One-dimensional Finite Element Model Research Articles

Dynamic analysis of composite flywheel energy storage rotor

Dynamic analysis is a key problem of flywheel energy storage system (FESS). In this paper, a one-dimensional finite element model of anisotropic composite flywheel energy storage rotor is established for the composite FESS, and the dynamic characteristics such as natural frequency and critical speed are calculated. Through the analysis of acceleration transient response, it is found that the flywheel rotor have two critical speeds during acceleration or deceleration process, which are prone to resonance and damage the bearing. Therefore, in order to avoid resonance or reduce resonance peak, the influence of bearing support stiffness, damping and speed-up rate on the critical speed and resonance peak is studied. The calculation results show that the first two order critical speed are affected by the support stiffness. When the stiffness increases, the critical speed of the flywheel rotor increases, but the growth rate decreases. When the damping increases, the critical speed is basically not affected, and the vibration amplitude decreases rapidly. In addition, the resonance peak value of transient response can be effectively reduced by increasing the speed-up rate.

Novel Unscented Kalman Filter-based method to assess the thermal behavior of carbon brake discs for high-performance motorcycles

In the past few decades, braking systems with carbon discs have become the dominant technology for many racing applications, such as in the MotoGP class. Indeed, they provide higher friction coefficients. Moreover, thanks to their lightweight materials (with respect to conventional steel brakes), the unsprung masses and the gyroscopic effects can be reduced. Therefore, the motorcycle dynamic performance can be significantly improved. The usage of carbon brakes requires a very accurate assessment of their thermal behavior. In fact, although their operating temperature in real racing conditions may cover a wide range, their optimal braking performance can be achieved only within a relatively narrow temperature range. This work focuses on the development of the Unscented Kalman Filter (UKF) algorithm as a suitable mathematical tool for assessing the temperature gradient of the carbon disc mounted on the motorcycles competing in the MotoGP™ world championship. A one-dimensional (1D) finite element (FE) model of the disc is developed to provide the a priori state estimate that the filter will combine with the information measured by the temperature sensor available on board to compute the optimal posterior temperature estimation. Besides estimating temperature, the UKF is also exploited to identify the convection heat transfer coefficient (h) of the disc, which is a fundamental parameter for a proper model calibration.

Flexural vibration of elastic composite beams using a third-order deformation kinematics

The present study introduces a one-dimensional finite element (FE) model that utilizes third-order deformation kinematics to analyze the flexural vibration of two-layered composite beams with partial shear slip. The proposed model incorporates a three-node straight beam element, utilizing the field-consistent approach and full numerical integration of the stiffness matrix. This approach is adopted to effectively address stress oscillation and shear locking issues, ensuring accurate and reliable results. The analysis focuses on the third-order deformation kinematics of longitudinal displacement within the beam depth, examining each of the two layers individually. The interface between the two material layers is joined using deformable shear connectors, which are represented as dispersed shear springs over the length of the beam. This study focuses on conducting a flexural vibration analysis of two-layered composite beams. The analysis includes the examination of both free vibration and forced vibration responses while considering or omitting the influence of damping under various loading conditions. The validity of the proposed FE model is assessed by the utilization of a two-dimensional model developed within the ABAQUS software. Additionally, the suggested model is evaluated through the process of verification by comparing it with previously published results.

Open-Circuit Potential Drift in Intercalation Electrodes: Role of Charge Redistribution in a Prussian Blue Analog

Prussian blue analogs (PBAs) are used as electrode materials in energy storage and water deionization cells due to their reversible cation intercalation capability. Despite extensive research on their performance and intercalation mechanisms, little attention has been given to their behavior under open-circuit conditions. Recent studies using symmetrical PBA electrodes in two electrode deionization cells reported that after constant current cycling in dilute NaCl (<0.2 M), the cell voltage dropped under open-circuit conditions, which substantially increased the amount of energy consumed for deionization. However, it remains unclear which electrode (anode/cathode) experienced potential drift and if it was influenced by the low salinity of the electrolyte. Here, we performed a series of electrochemical experiments under different charging and discharging regimes and electrolyte compositions to determine the processes that contributed most significantly to open-circuit potential drift. The data indicated that charge redistribution within the electrode was the main contributor to open circuit potential drift, with electrode dissolution and parasitic reactions playing negligible roles. A one-dimensional finite element model was constructed to simulate charge redistribution by accounting for cation diffusion under open-circuit conditions. The open-circuit potential profiles generated by the model were validated against experimental trends, confirming the occurrence of charge redistribution. A Monte Carlo analysis of the model was conducted to determine the relationship of potential drift to key factors such as applied current, electrode thickness, diffusion coefficient of intercalating ions, and intercalation capacity. Subsequently, a dimensionless number (Da) was developed based on the Dahmköhler number to relate the extent of potential drift resulting from combinations of these factors. The analyses revealed a strong positive correlation between simulated potential drift and Da. Among the key factors studied here, the diffusion coefficient and applied current had the largest impact on Da and, consequently, on potential drift.

