One-dimensional Finite Element Research Articles

Effect of valley topography on dynamic response of arch dams

Arch dams are typically built in the mountain and gorge regions with complex terrain. In the current engineering practice, foundation models are commonly simplified as the half-space with the canyon of regular geometry. The complex topography conditions above the dam crest are neglected. This study investigates the effect of realistic valley topography on the dynamic response of arch dams. The direct finite element method is generalized and applied to the dam-reservoir-foundation system with realistic valley topography. The input ground motions are transformed into the effective earthquake loads at the truncated boundaries by performing several dynamic reaction calculations using one-dimensional (1D) and two-dimensional (2D) auxiliary finite element models. The effect of valley topography on the seismic response of the Baihetan arch dam is evaluated as a case study. Results indicate that the valley topographic irregularities significantly influence the dynamic responses of the arch dam, including relative displacement and stress distribution. Notably, the valley topography effect on the seismic response of arch dams depends on the incident ground motions and is hardly predicted in advance, demonstrating the necessity to account for the realistic topography conditions.

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.

The carbon release triggered by 1.32 Ga sill emplacement and its potential environmental implications

Magmatic activity is one of the important pathways for the delivery of deep Earth carbon to the surface. The massive carbon release in this process can have significant impacts on atmospheric-oceanic environment. Previous studies have done a lot of work on the relationship between Phanerozoic magmatic activity and carbon release, but there is relatively limited attention has been given to investigating the association between Precambrian magmatic activity and carbon release. The Yanliao Large Igneous Province at 1.32 Ga exhibits extensive development of sills, and the reaction between sills and surrounding rocks triggers the release of carbon. Simultaneously, the magmatic activity during this period is considered as the final response to the breakup of the Columbia supercontinent, coinciding with the occurrence of the Mesoproterozoic Oxygenation Event To explore the connection between this magmatic activity and global carbon cycling, environmental changes and planetary evolution, nine representative stratigraphic columns are selected from the Yanliao area. We use the SILLi 1.0 1D model by utilizing the one-dimensional finite element method (FEM) to simulate and estimate the amount of carbon release triggered by sill emplacement. The simulation results indicate that the emplacement of sills increased the surrounding rock temperature and vitrinite reflectance, leading to a decrease in the total organic carbon (TOC) content. A large amount of organic carbon and inorganic carbon was released, which was initiated by the reaction between sills and surrounding rocks, with a total carbon release up to 1.24 × 1013 tons. The estimated CO2 equivalent released during this magma activity episode is expected to be greater than 4.58 × 1013. In Mesoproterozoic strata, the emplacement of sills activates carbon within the lithosphere could have implications for the global environment. Further work needs to be done in other ancient cratons that possess Lower Riphean strata to find additional evidence of the impact of this magmatic event on the Earth system. From this study, it is evident that magmatic activity during the Precambrian period could promote the activation of carbon in crustal sediments and influence global environment, which can a reference for people to understand the planetary evolution process.

Stability of Beam Bridges Under Bridge-Vehicle Interaction

In this paper, we provide an accurate and reliable formulation for simulating the interactions of both train/bridge subsystems and suitable for high-speed railway lines as well as for existing lines worldwide that are being renewed or modernized. We model the train as a series of suspended masses, taking into account the energy dissipation and the suspension system for each train vehicle. On the other hand, the bridge supporting the rails with irregular elevations will be modeled as an Euler-Bernoulli beam. The mathematical formulation of the interaction problem between the two subsystems requires the writing of two sets of equations, which interact with each other through contact forces. Using a one-dimensional finite element formulation, a series of equations are constructed by Modeling the beam structure. In addition, the suspended mass equations are first discretized using Newmark's finite difference formulas, which then reduce the degrees of freedom (DOF) of the vehicle to those of the bridge element. This solves the coupling problem between the two subsystems. The derived component is known as the vehicle/bridge interaction (VBI) element. On the other hand, an iterative procedure will be used subsequently to solve the non-linearity problem of the resulting system of differential equations. MATLAB programs provide results that identify the critical parameters influencing the bridge's dynamic stability.

