Euler-Bernoulli Beam Element Research Articles

Experimental validation of an efficient strategy for FE model updating and damage identification in tubular structures

ABSTRACT Early identification of damages in tubular structures is crucial for their long-term safety and functionality, as they are essential in various modern life applications. Experimental and numerical modal data may slightly differ due to unknown structural characteristics and uncertainties, which are typically addressed using finite element (FE) model updating procedures. Instead of using the Euler-Bernoulli beam element, this paper utilises the semi-rigidly connected frame element (S-RCFE). By incorporating extra design parameters, such as the end fixity factor of all connections, the S-RCFE offers a unique opportunity to establish a strong agreement between experimental and numerical models through an optimisation-based FE model updating procedure. A well-calibrated FE model represents the actual behaviour of the structure and leads to achieving accurate results in the damage detection step. This paper employs the improved grey wolf optimiser (IGWO) and weIghted meaN oF vectOrs (INFO) to minimise 11 objective functions with adjustable coefficients. The statistical investigations reveal that the IGWO effectively minimised five out of six objective functions, which were defined based on the modified total modal assurance criterion (MTMAC). The rest of the objective functions based on the modal assurance criterion (MAC), natural frequency vector assurance criterion (NFVAC), differences in natural frequencies, and a combination of the MAC and NFVAC could not obtain accurate outcomes for the model updating problem. The statistical comparison indicates that the INFO algorithm is unreliable for the FE model updating despite achieving at least one successful result in ten independent runs. The INFO algorithm and the IGWO algorithm demonstrate comparable performance in damage detection. The analysis also shows that the coefficients of MTMAC, alpha and beta, should be adjusted to 0.65 and 1, respectively, to achieve the most accurate damage detection result.

Aeroelastic tailoring of stiffened cantilever plate using composites and structural layouts: A parametric study

AbstractThis paper studies the aeroelasticity of a stiffened cantilever plate using composite material and novel structural layouts. A comprehensive parametric study is conducted to determine the influence of different design parameters on the aeroelastic boundaries. Design parameters include plate sweep angle, ply orientation, stringer cross-section and stringer sweep angle. Nastran is used to run the aeroelastic analysis, and the process is automated using ${\rm{Matla}}{{\rm{b}}^{}}$ . The structure of the plate is modelled using laminate elements whereas the stringers are modelled using the Euler-Bernoulli beam elements. The unsteady aerodynamic loads are modelled using doublet-lattice method (DLM) and the structural and aerodynamic meshes are connected using an infinite plate surface (IPS) spline. A mesh sensitivity analysis is conducted to ensure fine meshes for the aerodynamics and structure. The study’s findings demonstrate the benefits of employing forward swept (Fw) stringers since it increases flutter speed by almost 38% compared to the unswept stringers case and prevents divergence. Moreover, the static aeroelastic analysis illustrates that the utilisation of Fw swept stringers can reduce the average tip displacement and tip twist effectively. T-shaped stringers are recommended to stiffen the plate due to their lower impact on the total mass of the plate. In some configurations, the structural layout has a much higher effect on the aeroelastic instabilities when compared to the material effect (ply orientation). However, results suggest combining both for some cases to get balanced washin and washout effects.

Improvement on the axial force accuracy of the ANCF Euler-Bernoulli beam element with the second-order approximate function of the centerline and precise constraint equations

The conventional Euler-Bernoulli beam element of the absolute nodal coordinate formulation (ANCF) yields incorrect axial force due to the existence of the first-order approximate function of the centerline and over-constraint equations. This work aims to improve the axial force accuracy of the element by using the second-order centerline approximate function and precise constraint equations. The second-order function includes the quintic Hermite shape function and the vector of nodal coordinates containing zeroth to second-order derivatives of position. The elastic force vector of the element and its tangent stiffness were then formulated based on the decoupled elastic line method. The exact kinematic requirements of three types of constraint points were fully clarified. On this basis, the corresponding concise constraint equations, constraint Jacobian and Hessian matrices were rigorously derived in the context of ANCF, where G2 continuity was demonstrated to be satisfied at the node acted by an inclined concentrated force, the relative rotation constraint of the rigid joint was described using the dot product of the gradients on both sides of the joint, and the fixing gradient direction at the partially-clamped end was expressed by using the zero cross product of the end gradients in the initial and deformed configurations. Large deformation problems of typical beams under fixed and follower loads were solved using five types of elements, where the results of the ABAQUS B22 elements were taken as a reference for validation. It is found that when using the first- and second-order beam elements having over-constraint equations of the three types of constraint points, obvious axial force error occurs near the corresponding constraint points. In comparison, a few second-order elements containing the derived constraint equations output correct axial force consistent with ABAQUS. However, a large number of the first-order elements containing the correct constraint equations still yield inaccurate axial force in certain beam regions.

