to study the effect of the helix-buried depth on the load-bearing capacity and failure mechanism. The investigated variables include the distance between helixes, the number of helixes, and the diameter of the upper helix. Physical model tests were conducted, and two- and three-dimensional numerical analyses were performed by using the finite element method with an advanced soil model to illustrate the failure mechanisms of helical piles. The aim was to reveal the efficiency of the finite element method in modelling helical piles placed in weak sandy soil. A simplified linear geometry for helixes was established in a two-dimensional finite element model whereas a real geometry for helixes, which was a more realistic approach, was created in a three-dimensional finite element model. The results show that the three-dimensional model indicates better agreement with the physical model compared to the two-dimensional model, and all investigated variables highly affect the load-bearing capacity of helical piles.

Analysis of DC bias characteristics of transformer by using fixed-point time-step FEM and dynamic J–A hysteresis model

The injection of the Direct Current (DC) bias component will lead to oversaturation of the transformer core and affect its safe operation. In this paper, the vector magnetic potential A and winding current I are used as the variables solved in the time-step finite element method to simulate the nonlinear transient magnetization characteristics of the transformer under DC bias, and the fixed-point reluctivity is introduced to deal with the nonlinear iterative problem. The field-circuit coupling relationship is established through the electromagnetic induction law, and the two-dimensional time-step finite element model of the transformer core is found. The dynamic J–A hysteresis model is used to deal with the hysteresis effect of iron cores. The fixed-point reluctivity of difference form is introduced to solve the problem of uneven transition and multi-value of magnetization curve with hysteresis in the iterative process. The determination scheme for the equivalent thickness of the core model and the initial iterative value are discussed. A laminated core transformer is made for experiments, and the accuracy and applicability of the model proposed in this paper are verified by comparing the calculation and experimental results. The influence of different voltages and different DC bias components on the electromagnetic characteristics of the transformer is analyzed.

Fragility analysis of a concrete gravity dam under mainshock-aftershock sequences

This study presents the fragility analysis of a concrete gravity dam under the mainshock-aftershock sequences using the incremental dynamic analysis. Nonlinear dynamic analysis is carried out on a concrete gravity dam considering reservoir and foundation for various intensities of mainshock-aftershock sequences using a two-dimensional finite element model. Several as-recorded mainshock-aftershock sequence data is collected from the available database and used in the dynamic analysis as ground motion input. The cumulative impact resulting from the aftershocks is quantified in terms of crack length and an energy-based damage index. Based on the analysis, different limit states are defined namely slight, moderate, extensive, and severe. Fragility curves are subsequently developed based on these defined limit states. Results indicate that aftershocks increase the fragility of gravity dams significantly. For a typical spectral acceleration of 0.5 g, the probabilities of attaining slight, moderate, extensive, and severe limit states are 94%, 89%, 42%, and 3%, respectively. However, when aftershocks are considered, these probabilities increase to 99.8%, 94.8%, 67.8%, and 7%, respectively.

Failure analysis of welded joint with multiple defects by extended Finite Element Method and Engineering Critical Analysis

Failure analysis of welded joint with multiple defects was performed taking into account the effect of all defects, not just a dominant one. Four cases of multiple defects in welded joint under the uniaxial tensile loading were investigated using extended Finite Element Method. Two-dimensional Finite Element Models were made according to the tensile specimens with initial crack located in a critical area of welded joint. For each multiple defects case, numerical simulation was performed with three initial crack depth. Engineering Critical Analysis was made using Failure Assessment Diagrams for each defect that was determined as critical for its welded joint case. Numerical simulation showed that the geometry of the most prominent one from a point of view of structural integrity. It was concluded that the vertical misalignment in combination with a secondary defect, had the most adverse effect which can lead to failure of welded structure.

Numerical study on optimized application of engineered cementitious composites in RC coupled shear wall structures

Due to the superior tensile strain-hardening and multi-cracking properties, engineered cementitious composites (ECC) can be adopted in reinforced concrete (RC) shear walls and coupling beams to improve the seismic performance and damage tolerance with simplified reinforcement details. This study numerically investigates the optimized application of ECC in coupled RC shear wall structures based on refined two-dimensional finite element models incorporating constitutive models of ECC and concrete for nonlinear shear behaviors. The balance between cost and performance is adequately considered from the material, member, and structural levels. At the material level, the reasonable tensile properties of ECC are suggested based on the parametric analysis of coupling beam and shear wall specimens. At the member level, the effect of diagonal bar ratios on the seismic performance of coupled walls is investigated to propose reasonable diagonal bar ratio of ECC coupling beams. Finally, at the structural level, nonlinear dynamic time-history analysis of a typical 11-story coupled wall structure based on practical engineering is conducted to investigate the influence of the application ranges of ECC on the seismic performance of the wall system. The damage indexes, including story curvature and crack width, are analyzed and compared. Based on the analytical results, recommendations related to some key issues on the application of ECC in traditional RC structures are provided, including the application range and tensile properties of ECC, as well as the reinforcement details.

Study on the tensile and compressive mechanical properties of multi-scale fiber-reinforced concrete: Laboratory test and mesoscopic numerical simulation

To investigate the tensile and compressive mechanical properties of multi-scale polypropylene fiber-reinforced concrete (PFRC), two-dimensional microscopic finite element models of PFRC were established, and their reliability was verified using laboratory test results. The failure development process and tensile and compressive behaviors of multi-scale PFRC were simulated. In addition, the influence of the length and dosage of polypropylene fibers (PFs) on the mechanical properties of concrete was investigated using mesoscopic numerical simulations. The numerical models established in this study fill the gap in existing research by revealing both the distribution of multi-scale PFs and the true shape of the aggregates. The results predicted by the proposed numerical models were in good agreement with the experimental results. Moreover, the ideal PF length was 30 or 40 mm, and the optimum fiber dosages of two fine polypropylene fibers (FPF1, FPF2) and coarse polypropylene fiber (CPF) were 0.6 kg/m³, 0.6 kg/m³, and 4.8 kg/m³, respectively. This study reveals the influence of parameters such as the length and dosage of multi-scale PFs on the mechanical properties of concrete, providing a reference for engineering applications.

