Vector Form Intrinsic Finite Element Method Research Articles

Vector form intrinsic finite element analysis for nonlinear parametric resonances of planar beam structures

The parametric resonance of a beam structure may lead to a disastrous consequence. To assess the safety of a structure, structural engineers need a straightforward and practical method to calculate the large-amplitude nonlinear parametric resonance responses of the beam structure. This paper proposes a newly developed vector form intrinsic finite element (VFIFE) calculation scheme to analyse the nonlinear parametric resonance of planar beam structures. By taking into account the geometric stiffness effect of the internal axial force for the frame element, a new relationship between internal nodal forces and deformation components is first established based on the VFIFE principle and the parametric resonance mechanism of frame structures. A numerical example of a portal frame is presented to demonstrate the efficacy of this new calculation scheme. A parametric resonance test of the cantilever beam is conducted to verify the applicability of the VFIFE method. The numerical results show that the proposed scheme can well simulate the nonlinear phenomena of parametric resonances. The numerical predictions are consistent with the experimental observations. A filtering-based finite-time Lyapunov exponent approach is presented to determine the stability boundary of the structure. The numerical stability boundary of parametric resonance agrees well with the experimental boundary. Possible causes of deviations between the numerical and experimental results are discussed. The proposed VFIFE scheme is a simple and effective means of analysing the stability and nonlinear responses of the parametric resonance of planar beam structures.

An efficient partitioned framework to couple Arbitrary Lagrangian-Eulerian and meshless vector form intrinsic finite element methods for fluid-structure interaction problems with deformable structures

The Vector Form Intrinsic Finite Element (VFIFE) is an advanced meshless Lagrangian structural solver. This study introduces a partitioned framework to integrate Arbitrary Lagrangian-Eulerian and VFIFE methods into fluid-structure interaction (FSI) problems featured by large structural displacements and deformations. The VFIFE method enables the FSI simulations with deformable structures due to the nature of Lagrangian particles, which is challenging for traditional computational fluid mechanics techniques. In addition, the VFIFE can be effectively equipped with the partitioned coupling schemes because of the versatility of governing equations. In this algorithm system, several matrix problems in finite element methods and mapping and interpolation in the fluid-structure interface can be avoided. The significant potential of this algorithm in tackling complex FSI problems is demonstrated through various benchmarks, encompassing scenarios like Taylor-Green vortex, flow over a rigid cylinder (Re = 40 ∼ 200), forced vibration of a rigid cylinder, vortex-induced vibration (VIV) of an elastically mounted cylinder, and VIV of a rigid cylinder with an attached flexible cantilever beam. Finally, an experiment on flow past a curtain in a water tank is conducted to further evaluate the precision and stability of the current coupling strategy in three dimensions, demonstrating the feasibility of such methods in flexible structures.

Probability life calculation model of beam element application and study in welded structures reliability analysis

Statistical size and geometrical size are the main factors affecting the service life of mechanical structure calculation. To explore the reliability of the lifespan of beam structures, a probability lifespan numerical calculation method based on Vector Form Intrinsic Finite Element Method (VFIFEM) was proposed, and the method was verified through full lifespan experiments on I-beam welded structures. First, a fatigue fracture model that considers the coupling of residual stress (RS) and cyclic load variations was established. Based on this fatigue fracture model, a probability lifespan calculation model for beam elements was defined by proposing a cross-sectional shape correction coefficient and a position correction coefficient. The proposed probability lifespan model for beam elements was used to calculate the I-beam welded structure, and the calculated results were compared with the full lifespan experiment results, which were close in statistical results, with all experimental results falling within the [10%, 90%] interval except for one experiment. This method effectively couples the influence of statistical size and geometric size on probability lifespan, providing a new approach for the structure probability lifespan calculation in the future.

Buckling Analysis of Thin-Walled Circular Shells under Local Axial Compression using Vector Form Intrinsic Finite Element Method

The buckling failure of thin-walled circular shells under local axial compression is common in engineering. This study uses the vector form intrinsic finite element (VFIFE) method to investigate the buckling behavior of thin-walled circular shells under local axial compression by introducing a multilinear hardening model, taking into account geometric and material nonlinearity. A buckling analysis program based on the VFIFE method was developed and verified by comparison with experimental results. The buckling mode and postbuckling behavior of thin-walled circular shells were studied by using the verified program. The results show that the VFIFE method with a multilinear hardening model can accurately calculate the buckling load of local axially compressed thin-walled circular shells, and effectively simulate the buckling development process, which offers great advantages in predicting the postbuckling of structures.