Rotordynamic analyses with variable-kinematic beam and shell finite elements

This work investigates the dynamic response of various rotating cylindrical structures using low- and high-fidelity one-dimensional (1D) and two-dimensional (2D) finite element models. The adopted mathematical formalism is based on the Carrera Unified Formulation (CUF). CUF offers a procedure to obtain higher-order beam and shell models hierarchically and automatically. These theories are formulated by expanding the unknown variables over the beam cross-section or along the shell thickness. Various beam and shell models can be implemented depending on the choice of the polynomial employed in the expansion. Both Taylor-like and Lagrange polynomials are considered for developing different kinematic models. The linearized equations of motion include the Coriolis and initial stress contributions. Various thick and thin cylinders and disk structures with different boundary conditions are considered. The beam and shell results are compared with analytical and three-dimensional (3D) finite element (FE) solutions from the literature.

A physics-informed and data-enhanced tensile stress-strain model for UHPFRC

Despite the rapid developments in fundamental investigations and engineering applications of ultra-high-performance fiber reinforced concrete (UHPFRC), there is still lacking of a reliable tensile stress-strain model for UHPFRC in design guidelines. A generalized tensile stress-strain model for UHPFRC was developed for the first time. Through properly identifying unified model parameters, widely acknowledged experimental results were successfully reproduced by using a one-dimensional finite element model (FEM). A rich database was generated and granted with physics by the FEM model. Physical-consistent strength, ultimate strain and stress-strain models of UHPFRC were proposed, trained by model-generated data, and enhanced by experimental data. The proposed strength model and ultimate strain model predicted extensive experimental results with reasonable accuracy, giving mean absolute percentage errors (MAPE) of 12% and 25.3%, respectively. The established stress-strain model also predicted satisfactorily the full-range stress-strain curves tested by different research groups. It was evidenced that higher mean matrix cracking strength leads to higher ultimate strengths, less cracks, higher crack widths of UHPFRC at the ultimate state. This was elaborated for the first time, as caused by the dual action of snubbing effects and multi-crack interactions.

Uniform Step Loading of a Partial Interaction Composite Beam

In the present paper, a one-dimensional finite element model for the analysis of composite beams of partial interaction is constructed. This model was verified against some analytical results available in the literature and achieved very good agreement with the natural frequencies and the time histories it was compared to. Then it was utilised to analyse partial interaction composite beams under the effect of uniform step loads and provided important information about the expected dynamic amplification factors, which turned out to be particularly high, and the effects of the linear stiffness ratio of the interface and the boundary conditions of the lower layer of the beam. The results, in particular, showed that even for extreme cases the orders of magnitude of the slip and the corresponding uplift remain the same. This pointed out an important finding that the uplift in the researched context, at least, is not negligible as it is widely assumed in the literature.

Identification of Nonlinear Soil Properties from Downhole Array Data Using a Bayesian Model Updating Approach.

An accurate seismic response simulation of civil structures requires accounting for the nonlinear soil response behavior. This, in turn, requires understanding the nonlinear material behavior of in situ soils under earthquake excitations. System identification methods applied to data recorded during earthquakes provide an opportunity to identify the nonlinear material properties of in situ soils. In this study, we use a Bayesian inference framework for nonlinear model updating to estimate the nonlinear soil properties from recorded downhole array data. For this purpose, a one-dimensional finite element model of the geotechnical site with nonlinear soil material constitutive model is updated to estimate the parameters of the soil model as well as the input excitations, including incident, bedrock, or within motions. The seismic inversion method is first verified by using several synthetic case studies. It is then validated by using measurements from a centrifuge test and with data recorded at the Lotung experimental site in Taiwan. The site inversion method is then applied to the Benicia-Martinez geotechnical array in California, using the seismic data recorded during the 2014 South Napa earthquake. The results show the promising application of the proposed seismic inversion approach using Bayesian model updating to identify the nonlinear material parameters of in situ soil by using recorded downhole array data.