Solar fuels design: Porous cathodes modeling for electrochemical carbon dioxide reduction in aqueous electrolytes

The reduction of carbon dioxide emissions is crucial to reduce the atmospheric greenhouse effect, fighting climate change and global warming. Electrochemical CO2 reduction is one of the most promising carbon capture and utilization technologies, that can be powered by solar energy and used to make added-value chemicals and green fuels, providing grid-stability, energy security, and environmental benefits. A two-dimensional finite-elements model for porous electrodes was developed and validated against experimental data, allowing the design and performance improvement of a porous zinc cathode morphology and its operational conditions for an electrolyzer producing syngas via the co-electrolysis of CO2 and water. Porosity, pore length, fiber geometric shape, inlet pressure, system temperature, and catholyte flow rate were explored, and these parameters were thoroughly tuned by using the smart-search Nelder-Mead's multi-parameter optimization algorithm to achieve pronouncedly higher, industrial-relevant current density values than those previously reported, up to 263.6 mA/cm2 at an applied potential of −1.1 V vs. RHE.

Rotordynamic analyses of stiffened cylindrical structures using high-fidelity shell models

The dynamic response of various rotating stiffened cylindrical and disk structures has been performed using low- and high-fidelity two-dimensional finite element models. The methodology is based on the Carrera Unified Formulation, in which the shell models are obtained hierarchically and automatically. These theories are formulated by expanding the unknown variables over the shell thickness. Various shell models can be implemented depending on the choice of the polynomial employed in the expansion. Lagrange polynomials are considered for developing different kinematic models and for easily modeling the stiffeners. The stiffener deformation is precisely captured through higher-order models, and the mechanical continuity between the stiffeners and skin is automatically guaranteed at the Lagrange points. The linearized equations of motion include the Coriolis and initial stress contributions. Stiffened cylinders and disks with different boundary conditions are considered. The results are compared with the three-dimensional finite element solutions from the literature or obtained using commercial software.

Finite element investigation of cutting speed effects on the machining of Ti6Al4V alloy

In modern times, titanium alloy has a great application prospect in the medical field. Still, the pitiful machinability of titanium alloy material brings incredible difficulty to its ultra-precision cutting. This work presented the effect of parametric sensitivity analysis of the orthogonal cutting process using the finite element method, which dramatically enhances the cutting performance of Ti–6AL–4V. The simulation results are attained by applying Abaqus® explicit 6.14 software. The mechanical reaction of two-dimensional finite element models has been examined for cutting forces. Additionally, the impacts of rake angle, clearance angle, and nose radius on the stress distribution in orthogonal cutting of Ti–6AL–4V have been investigated. Also, to make certain numerical accuracy, the Johnson–Cook constitutive models for Ti6Al4V alloy are implemented. In the end, FE simulation outcomes were supported by the reported results in the literature.

Finite Element Analysis on Thermoelastic Instability of Multidisc Clutches Involving Deformation Modes of Multilayer Material Friction Disc

Abstract A two-dimensional finite element model was developed to investigate thermoelastic instability in multilayered friction discs with finite thickness, considering the deformation modes of the steel core. The model was used to simulate four unstable modes that can occur during the engagement process, and the Fourier reduction was applied to calculate the change in critical speed under these modes. Additionally, the influence of thermal physical parameters, including the elastic modulus, thermal expansion coefficient, Poisson’s ratio, and thermal conductivity of the friction pair, on thermoelastic instability was examined. The findings indicate that the critical speed of the friction pair is lower under the symmetric (friction disc)–antisymmetric (steel disc) mode compared to the other three modes. Consequently, the symmetric–antisymmetric mode is the first to be excited and serves as the dominant mode during thermoelastic instability. Moreover, there exists a specific wave number at which the system exhibits the lowest critical speed and poorest stability. Enhancing the thermal conductivity of the friction disc and steel disc, as well as reducing the thermal expansion coefficient of the steel disc and the elastic modulus and Poisson’s ratio of both discs, can improve the thermoelastic stability of the friction pair. Notably, the thermal expansion coefficient of the friction disc has minimal impact on thermoelastic instability. These results provide a theoretical foundation for exploring the relationship between the thermal failure of friction pairs and rotational speed, as well as optimizing overall performance design.

Simulation of Eddy Current Losses in Twisted Wires

Twisted wires made of insulated strands, known as stranded conductors or litz wires, are used in various areas where the eddy current loss within the wire needs to be reduced. These areas include induction heating, resonance-based wireless energy transfer, and certain radio frequency devices. Some litz wires consist of thousands of individual conductor strands that are twisted together in multiple stages, creating a hierarchical bundle structure. Computer simulations (typically using finite element analysis) are used in the optimal design of the bundle structure. However, detailed three-dimensional models are computationally demanding. In this work, a two-dimensional finite element model was presented for simulating the eddy current loss in cables made of twisted wires. The key element of the model is considering the bundle structure (generally referred to as 3D configuration conditions) within the cross-sectional model domain. The accuracy of the proposed model is tested against 3D finite element simulations. The new method is shown to be accurate, and its computational cost is by orders of magnitude lower than that of 3D models.