Two-dimensional viscoelastic beam element for ultra-large space structures based on absolute nodal coordinate formulation

Internal damping is an important factor in the dynamic behaviors of ultra-large space structures in zero damping space environment. To precisely describe the damping, this paper proposes a two-dimensional viscoelastic Euler-Bernoulli beam element based on absolute nodal coordinate formulation and Kelvin-Voigt damping model, where the damping stress is linearly dependent on the stress rate. Firstly, a precise generalized damping force model is developed using the principle of virtual work. A simplified generalized damping force model is then proposed to improve simulation efficiency by neglecting the axial damping force and a part of the transverse damping force. Numerical simulations show that the proposed damping force models will not affect the rigid-body motion of the beam. Then, a simple formula is presented to estimate the damping ratio of the beam for different parameters, which shows good agreement with the logarithmic decrement method in simulations. Finally, the effects of viscoelastic damping on the dynamic behaviors of a Sun-facing beam in space are investigated. Simulation results reveal that the viscoelastic damping can greatly reduce the vibration amplitude of the beam near the resonance frequencies.

A Unified Meshfree Path to Arbitrary Order Hermite Finite Elements for Euler-Bernoulli Beams

The fourth-order governing equation of Euler-Bernoulli beams necessitates the employment of C1 Hermite shape functions in finite element analysis. However, unlike the C0 finite element shape functions that can be easily formulated as Lagrangian polynomials in a unified manner, the Hermite shape functions of Euler-Bernoulli beam elements are usually constructed case by case. In this work, a simple and unified meshfree path is proposed to develop arbitrary order Hermite shape functions of Euler-Bernoulli beam elements. This approach is realized by proving that the Hermite reproducing kernel meshfree shape functions degenerate to the interpolatory Hermite finite element shape functions under a proper choice of support sizes. The proposed approach provides an explicit formalism for Hermite finite element shape functions, which enables an easy construction of arbitrary order Hermite beam elements. Accordingly, in addition to the conventional cubic Hermite beam elements, explicit shape functions, mass and stiffness matrices for quintic and septic Hermite beam elements are presented. Meanwhile, the frequency errors and general higher order mass matrix formulation for these Hermite beam elements are elaborated as well. These theoretical results are consistently demonstrated by numerical examples with respect to both static and free vibration analysis.

Development of an anti-vibration aircraft model support system with magnetorheological annular squeeze dampers for wind tunnel

Sting support is an important equipment in wind tunnel test and is also vulnerable to resonance under the influence of wind flow, which will reduce the accuracy of test data and even pose a hazard to the wind tunnel. To address the vibration problem, an innovative magnetorheological sting support (MRSS) was proposed in this paper. Specifically, the vibration reduction mechanism was explained by using a combination of Euler-Bernoulli beam and Kelvin-Voigt element. Furthermore, the relationship between the stiffness and damping of the magnetorheological damper (MRD) and the natural frequency (NF) and damping ratio (DR) characteristics of the MRSS was illustrated. To provide controllable damping and stiffness for the support system, an MRD with annular squeeze mode was designed, taking into account various factors such as low influence on wind flow, sting shape, and magnetic circuit requirements, and was also optimized by considering target magnetic field and low power consumption as the objectives. Tests on the manufactured MRD demonstrate the effectiveness of the structure design and optimization. Also, the response time characteristic satisfies the system vibration control. Subsequently, the controllability and superior fail-safe property of MRSS were verified through laboratory and wind tunnel tests. Finally, an on–off control logic was developed, and real-time vibration control tests were conducted in various impulse excitation, the resonance peak was significant attenuated by 27.1 dB. Additionally, the resonance peak was attenuated by 17.6 dB in the passive state. The experimental results showed that the MRSS was able to suppress the vibration with efficiency and reliability.