On the buckling crossover of thick-walled pipe bend under external pressure

Pipe bend is a common junction in pipeline system. In this study, the post-buckling behavior of deep-sea thick-walled pipe bend under external pressure is studied by numerical simulation. A 4-node tetrahedron solid element based on vector form intrinsic finite element method (VFIFE) is introduced to simulate the whole buckling process. First, the VFIFE models of the thick-walled pipes are built and the results of the VFIFE method, traditional finite element method, and the experiments from other publications are compared to verify the proposed method. Then, collapse modes and collapse mechanism of the pipe bend when buckling propagates to the elbow under dynamic and quasi-static conditions are analyzed. Finally, the influence of different geometric parameters on the crossover pressure of the pipe bend is studied. These results can be used to support the buckling arrest design of pipe bends.

The V-MVLE model for cyclic failure behavior simulation of planar RC members

As a widely used planar structural component, the reinforced concrete (RC) shear wall in service is usually subjected to axial, bending and shear loading, possessing high dissymmetry damage mechanics of concrete and failure mode of steel bars. To obtain a satisfactory level of simulation accuracy for the cyclic failure behavior of RC shear walls, progresses were made both in microscopic and macroscopic modeling method. In this study, a hybrid planar model based on vector form intrinsic finite element (VFIFE) and macroscopic multi-vertical line element (MVLE) was proposed, which combined the merits of detailed response of the microscopic model and high calculation efficiency of the macroscopic model. Owing to particle-based formulation along the path element, no assembling of a global stiffness matrix was required by the VFIFE method, which attributed the advantages in large deformation and reinforcement fracture behavior analysis for the proposed model during cyclic failure phase. Via the proposed hybrid model of MVLE, the RC shear walls with various parameters, involving axial compression ratios and height–weight​ ratios, were simulated to allow comparison between the experimental and analytical results in reversed cyclic tests, which demonstrated good agreement and satisfied calculation efficiency.

A novel framework for modeling floating offshore wind turbines based on the vector form intrinsic finite element (VFIFE) method

Currently, there is a rapid demand for the development of floating offshore wind turbines (FOWTs) for deployment in sites with deep water depths. FOWTs are highly complex structures that are subjected to combined loading from wind, hydrodynamic, hydrostatic, and mooring loads, and these loads have a significant influence on their dynamic behavior. The complexity of such a multi-body system makes the dynamic analysis considerably challenging and demands an efficient model to capture the physical characteristics of the system accurately. This paper proposes a novel framework for modeling floating offshore wind turbines (FOWTs) based on the vector form intrinsic finite element (VFIFE) method. In this framework, the multi-body dynamics (MBD) is used to handle the rigid body motion, and the analysis of structural deformation and the solution of governing equation of motions (EOMs) is implemented based on the VFIFE method. The methodology considers the FOWT as two rigid bodies: (a) the tower, which is a structural assembly of platform and nacelle; and (b) the rotor that can mechanically rotate relative to the nacelle. Further, a dynamic and flexible model of the mooring system is included, and their axial extension, inertia, and hydrodynamic loads are considered. The EOMs of the FOWT and mooring system are derived by the Newton-Euler (NE) and Newton's second law, respectively and the central difference scheme is implemented to solve the EOMs. Finally, the developed model is subjected to different load cases under the combined action of wind and waves, and the responses of platform motion and the axial tension of the mooring system are calculated and verified against the FAST. After thorough verification of the VFIFE model which showed excellent agreement with FAST results, the proposed model is used (a) to highlight the variations caused by neglecting the dynamic of the mooring system where the results are compared with the quasi-static mooring model developed using the MAP++ module in FAST, and (b) reveal the coupled mechanism of the platform pitch and yaw motion when the rotor is spinning.

Motion modeling of cable-driven continuum robots using vector form intrinsic finite element method

ABSTRACT This paper presents the motion modeling of a cable-driven, single backbone continuum robot via the vector form intrinsic finite element (VFIFE) method. The VFIFE method is a solution framework based on vector mechanics. The algorithm describes a continuous body by using a finite number of particles instead of a mathematical function. We first approached the model by defining path elements and allocating particles (mass nodes) for the structure. We then established constitutive conditions as the generalized forces derived from both the external environment and internal deformed structural elements. We found that the dynamic equation of particles can be governed by Newton’s law of motion and solved by a general explicit time integration technique. Furthermore, we performed static modeling of the system by employing a dynamic relaxation algorithm with kinetic damping in the dynamic equations. Finally, from experiments, we validated the simulated static model of a single backbone continuum robot. It is shown that this method is capable of describing a continuum robot’s motion by solving for frame structures that undergo large deformation.