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.

Cross-sectional analysis of initially curved composite beams with rectangular and circular sections using an asymptotic meshless method

An analytical meshless cross-sectional dimensional reduction method is developed to perform structural analysis of initially curved composite beams. By introducing the Pascal polynomials in the Cartesian coordinates system for beams with rectangular cross-sections and in the polar coordinates system for the beams with circular cross-sections to the warping field, a three-dimensional beam problem can be split into a two-dimensional cross-sectional analysis and a one-dimensional along the reference line of the beam. The obtained cross-sectional stiffness matrix based on higher-order of the strain energy can be incorporated into a one-dimensional finite element solution for initially curved composite beams, for the purpose of strain and stress analysis. Finally, the three-dimensional strain through the thickness of the beam can be achieved by the recovery analysis. The present method takes advantage of Pascal polynomials so that the solution procedure will be more simplified and computationally more efficient compared to three-dimensional finite element (3D FE) method. The proposed method for different isotropic and anisotropic beams is examined and compared with the literature, 3D FE, and Variational Asymptotic Beam Sectional (VABS) package which is a finite element based cross-sectional analysis tool for composite beams.

On the evaluation of lateral-torsional buckling of web-tapered cantilevers with doubly symmetric I-section

Recently, structural engineers have tended to design stronger and lighter structures due to economic reasons, technical developments in computer-aided design, and improvements in manufacturing. The demand for designing stronger and lighter structures has led to the compulsory considering structural efficiency and stability loss at the design level. Lateral-torsional buckling (LTB) is a major stability loss for web-tapered cantilevers with doubly symmetric I-section, which are aesthetic and structurally efficient. The elastic LTB loads of these cantilevers should be calculated at the design level since the LTB may happen before bending stress reaches yield. Studies related to the LTB of cantilevers are rare and require numerical solutions since the LTB mode shape of cantilevers is complex compared to simply supported beams. The present study introduces an analytical procedure based on the energy method for calculating elastic LTB of web-tapered cantilevers with doubly-symmetric I-section in two different forms. The analytical model considers different transverse load types, positions of loads, and web tapering degrees. The analytical solutions were validated with one-dimensional finite element analysis using a beam element. Excellent accordance between results was demonstrated. The general LTB behavior of web-tapered cantilevers with doubly symmetric I-section was clarified with detailed comments based on results obtained from the presented analytical model.

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.

1D higher-order theories for quasi-static progressive failure analysis of composites based on a full 3D Hashin orthotropic damage model

This work investigates the crack propagation in composites by adopting a novel full three-dimensional (3D) Hashin-based orthotropic damage model combined with higher-order one-dimensional (1D) finite elements based on the Carrera Unified Formulation (CUF). Previous literature has proven that CUF provides structural formulations with great accuracy and improved computational efficiency. Moreover, a Layer-Wise (LW) formulation can be implemented within the CUF framework, allowing an accurate description of the 3D stress state in composite laminate, representing crucial information for progressive failure analysis. A Newton–Raphson predictor–corrector algorithm is used for the numerical solution of classical case tests, i.e., compact tension and three-point bending tests. The obtained results are compared with experimental outcomes and with solutions from well-established 2D damage models and a 3D Abaqus numerical model, demonstrating the capability of the proposed method to efficiently capture both the failure load and shape of the crack pattern.