Nonlinear dynamics of a drillstring system with PDC bit in curved wells based on the finite element method

In this paper, a nonlinear mathematics model for axial-torsional-lateral dynamics of drillstring system equipped with a PDC bit in curved wells is established and analyzed. In the proposed model, using the finite element method, the drillstring structure is spatially discretized by Euler-Bernoulli beam elements with twelve degrees of freedom. Based on rock surface morphology of bit-rock interaction, a more realistic cutting and friction model with state-dependent delay effects is introduced to represent the bit-rock interaction. Meanwhile, a new top boundary condition is proposed to simulate the desired weight on bit (WOB). The nonlinear dynamic model is discretized in time-domain employing the generalize-α method, and the modified Newton iteration method is employed to calculate displacement response at the while-time step. Finally, the parametric analysis is carried out for discussing the influences of weight on bit and rotating speed on the nonlinear vibration of the drillstring system, respectively.

Structural vibration control of spar-buoy floating offshore wind turbines

Floating offshore wind turbines (FOWTs) have complex dynamics problems and strong coupling effects within their entire systems, and they are sensitive to winds and sea waves that may cause structural fatigue damages and power production fluctuations. Structural vibration control is a promising way to reduce FOWT responses, but most previous studies focused on linear control strategies with the limitations of requiring large strokes and having narrow effective frequency bandwidth. Nonlinear energy sinks (NESs) have emerged as an alternative to overcome the above limitations of linear control methods. In the present study, an OC3-Hywind spar-buoy FOWT is selected as a prototype structure for developing an in-house model to investigate its associated aerodynamics, hydrodynamics, and structural dynamics. The wind turbine blades and tower are modelled by three-dimensional Euler-Bernoulli beam elements and the floater is assumed as a rigid body. The blades’ pre-twist, pitch, and rotating angles are also considered to develop the system’s time-varying mass, stiffness, and damping matrices. The nonlinear quasi-static model is adopted to calculate the forces generated by the mooring cables. The straightforward and efficient in-house model is validated against FAST. Subsequently, a bistable track NES with a profile combining both negative second-order and positive fourth-order terms is proposed, designed, and incorporated into the model to mitigate FOWT responses under two investigated environmental conditions. Results show that the in-house model is of high accuracy in estimating dynamic characteristics and responses of FOWTs, paving the way for preliminary design and analysis of FOWTs with different platform types. Moreover, the bistable track NES can effectively control the fore-aft displacements at the tower top with practical strokes.

Equivalently analytical solution for the large deformation of slender beams under follower loads: a second-order ANCF approach

Follower loads interact with the object's configuration, and the two are unknown variables in geometrically nonlinear analysis. This work aims to solve the large deformation of slender beams under follower loads via the Bernoulli–Euler beam element of absolute nodal coordinate formulation. The second-order approximate function of the beam centerline is utilized to model the beam configuration and the Frenet frame. The elastic force vector and its tangent stiffness matrix are formulated following the decoupling elastic line approach. The constraint of adjacent elements is imposed using Lagrange multipliers. The exact kinematics characteristics of typical follower loads are demonstrated; sequentially, the external force vectors and the load stiffness matrices are rigorously derived based on the configuration and the Frenet frame modelled by the second-order approximate function. Benchmark problems of straight and curved beams under different follower loads are solved, wherein the accuracy and efficiency of the proposed approach are validated as compared to relevant analytical and numerical solutions. It is found that the proposed element yields equivalently analytical nodal solutions, including position, rotation and curvature; considerably fewer proposed elements are used as compared with other finite element methods; the load stiffness matrix of the bending moment raises computational efficiency of the proposed element; the obtained solutions are more accurate than that of the B22 element of ABAQUS when solving pressure loading cases. By further extending the proposed approach, it can enable the unveiling of the spatio-temporal evolution characteristic of slender structures and follower loads from the equivalently analytical perspective.

Frequency dependent effective modulus of square grid lattice using spectral element method

A spectral element method-based formulation is developed to obtain the frequency-dependent effective Young’s and shear modulus of a two-dimensional square grid lattice. The methodology presented in this work is a simplified approach to obtain effective parameters. The lattice is assumed to be constituted of Euler–Bernoulli beam elements which are arranged in a specific order to obtain the said geometry. Spectral element formulation of the beam element considering axial and flexural deformation is presented, which in due course is employed to obtain the global spectral element matrix of the unit cell. A detailed procedure to obtain the frequency-dependent stiffness matrix of the unit cell is presented on which proper boundary conditions are applied using specific transformation matrices for each case. The frequency-dependent properties are also calculated using the software package COMSOL Multiphysics to validate the results. Frequency responses of the unit cell are obtained using the proposed methodology as well as the software package, and the results are compared. It is observed that the proposed methodology predicts the peaks at nearly the same frequency range as obtained through the finite element solution obtained in COMSOL Multiphysics. Finally, the results are presented which show the frequency-dependent effective parameters for the unit cell. The methodology presented here opens up a new way to calculate the effective properties of two-dimensional lattice structures and with some modifications can also be extended to three-dimensional lattice structures.