Development of a numerical mooring line model for a floating wind turbine based on the vector form intrinsic finite element method

The utilization of renewable energy has great significance to reduce CO2 emissions. Floating offshore wind turbines (FOWTs) is regarded as most cost-effective solution to harness the offshore renewable energy in deep-water. Fully coupled analysis is regarded as the state-of-art simulation method for FOWT's design and analysis. Until now, various methods (lumped mass model, quasi-static model, finite element model et al.) are used in mooring line modelling in the fully coupled simulation for FOWTs. In this paper, a new dynamic model for catenary mooring line is proposed based on the vector form intrinsic finite element (VFIFE) method. This method is designed to calculate motions of a system, which the motion may include large rigid body motions and large geometrical changes, or very large deformations. The inertia and hydrodynamic and the seabed interaction are contained in this model. Newton's law of particle is assumed to derive the governing equations of motion. An explicit algorithm is used to calculate the numerical results. The feasible and accurate of the dynamic model are verified by comparing with the experimental data and other validated codes. In the comparisons the results of VFIFE method has a good agreement with the references. Thus, the dynamic model proposed in this paper is capable for the dynamic analysis of mooring lines. Furthermore, the influence of the forced motion frequency (and amplitude) of mooring system on the hysteresis loop area is studied, which reveals the mechanism of the energy dissipation from the viscous damping of fluid and the gravitational potential energy of the line.

High-Speed Spiral Bevel GEAR Dynamic Rules Considering the Impact of Web Thicknesses and Angles

Gear transmission system dynamic responses under high-speed and heavy-duty working conditions were obviously affected by support structures, especially in lightweight design. However, web thicknesses and angles were usually ignored in dynamic modeling process. Therefore, a full mesh model with web structure was built and its dynamic characteristics were analyzed by a modified vector form intrinsic finite element (VFIFE), which is proposed to solve high-speed dynamic problems with good efficiency. For spiral bevel gear pair dynamic characteristics, the impacts of web thicknesses and angles were simulated and discussed. Simulation results showed that web support angles will affect gear meshing performance and dynamic characteristics more remarkable than web thickness did. In addition, the good performance of the proposed modified VFIFE method was proved, which showed good computing efficiency.

A modified damping model of vector form intrinsic finite element method for high-speed spiral bevel gear dynamic characteristics analysis

The vector form intrinsic finite element (VFIFE) method is springing up as a new numerical method in strong non-linear structural analysis for its good convergence, but has been constricted in static or transient analysis. To overwhelm its disadvantages, a new damping model was proposed: the value of damping force is proportional to relative velocity instead of absolute velocity, which could avoid inaccuracy in high-speed dynamic analysis. The accuracy and efficiency of the proposed method proved under low speed; dynamic characteristics and vibration rules have been verified under high speed. Simulation results showed that the modified VFIFE method could obtain numerical solutions with good efficiency and accuracy. Based on this modified method, high-speed vibration rules of spiral bevel gear pair under different loads have been concluded. The proposed method also provides a new way to solve high-speed rotor system dynamic problems.

Buckling analysis of subsea pipeline with integral buckle arrestor using vector form intrinsic finite thin shell element

Buckling damage is one of the biggest safety issues for subsea pipelines. Buckling behaviors of the subsea pipeline with integral buckle arrestors under external pressure are studied experimentally and numerically herein. Pressure chamber tests of four full-sized pipeline with identical thickness and different diameters are presented. An emerging vector form intrinsic finite element method (VFIFE) is introduced to simulate the whole buckling process both in dynamic and quasi-static cases, including local collapse, propagation, buckling prevention, and crossover. Numerical schemes for multifold nonlinearities and multithreaded computation are proposed and tested. Results of experiments and numerical simulations, as well as computations of the traditional finite element method and DNV specifications, are compared. Thusly it is indicated that the VFIFE model can accurately (within ± 1.5%) predict the buckling loads that initiate local collapse, propagation and crossover, and simulate the dynamic and quasi-static buckling modes for pipelines with practical range of diameter-to-thickness ratios greater than 20. For thick parts where integral arrestor with diameter-to-thickness ratios smaller than 20 located, the VFIFE thin shell element may underestimate the structural strength about 8.0%. The VFIFE can directly simulate the pipeline buckling behavior without special processing for the iterative calculation and the stiffness matrix convergence, and achieve the parallel efficiency over 90% for a common computer (12 threads, 4G RAM). Thus, the VFIFE can provide a new, practical and universal analytic strategy for subsea pipeline buckling analysis.