Comparative analysis of insulated floating cover of water pit thermal energy storage

Water pit thermal energy storage (PTES) as a sensible heat storage technology has been applied in many places with significant success. The insulated floating cover (IFC) of water pit is the key component of the PTES thermal storage efficiency and accounts for more than half of the total cost of the entire water pit. In this paper, a one-dimensional finite element model (1D FEM) and a zero-dimensional lumped thermal system model (0D LTSM) are established for the composite IFC of PTES, and their respective results are compared with experiments respectively. LTSM results match the FEM resolution results if the LTSM is sufficiently refined by discretized each layer into several sub-systems with their own mass and thermal resistance. In this LTSM, 5 sub-systems are used in the thermal insulation layer, and 2 sub-systems are used in the upper and lower impervious barrier respectively. The results show that the LTSM can accurately describe the transient heat transfer process of the composite IFC. The results of LTSM and FEM are in good agreement with 99.2%, which is about 2.6% different from the experimental results.

Preliminary Design of a Mini Gas Turbine via 1D Methodology

To address the increasing interest towards more environmentally friendly naval transportation and the introduction of IMO2020 restrictions on pollutant emissions onboard ships, the present work details the preliminary design of a mini gas turbine engine, i.e., a gas turbine engine with an output power up to 5 MW, for onboard energy generation. In comparison to conventional propulsion systems, gas turbine units benefit from known compactness, which can be further enhanced by employing single-stage uncooled radial machines, according to similar works in the field. As such, the present paper aims to set up a complete procedure that allows a reliable and fast (i.e., requiring a limited computational effort) preliminary design of one-stage centrifugal compressors and radial turbines operating at a high pressure ratio via the use of classical one-dimensional theory. The aerodynamic design outputs in terms of forces and torques are then used to perform a preliminary mechanical design of the shaft by means of a one-dimensional finite element model with commercial software to estimate the corresponding shaft line stress. Despite some necessary geometrical and modeling simplification of the design problem, which results in the unavailability of detailed information on individual components, the employed procedure nevertheless allows a comprehensive overview of the possibilities in terms of maximum machine performance achievable at an early design stage with the associated limited computational requirements. The design procedure and the geometry achieved for the application are presented along with aerodynamic and structural results.

Experimental and numerical investigations on monotonic tensile behavior of grouted sleeve couplers with different splicing configurations

This study presents experimental and numerical investigations on the tensile behavior of grouted sleeve (GS) couplers splicing steel bars with transition splicing and different strength grades intended for use in shifted plastic hinge applications. Sixteen GS specimens, with testing parameters that included GS coupler size, steel bar diameter, and transition splicing index, were assembled and tested under static monotonic tensile tests. Also, one-dimensional finite element (FE) modeling was conducted to establish the bond–slip constitutive models, which govern the bar–grout interfaces at different regions of the GS coupler, by inverse analysis.Experimental results showed consistent failure mode, which was bar rupture away from the coupler region, for all splicing configurations of GS couplers, which demonstrated the ability of GS couplers to fully develop the ultimate stress in the spliced bars. Results also revealed an approximately piecewise linear relationship that governs the ratio between the strain within the coupler region and strain in the spliced normal strength steel bar, in which the strain ratio decreases with larger sleeve sizes and higher transition indices. Furthermore, results showed that GS couplers exhibited considerable slip that increased with bar size and can be of benefit to GS precast members that are subjected to significant rotation demands. The proposed bond–slip models for GS couplers were simple but accurate in slip prediction and they can be very helpful in the analytical modeling of precast members containing GS couplers.

Experimental verification of a beam element for thin-walled beams with torsion, distortion, and shear lag

Beam-type elements based on the theories of Euler–Bernoulli, Timoshenko, and Vlasov are widely used in civil engineering. However, shell and solid finite elements are often used when the effects on normal stresses of either shear deformation or distortion are considered important. Numerically validated in an earlier study with finite element models for shell-type structures, the same one-dimensional finite element model is further developed in this study with a low number of degrees of freedom per node that includes all the structural mechanisms without using 3D finite element models. Laboratory testing of an instrumented steel box girder is conducted, to improve validation of the goodness of fit of the finite element model with real structural behavior.

Development of refined one-dimensional finite element models using a nodal kinematics optimization method

This paper presents refined one-dimensional (1D) finite element models develop by an effective nodal kinematics optimization method. The refined models belong to Best Theory Diagrams, which are built by using the Carrera Unified Formulation (CUF), Axiomatic/Asymptotic method and a Genetic Algorithm (GA). The influence of different chromosome types on the refined models and GA performance have been investigated. It is shown that the proposed method can improve the accuracy of regular 1D-CUF finite element models. Furthermore, the results suggest that it is possible to built refined models for compound loads from the ones optimized for individual loads.