Конечно-элементная модель перегрузочного крана КПП 16/32т для перевалки грузов в речных и морских портах

Transshipment cranes of the checkpoint of the Lenpodyemtransmash plant are widely used in river and sea ports, at industrial enterprises for grappling transshipment of bulk cargo and for working with piece loads or containers, as well as for transshipment of scrap metal and rolled metal using lifting electromagnets. It is proposed to eliminate the uncertainties caused by the incompatibility of one-dimensional (rod) and two-dimensional (plate) finite elements having a different number of degrees of freedom, 12 and 20, when developing digital twins of portal cranes of the Lenpodyemtransmash plant on the example of the CHECKPOINT 16/32t crane by approximating axisymmetric shells of the portal head with rod finite elements. The method is based on the equality of the potential shear energy of the finite element model of the plate and the potential energy of the approximating rod model, the elements of which work on tension/compression, which made it possible to move from the finite element model of the GEARBOX 16/32t reloading crane, built on the basic finite elements of Kirchhoff plates, to the finite element model of the crane based on the core base finite elements. A mathematical model of a matrix equation of static equilibrium with many degrees of freedom is proposed, the numerical solution of which by the Gauss method allows us to proceed to six-component internal forces in each finite element due to the corresponding vector of external loads reduced to the degrees of freedom of the calculated finite element model. The possibility of inter-pretation of bearing elements of spatial metal structures of portal cranes by both one-dimensional rod and two-dimensional plate finite elements is investigated, a re-evaluation of traditional views on the computational analysis of the stress-strain state of metal structures of portal cranes in the field of reliable determination of their bearing capacity during operation in ports, especially in the field of assessing post-repair risk analysis and the resource of reloading cranes is proposed, those who have completed the standard service life in the port and have undergone capital repairs. A calculated rod finite element idealized model of a PPC 16/32t gantry crane for transshipment of cargo in river and sea ports is constructed, demonstrating the transition from a real design to a calculation model based on geometric principles of discretization of both rod and continuum elements by the basic rod end elements of the crane, as a result of which the digital calculation model should be detailed and complex, like a system with many degrees of freedom. The algorithm of application of the digital calculation model of the crane is given on the example of static finite element calculation analysis of the KPP 16/32t crane.

Equivalent analytical formulation-based multibody elastic system analysis using one-dimensional finite elements

Equivalent analytical formulation-based multibody elastic system analysis using one-dimensional finite elements

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 regularized higher-order beam elements for damage analysis of reinforced concrete beams

This work presents a numerical method for damage analysis of reinforced concrete beams using the higher-order beam theory based on Carrera unified formulation. The component-wise approach is employed to model the concrete and steel reinforcing bars as two independent one-dimensional finite elements. A modified Mazars damage model with tensile and compressive damage propagation laws is utilized for concrete, and an elastic-perfectly plastic law is used for steel rebars. To address the instability and mesh dependence caused by the strain-softening behavior of concrete, a fracture energy regularization technique based on the crack band model is developed, especially for the higher-order beam theory. The proposed method is validated by comparing its numerical results with three experimental benchmark results. The comparison indicates that the method accurately predicts the damage distribution of concrete and the flexural behavior of RC beams under quasi-static loading conditions while remaining computationally efficient.

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.

Lateral torsional buckling analysis of corrugated steel web girders using homogenization approach

Corrugated web beams have become popular in recent years due to their high strength-to-weight ratio, ductility and high shear resistance without stiffeners. The developments in the automated production of corrugated steel plates have further amplified their use as structural elements in bridges and buildings. In this paper, we develop a strain energy-based homogenization scheme to convert corrugated sections into equivalent flat sheets with modified elastic properties. The thin-walled theory is implemented in a one-dimensional (1D) finite element (FE) framework along with a modified analytical expression to study the lateral torsional buckling of corrugated web girders. The homogenization-based FE modelling reduces the computational requirement of finer mesh sizes on the corrugation profile. The present thin-walled FE model is implemented to different corrugation profiles and lengths, and their responses are compared with methodologies available in the literature. The effects of the geometrical parameters and loading on the lateral torsional buckling behaviour are investigated and important observations are made for structural designs.