BUCKLING ANALYSIS OF DEEPWATER PIPELINES BY VECTOR FORM INTRINSIC FINITE ELEMENT METHOD

Local buckling damage is one of the biggest safety issues during the operation of deepwater pipelines. The innovative vector form intrinsic finite element method (VFIFE) is used to analyze the buckling behavior of deepwater pipelines. After deriving the calculation formula of VFIFE space shell elements considering the nonlinear elastoplastic material, we developed a Fortran calculation program and a MATLAB post-processing program to simulate the collapse and buckling propagation process. The collapse pressure and the buckling propagation pressure were calculated. A full-scale pressure chamber test was conducted to analyze the buckling load and buckling morphology. The VFIFE results were compared with those of the test, traditional finite element method (FEM) and DNV method. The VEIFE can directly simulate the pipeline collapse, the buckling propagation, the collapse pressure, and the buckling propagation pressure. The VFIFE results are in line with the actual situation and in good agreement with those of the other methods. The VFIFE has the advantages of not requiring special calculation processing and tracking of the entire behavior, thus providing a new and universal analytic strategy for buckling simulation of deepwater pipelines.

A full three-dimensional vortex-induced vibration prediction model for top-tensioned risers based on vector form intrinsic finite element method

A novel three-dimensional model is proposed to study vortex-induced vibration (VIV) problems of top-tensioned risers. The model is based on the vector form intrinsic finite element (VFIFE) method and applicable to the fully-coupled cross-flow and in-line riser VIV scenarios. The axial time-varying dynamics and movement at the top end boundary of risers are also considered in the model. By using the VFIFE method, the structure is reduced to a set of particles whose motion satisfies Newton's second law and its response is described by the position change of particles in space. The fluctuating fluid force acting on the structure induced by vortex shedding is simulated using the classical van der Pol wake oscillator equation. In order to intuitively describe the time-varying top tension of the real structure, the real-time changes in top tension caused by the array of tensioners simulated by spring is also considered. The results of numerical simulation on top tension, dominant mode numbers, frequencies, and amplitudes are compared with the experiment to prove that the VFIFE method is feasible and effective in predicting the three-dimensional vortex-induced vibration response.

Vector form intrinsic finite-element analysis of static and dynamic behavior of deep-sea flexible pipe

The aim of this study was to develop a new efficient strategy that uses the Vector form Intrinsic Finite-element (VFIFE) method to conduct the static and dynamic analyses of marine pipes. Nonlinear problems, such as large displacement, small strain, and contact and collision, can be analyzed using a unified calculation process in the VFIFE method according to the fundamental theories of point value description, path element, and reverse motion. This method enables analysis without the need to integrate the stiffness matrix of the structure, because only motion equations of particles established according to Newton's second law are required. These characteristics of the VFIFE facilitate the modeling and computation efficiencies in analyzing the nonlinear dynamic problem of flexible pipe with large deflections. In this study, a three-dimensional (3-D) dynamical model based on 3-D beam element was established according to the VFIFE method. The deep-sea flexible pipe was described by a set of spatial mass particles linked by 3-D beam element. The motion and configuration of the pipe are determined by these spatial particles. Based on this model, a simulation procedure to predict the 3-D dynamical behavior of flexible pipe was developed and verified. It was found that the spatial configuration and static internal force of the mining pipe can be obtained by calculating the stationary state of pipe motion. Using this simulation procedure, an analysis was conducted on the static and dynamic behaviors of the flexible mining pipe based on a 1000-m sea trial system. The results of the analysis proved that the VFIFE method can be efficiently applied to the static and dynamic analyses of marine pipes.

Vector Form Intrinsic Finite Element Method for Analysis of Train–Bridge Interaction Problems Considering The Coach-Coupler Effect

In this paper, the vector form intrinsic finite element (VFIFE) method is presented for analysis the train–bridge systems considering the coach-coupler effect. The bridge is discretized into a group of mass particles linked by massless beam elements and the multi-body coach with suspension systems is simulated as a set of mass particles connected by parallel spring-dashpot units. Then the equation of motion of each mass particle is solved individually and the internal forces induced by pure deformations in the massless beam elements are calculated by a fictitious reverse motion method, in which the structural stiffness matrices need not be updated or factorized. Though the vector-form equations resulting from the VFIFE method cannot be used to compute the structural frequencies by the eigenvalue approach, this study proposes a numerical free vibration test to identify the bridge frequencies for evaluating the bridge damping. Numerical verifications demonstrate that the present VFIFE method performs as accurately as previous numerical ones. The results show that the couplers play an energy-dissipating role in reducing the car bodies’ response due to the bridge-induced resonance, but not in their response due to the train-induced resonance because of the bridge’s intense vibration. Meanwhile, a dual-resonance phenomenon in the train–bridge system occurs when the coach-coupler effect is considered in the vehicle model.