A Coupled Hydrodynamic–Structural Model for Flexible Interconnected Multiple Floating Bodies

Evaluating the structural safety and seakeeping performance of very large floating structures (VLFS) using the rigid module flexible connector (RMFC) method remains challenging due to the complexity of the coupled hydrodynamic–structural responses in this system. In this study, a coupled hydrodynamic–structural frequency–time domain model is developed based on the RMFC method employing the planar Euler–Bernoulli beam elements to investigate the dynamic responses of multi-module floating systems. To reveal the dynamic characteristics of the systems, the coupled hydrodynamic–structural responses are investigated using a frequency–time-domain numerical model with viscous correction, in which the mass and stiffness attributes of connectors are incorporated into the system. Given the effects of hydrodynamic interaction, consideration is given to the case of three modular boxes connected by flexible beams aligned in series in shallow water to validate the present model. Higher efficiency and accuracy can be found in the system using viscous correction in potential flow theory and introducing state–space model to replace the convolution terms in the Cummins equation for the time domain. Moreover, this model can be extended to a considerable number of floating modules, which provides possibilities to analyze N-module floating systems.

Dynamic modeling and analysis of planetary gear train system considering structural flexibility and dynamic multi-teeth mesh process

The structural flexibility of planetary gear trains (PGTs) is a significant factor that affects tooth loads and system vibrations, especially in heavy-duty wind turbine gearboxes. Therefore, it is crucial to investigate the influence mechanisms of complex structural deformations on tooth loads and system vibrations. In this work, a dynamic modeling approach is proposed for the complex carrier and ring gear based on the condensation theory of finite elements. The dynamic model of the sun shaft is modeled using the Euler-Bernoulli beam element, and the planetary gear set is modeled using the lumped parameter method. Then, the dynamic multi-teeth mesh process is developed using variable-speed characterization variables and virtual vibration line displacements. Lastly, the rigid-flexible coupling dynamic model of PGT is established and validated. The results indicate that treating components as rigid solids may lead to an underestimation of the impact of input torque variation on system vibrations. When the input torque remains stable, the tooth stiffness can be used to assess the overall change trend of tooth loads. However, when the input torque varies significantly, it is necessary to take into account the comprehensive structural deformations.

Vibration energy accumulation and absorption characteristics of pseudo acoustic black hole wedge

The Acoustic Black Hole (ABH) is an effective structure for harvesting and dissipating energy from flexural waves. It works by reducing the thickness of the ABH wedge in a power law relationship with m ≥ 2, which rapidly decreases the local phase velocity of flexural waves and leads to an energy convergence effect. However, the vibration performance may differ if the tapered wedge does not meet the requirements of a typical ABH. This article introduces and discusses two types of “pseudo-ABH” wedges: linear-degenerate ABH and step-degenerate ABH. These wedges do not follow the power-law and continuity conditions of typical ABH, respectively. To establish the dynamic models of pseudo-ABH wedges, the lumped-mass transfer matrix method (LTMM) and traveling wave analysis are introduced and validated using analytic solutions of the non-uniform one-dimensional Euler-Bernoulli beam and finite element method. Meanwhile, a good match between the results of the Timoshenko and Euler-Bernoulli beam theory also indicates the correctness of our model. The energy ratio and reflection coefficient are defined to characterize the energy accumulation effect and vibration absorption performance of the pseudo-ABH wedges. The vibration performance of the linear-degenerate ABH is closer to the typical ABH than the step-degenerate ABH. The step-degenerate ABH has more effective energy accumulation and reduction performance for individual frequencies. However, as the number of segments in the step-degenerate ABH increases, its dynamic performance becomes closer to that of the typical ABH. The novelty of this article is to study vibration energy accumulation and absorption characteristics of pseudo acoustic black hole wedges using LTMM model, disclose the differences of linear and step degenerate ABH for their performance, and recommend the step degenerate ABH in place of the typical ABH of a power law thickness relationship.