Evaluation of the effects of the seismic wave incidence angle on soil-structure interactions via advanced finite beam elements

This work investigates the interactions between the soil and a superstructure subjected to various seismic waves using variable-kinematics finite beam elements. Artificial boundary conditions based on springs and dashpots with appropriate elastic and viscous coefficients were adopted to ensure the absorption of the incident waves and simulate the infinite domain condition. The one-dimensional finite element formulation is obtained with a unified formalism that enables arbitrary structural models to be adopted. Lagrange-type expansions have been used in this work to approximate the beam kinematics and facilitate the application of artificial boundary conditions. Both pressure and shear waves with different incidence angles have been considered, and the dynamic responses calculated with the current approach have been compared with analytical solutions when available. The results have demonstrated the accuracy and potentialities of the methodology and provided reasonable confidence for future applications.

Thermal buckling of steel tube using finite element method

The present research work focuses on obtaining the critical buckling temperature (ΔTcri) of an offshore pipeline model from one-dimensional and three-dimensional finite element analysis. In this work, the pipeline model considered for analysis has a prismatic and hollow cross-section. The dimensions used for the pipeline model are: Length (L) = 360 mm, Outer Diameter (D) = 12 mm, and Thickness of the pipeline model (t) = 1 mm. The one-dimensional (1D) finite element analysis is conducted with proper element selection as BEAM188 element, and the three-dimensional (3D) finite element analysis is carried out using the SOLID186 element. The mesh element length or size for 1D analysis is 20 mm, while it is 1 mm for 3D analysis, as determined by a detailed convergence study on both 1D and 3D finite element models. The pinned–pinned boundary conditions used for 1D finite element analysis are (at × = 0 mm, u = 0 &v = 0; at × = 360 mm, u = 0 &v = 0). Similarly, the following boundary conditions are used for 3D finite element analysis: at z = 0 mm, u (x, y, 0) = 0, v (x, y, 0) = 0, and w (x, y, 0) = 0, and at z = 360 mm, u (x, y, 360) = 0, v (x, y, 360) = 0, and w (x, y, 360) = 0. The displacements along the ×,y, and z directions are represented in the 3D analysis as u, v, and w. The critical buckling temperature values (ΔTcri) obtained in the 1D and 3D thermal buckling analysis are (ΔTcri)1D = 72.06 °C and (ΔTcri)3D = 72.27 °C.

Design, fabrication, nonlinear analysis, and experimental validation for an active sandwich beam in strong electric field and thermal environment

In the present work, an efficient one-dimensional finite element (1D-FE) framework considering layerwise mechanics with full electro-mechanical coupling has been developed for the laminated smart sandwich beams submitted to active damping. Nonlinear constitutive relations of piezo-thermo-elasticity at large electric field with temperature-dependent material properties have been considered. The efficient layerwise theory (ELWT) considers the normal deformation of the piezoelectric sensing/actuating patches/layers due to the more significant value of piezoelectric strain coefficient d33. The electric potential variation across the thickness of the PZT sensor/actuator has been assumed quadratic. The state space format of the dynamical system has been constructed based on a reduced order model in modal space. The feedback linearization approach has been applied to the nonlinear system of equations to design an equivalent linear optimal control strategy. An experimental facility has been developed to test the accuracy of the present nonlinear FE model. This facility consists of a thermal chamber with a heating system, air gun, actuation & sensing units with band-pass filters, a smart sandwich beam equipped with PZT-SP5H patches, a data acquisition system, and a computer with LabVIEW software. Open- and closed-loop responses from the present 1D-FE model have been compared with those obtained through experimentation at different temperatures. It has been observed that the current nonlinear FE model correctly captures the dynamic behavior of the vibrating smart sandwich beam at different operating temperatures and strong electric field. The study shows a strong dependence of the PZT materials on thermal chamber temperature and actuation field. New results for a smart sandwich beam are also presented to study the performance of PZT-SP5H patches as sensors/actuators for nonlinear active shape and vibration control in a thermal environment. The effect of piezoelectric actuator/sensor thickness, patch size, position, and applied mechanical load on the active shape and vibration control has been discussed.