Vector form intrinsic finite element method for nonlinear analysis of three-dimensional marine risers

Marine risers are dynamic sensitive systems and robust numerical models that describe their complex behavior are needed. The vector form intrinsic finite element (VFIFE) method is adopted to analyze the nonlinear behavior of marine risers with large deformations in three dimensional space. The method is based on vector mechanics theory and numerical calculation. The structural behavior is described by a simple physical model and strong-formed particle governing equations of motion. Three kinds of marine risers are presented to demonstrate the performance of VFIFE on analyzing marine risers under complex conditions. Hydrostatic and hydrodynamic loadings due to internal and external fluid acting on each element are considered. The modeling process is introduced in detail and the results are compared with the published literature. It is proved that the application of the VFIFE method in the nonlinear analysis of the three-dimensional marine risers is feasible and simply verified that loads outside of the plane have a more obvious impact on the risers, it is necessary to conduct three-dimensional analysis.

Vector form Intrinsic Finite Element Method for the Two-Dimensional Analysis of Marine Risers with Large Deformations

Robust numerical models that describe the complex behaviors of risers are needed because these constitute dynamically sensitive systems. This paper presents a simple and efficient algorithm for the nonlinear static and dynamic analyses of marine risers. The proposed approach uses the vector form intrinsic finite element (VFIFE) method, which is based on vector mechanics theory and numerical calculation. In this method, the risers are described by a set of particles directly governed by Newton’s second law and are connected by weightless elements that can only resist internal forces. The method does not require the integration of the stiffness matrix, nor does it need iterations to solve the governing equations. Due to these advantages, the method can easily increase or decrease the element and change the boundary conditions, thus representing an innovative concept of solving nonlinear behaviors, such as large deformation and large displacement. To prove the feasibility of the VFIFE method in the analysis of the risers, rigid and flexible risers belonging to two different categories of marine risers, which usually have differences in modeling and solving methods, are employed in the present study. In the analysis, the plane beam element is adopted in the simulation of interaction forces between the particles and the axial force, shear force, and bending moment are also considered. The results are compared with the conventional finite element method (FEM) and those reported in the related literature. The findings revealed that both the rigid and flexible risers could be modeled in a similar unified analysis model and that the VFIFE method is feasible for solving problems related to the complex behaviors of marine risers.

Static contact analysis of spiral bevel gear based on modified VFIFE (vector form intrinsic finite element) method

• A new method to determine the theoretical formulas of the 8-node hexahedral entity element for the VFIFE method was developed. • Matching contact algorithms are proposed and combined with the VFIFE method. • Finite element model of a spiral bevel gear pair was established and analyzed by the VFIFE method. • The computational accuracy of the VFIFE models with different mesh densities was discussed and summarized. Since the intrinsic limitations of FEM (Finite element method) and lumped-mass method, we derive the formula of 8-node hexahedral element based on VFIFE (vector form intrinsic finite element method) method and applied it in contact analysis of gears. This paper proposed a new method to determine pure nodal deformation, which could simplify the computation compared to the traditional VFIFE method. Combining the VFIFE method and matching contact algorithm, we analyzed spiral bevel gear meshing problems. Spiral bevel models with two different mesh densities are calculated analyzed by the VFIFE method and FEM. Performance indicators of gears are extracted and compared, including contact forces, contact and bending stresses, contact stress patterns and loaded transmission errors. The results show that the VFIFE method has a stable performance and reliable accuracy under coarse or refined mesh conditions, while the FEM inaccurately calculates the contact stress of the coarse mesh model. The examples demonstrate that the proposed method could precisely analyze gear meshing problems with a coarse mesh model, which provides a new solution for gear mechanics.

Form Follows Force: A theoretical framework for Structural Morphology, and Form-Finding research on shell structures

With the springing up of freeform architectures, the key problem to structural engineers is to generate structural forms with high structural efficiency subject to the architectural space constraints during the conceptual design process. In this research, a theoretical framework for Structural Morphology has been proposed, that provides an effective solution to the problem. To enrich the proposed framework, systematic Form-Finding research on shell structures is conducted.