Finite element model updating and damage identification using semi-rigidly connected frame element and optimization procedure: An experimental validation

Owing to ever-increasing complexity of engineering structures, developing a methodology for the early detection of defects has become crucial to ensure their long-term safety and reliability with the least amount of expense. There are always discrepancies between experimental and numerical modal data because of unknown structural parameters and uncertainties. The finite element (FE) model updating techniques attempt to minimize the differences by adjusting the unknown parameters of the FE model. Therefore, the FE model updating methods are essential for developing a baseline model and accurate damage identifications in subsequent steps. This paper employs the semi-rigidly connected frame element (S-RCFE) instead of the standard Euler-Bernoulli beam element for assembling the FE model of the experimental beam and establishing a high-fidelity numerical model. The S-RCFE with extra design parameters, including the end fixity factor of all connections, enables us to achieve a reasonable agreement between experimental and numerical models through the optimization-based procedure. In FE model updating step, two objective functions based on modified total modal assurance criterion (MTMAC) and changes in natural frequencies are used to minimize by three optimization algorithms, viz, grey wolf optimizer (GWO), gradient-based optimization (GBO), and an improved version of GWO (IGWO). The influence of the S-RCFE and standard Euler-Bernoulli beam on the model updating accuracy is also examined, and the efficiency of S-RCFE is evaluated. The statistical results reveal that GWO-MTMAC and IGWO-MTMAC can be successfully implemented for FE model updating with almost the same performance. However, IGWO provides the most reliable results with a relatively extensive computation time for damage identification in all scenarios. In some damage scenarios, the GWO and GBO perform comparably with very similar running time. Data used in this article can be found at https://github.com/Samir-Khatir/Data-modal-analysis-of-healthy-and-cracked-beam.git

A nonlinear fibre beam-column model for partially encased composite columns incorporating local buckling effect

Partially encased composite (PEC) columns are being widely used as vertical load carrying members in high-rise building structures. The complex structural behaviour of PEC columns at ultimate and failure states, related to local buckling of steel section and confinement effect of concrete, has posed significant difficulties and computational costs for accurate analysis of these members. To address this issue, this paper presents a nonlinear fibre beam-column (FBC) model for efficient and accurate analysis of PEC columns. A 2D Euler-Bernoulli beam element based on geometrically exact beam theory is employed, which has fibre cross sections accounting for the material nonlinearity of steel and concrete. A generalised effective width method (GEWM) is developed and integrated in the FBC model to simulate the stress redistribution in the steel section due to the progression of local and post-local buckling. Numerical examples demonstrate that the proposed FBC model can reasonably predict the behaviour of short PEC columns under concentric and eccentric compression, as well as the global buckling behaviour of long PEC columns. The computational cost of the proposed FBC model is considerably lower than that of 3D finite element analysis. The numerical examples also show that the incorporation of the local buckling effect (GEWM) leads to decreases in the ultimate and post-peak loads predicted by the FBC model. The effect of local buckling becomes insignificant for long PEC columns with length-to-depth ratios greater than 15.

Numerical modelling of compliant foil structure in gas foil bearings: Comparison of four top foil models with and without radial injection

In the literature, there exists no consensus on a best practice for modelling the compliant foil structure of Gas Foil Bearings (GFBs). This paper focuses on the top foil modelling and its original contribution to the modelling problem is a comparison of steady state analysis efficiency, and transient and steady state accuracy between four top foil models with and without gas injection. The bump foil is modelled using the Simple Elastic Foundation Model (SEFM), and the four top foil models are (a) neglecting the top foil, i.e. the foil structure is modelled as a basic SEFM, (b) Euler–Bernoulli (EB) beam elements, (c) non-curved shell elements, and (d) curved shell elements. The theoretical analysis is carried out using a multi-domain numerical model and exemplified using a rigid rotor supported by three-pad GFBs. Comparing steady state journal eccentricities, low discrepancies are seen between almost all investigated models. However, the basic SEFM is found to be insufficient for cases with injection. Using the curved model as a benchmark, it is found that the predictions of steady state journal eccentricities, transient response, and eigenvalues made by the model with non-curved shell elements are less accurate than those of the model with EB beam elements. Thus, despite a higher degree of simplification, the model with EB beam elements is found to be both more computationally efficient as well as more accurate for steady state analysis when compared to the model with non-curved shell elements. While the radial foil deformation for the curved model exhibits dependency on the axial coordinate, this dependency is significantly overestimated by the model using non-curved shell elements. This is most pronounced for the case without injection, and it could explain the inferiority of the model using non-curved shell elements for estimating steady state journal eccentricities. A stress analysis indicates that this is caused by the non-curved shell element model not accounting for the membrane stresses in the top foil.