New permafrost is forming on the exposed bottom of Zonag Lake on the Qinghai-Tibet Plateau

Most lakes on the Qinghai-Tibet Plateau have expanded in recent years. Zonag Lake, a critical habitat for Tibetan antelopes in the continuous permafrost zone, burst and overflowed after several years of expansion, resulting in a reduction of approximately 100 km2 in the lake area. Observations have revealed new permafrost is forming on the exposed bottom, accompanied by various periglacial landscapes. The permafrost aggradation on the exposed bottom is rapid, and the permafrost base reached 4.9 m, 5.4 m, and 5.7 m in the first three years, respectively. In this study, the future changes and influencing factors of recently formed permafrost are simulated using a one-dimensional finite element model of heat flow. The simulated results indicate that the permafrost on the exposed bottom is likely to continue to develop, appearing first quick back slow trend. Besides the surface temperature, the annual amplitude is also an important factor in affecting the aggradation of permafrost. The unidirectional permafrost aggradation in the study area is different from the bidirectional permafrost aggradation on the closed taliks around the Arctic. Additionally, snow cover and vegetation are two important factors influencing the future development of permafrost on the exposed lake bottom.

The Influence of Heel Height on Strain Variation of Plantar Fascia During High Heel Shoes Walking-Combined Musculoskeletal Modeling and Finite Element Analysis.

The therapeutic benefit of high heel shoes (HHS) for plantar fasciitis treatment is controversial. It has been suggested that plantar fascia strain can be decreased by heel elevation of shoes which helps in body weight redistribution throughout the length of the foot. Yet it is a fact that the repetitive tension caused by HHS wearing resulting in plantar fasciitis is a high-risk disease in HHS individuals who suffer heel and plantar pain. To explore the biomechanical function on plantar fascia under HHS conditions, in this study, musculoskeletal modeling (MsM) and finite element method (FEM) were used to investigate the effect of heel height on strain distribution of plantar fascia. Three-dimensional (3D) and one-dimensional (1D) finite element models of plantar fascia were generated to analyze the computed strain variation in 3-, 5-, and 7-cm heel heights. For validation, the computed foot contact pressure was compared with experimental measurement, and the strain value on 1D fascia was compared with previous studies. Results showed that the peak strain of plantar fascia was progressively increased on both 3D and 1D plantar fascia as heel elevated from 3 to 7 cm, and the maximum strain of plantar fascia occurs near the heel pain site at second peak stance. The 3D fascia model predicted a higher strain magnitude than that of 1D and provided a more reliable strain distribution on the plantar fascia. It is concluded that HHS with narrow heel support could pose a high risk on plantar fasciitis development, rather than reducing symptoms. Therefore, the heel elevation as a treatment recommendation for plantar fasciitis is questionable. Further studies of different heel support structures of shoes to quantify the effectiveness of heel elevation on the load-bearing mechanism of plantar fascia are recommended.

Unified one-dimensional finite element for the analysis of hyperelastic soft materials and structures

Based on the Carrera unified formulation (CUF) and first-invariant hyperelasticity, this work proposes a displacement-based high order one-dimensional (1 D) finite element model for the geometrical and physical nonlinear analysis of isotropic, slightly compressible soft material structures. Different strain energy functions are considered and they are decomposed in a volumetric and an isochoric part, the former acting as penalization of incompressibility. Given the material Jacobian tensor, the nonlinear governing equations are derived in a unified, total Lagrangian form by expanding the three-dimensional displacement field with arbitrary cross-section polynomials and using the virtual work principle. The exact analytical expressions of the elemental internal force vector and tangent matrix of the unified beam model are also provided. Several problems are addressed, including uniaxial tension, bending of a slender structure, compression of a three-dimensional block, and a thick pinched cylinder. The proposed model is compared with analytical solutions and literature results whenever possible. It is demonstrated that, although 1 D, the present CUF-based finite element can address simple to complex nonlinear hyperelastic phenomena, depending on the theory approximation order.

Estimation of the maximum permissible intrusive force for intrusion of a canine tooth: one-dimensional finite element study

The aim of the present research study is to estimate the maximum permissible intrusive force mathematically with one-dimensional finite element method and to achieve the safe intrusion of a canine tooth without any damage to periodontal ligament (PDL). For this purpose, one-dimensional finite element (FE) model of a canine tooth was developed consisting of tooth (crown and root) and PDL structure. The maximum permissible intrusive force was computed mathematically. For this purpose, the maximum permissible stress was considered as ‘EPDL/1.5’, where ‘EPDL’ is the Young’s Modulus of PDL and factor of safety (FOS) is 1.5. The maximum permissible intrusive force was computed to be approximately 10 g-force (gf). For verification of this computed force value, finite element analysis was carried out on 3-dimensional canine tooth, PDL and bone structures for better verification and it is proved that 10 g-force (gf) value is safe without any damage to PDL tissues.

Simulating nitrate release from an unsaturated coal waste rock dump.

Knowledge of the controls affecting the release of contaminants from waste rock dumps is critical for developing strategies to mitigate downstream impacts on water quality. In this study, a three-dimensional model of a large coal waste rock dump constructed in the Elk Valley, British Columbia, Canada was developed to capture the impact of construction history (1981-2012) and solute transport on nitrate (NO3-) release over a 100-year timeframe. The model consisted of 21, one-dimensional finite element models that represented the temporal evolution of the dump. Nitrate, derived from undetonated blast products, was assumed to be present at the time of waste rock placement and was simulated as a conservative species. The simulated pattern of NO3- release to the surface water receptor occurred approximately 8years before its measured arrival. This time lag is attributed to displacement of the water within a basal alluvial aquifer by dump effluent. The simulated patterns of historic releases corrected for the 8-year time lag, compare favourably with monitoring data and suggest the dominant hydrogeological and geochemical mechanisms are captured in the model. The model indicated the flushing of NO3- from the dump should be complete by about 2042 with a peak effluent concentration of NO3- in 2008. The addition of reclamation covers to the model resulted in an immediate decrease in the annual NO3- loading rate but extended the time frame for NO3- release from the dump relative to the no cover case. The model also showed that the timing of cover placement had little impact on NO3- release relative to the no cover case due to long duration of waste rock placement (~30years) over a relatively large footprint.

Validation and Application of a New Software Tool Implementing the PISA Design Methodology

The PISA (Pile Soil Analysis) research project has resulted in a new methodology for the design of offshore wind turbine monopile foundations. A new software tool called PLAXIS Monopile Designer (MoDeTo) has been developed that automates the PISA design methodology. It facilitates the calibration of the so-called soil reaction curves by automated three-dimensional finite element calculations and it allows for a quick design of monopiles using the calibrated soil reaction curves in a one-dimensional finite element model based on Timoshenko beam theory. The monopile design approach has been validated for sand- and clay-type soils which are common in North Sea soil deposits. The paper presents a validation exercise based on the PISA research project proposal of a rule-based parametric model—General Dunkirk Sand Model (GDSM)—for Dunkirk sand as well as an application of the tool for a project involving an offshore wind turbine on a monopile foundation in sandy layered soil in which the PISA design is compared to the conventional API design. The paper concludes with a discussion of the results and the differences between the various methods.

Dynamic analysis of railway with locally continuous supported superstructures

Purpose In this study, a railway superstructure is modeled with a new approach called locally continuous supporting, and its behavior under the effect of moving load is analyzed by using analytical and numerical techniques. The purpose of the study is to demonstrate the success of the new modeling technique. Design/methodology/approach In the railway superstructure, the support zones are not modeled with discrete spring-damping elements. Instead of this, it is considered to be a continuous viscoelastic structure in the local areas. To model this approach, the governing partial differential equations are derived by Hamilton’s principle and spatially discretized by the Galerkin’s method, and the time integration of the resulting ordinary differential equation system is carried out by the Newmark–Beta method. Findings Both the proposed model and the solution technique are verified against conventional one-dimensional and three-dimensional finite element models for a specific case, and a very good agreement between the results is observed. The effects of geometric, structural, and loading parameters such as rail-pad length, rail-pad stiffness, rail-pad damping ratio, the gap between rail pads and vehicle speed on the dynamic response of railway superstructure are investigated in detail. Originality/value There are mainly two approaches to the modeling of rail pads. The first approach considers them as a single spring-damper connected in parallel located at the centroid of the rail pad. The second one divides the rail pad into several parts, with each of part represented by an equivalent spring-damper system. To obtain realistic results with minimum CPU time for the dynamic response of railway superstructure, the rail pads are modeled as continuous linearly viscoelastic local supports. The mechanical model of viscoelastic material is considered as a spring and damper connected in parallel.