Multi-level curvature-based parametrization and model updating using a 3D full-field response

Model updating improves the correlation between the response of the real structure and the response of the finite-element (FE) model; however, the selection of the updating parameters (parametrization) is crucial for its success. Using full-field modal shapes, a large number of parameters can be updated, e.g., the Young’s moduli of all the finite elements; however, the structural response is not necessarily sensitive to an arbitrary parameter, making the optimization problem ill-conditioned. Additionally, the computation of the full sensitivity matrix is not feasible for relatively large FE models. Not all locations are equally important for model updating; at locations of the highest mechanical loads, more focus is required. In this research, the updating parameters are based on the curvature of the 3D full-field experimental shape, where locations with high curvature are associated with high sensitivity. The assumption is initially researched with the Euler–Bernoulli beam elements and second-order tetrahedrons. The proposed method is investigated on numerical and real experiments, where successful updating was confirmed. With the proposed parametrization and updating approach, a geometrically complex structure is parametrized and the parameters updated without significant user input, generalizing the model-updating procedure.

Innovative Timoshenko soil-pile integrated element for lager diameter laterally-loaded piles considering soil-pile interactions

The large diameter piles (LDP) are designed to provide strong bearing capacity, which should be carefully analysed to ensure the superstructures’ reliability. The conventional discrete spring element (DSE) method with the Euler-Bernoulli beam element is inappropriate for LDPs as the pile’s shear deformations may be considerable. Besides, the nonlinear soil-pile interactions (SPI) cannot be conveniently simulated with the DSE method. To accurately and effectively evaluate the lateral performance of LDP under extreme load, this paper develops an innovative soil-pile integrated element based on the Timoshenko beam theory. The Green-Lagrange strain is used to formulate the potential energy function with the SPI considered. The Gauss integration method is adopted to simplify the element formulation and evaluate the SPI within the element end nodes. The secant and tangent matrixes are derived for calculating the element deformations and internal forces. The transformation matrix describing the nodal parameters’ relation between element local and global coordinate is presented for practical numerical analysis. The soil-pile integrated element avoids using discrete soil spring elements, significantly reducing the modelling and computing efforts. The verification examples demonstrate that the proposed soil-pile integrated element has high accuracy and efficiency in geometrically nonlinear analysis.

On the Aeroelasticity of the Active Span and Passive Pitching Polymorphing Wing: A Parametric Study

This paper presents an aeroelastic analysis of a polymorphing wing capable of active span extension and passive pitch variation. The wing is split into two segments: an inboard segment responsible for span extension/retraction and an outboard segment capable of pitch variation. The two segments are connected through an overlapping spar and a torsional spring. A finite element aeroelastic model is developed where the wing structure is discretized into Euler–Bernoulli beam elements and the aerodynamic loads are calculated using Theodorsen’s unsteady model. A comprehensive parametric analysis is carried out with and without span extension to analyze the effect of varying critical design parameters, such as elastic axis position of outboard section and torsional spring rigidity, and conditions for aeroelastic phenomena of flutter and divergence are studied. A gust load analysis is carried out to quantify the capability of the outboard wing passive twist mechanism to alleviate loads. Finally, a nonlinear analysis is carried out by replacing the linear torsional spring with a nonlinear cubic spring to study the effects of cubic hardening and softening on the aeroelasticity of the polymorphing wing.

In-plane pipe whip: Post-failure dynamic response

Pressurised pipes are ubiquitous in chemical, nuclear and power plants. A sudden failure and release of high-speed fluid cause large inelastic displacements characterised by a whipping-type motion, which can ultimately hinder the surrounding structural and functional systems. In this paper, a beam user element has been developed, implemented and applied to analyse the in-plane flexural dynamic response of pipe whip. The two-dimensional Euler–Bernoulli beam element is based on the corotational kinematic formulation and elastoplastic constitutive models that include metal plasticity and moment–curvature relationships obtained from numerical bending tests, which highlighted the existence of two new dimensionless groups that govern the flexural response of slender pipes and enable the creation of moment–curvature master curves for thick and thin pipes. The corotational beam element formulation is compared against an analytical rigid-perfectly plastic model, numerical simulations employing shell elements and available experimental results, showing very good accuracy in the prediction of the inelastic deformation response of pipe whip and its hazardous area of influence. Furthermore, parametric studies are performed to investigate the effect of load intensity, cross-sectional geometry and concentrated tip mass on the post-failure deformation modes, plastic hinge formation and extension of the hazard zone. The presented results represent valid tools to assess the safety of industrial piping systems undergoing failure, and to optimally design pipe whip restraints.