Form Intrinsic Finite Element Method Research Articles

Influence of seabed trench on the structural behavior of steel catenary riser using the vector form intrinsic finite element method

The oscillation of steel catenary riser (SCR) would develop a trench in a few months, while the trench could affect the structural behavior of the riser in turn. However, the influence of the trenches on the fatigue damage of SCR is still controversial. In this study, the SCR model is established using the vector form intrinsic finite element (VFIFE) method, integrated with the nonlinear seabed model to develop the trenches. Different static platform offset distributions, low frequency (LF) surge motions, and the soil parameter and heave motion amplitude combinations are selected to investigate the influences on the trench formation. Dynamic analyses are performed to determine the effects of the trenches on the mechanical behavior of SCR based on the VFIFE model, with the predefined trenches inputted previously through the switching method and the inserting method. Simulation results prove that the trenches developed only by heave motion or including the LF surge motion have a positive effect in reducing the fatigue damage, while the trenches considering static platform offset have little influence. Furthermore, the effects of shear strength distribution of trench surface, trench depth, and trench position on the dynamic performance of SCR are discussed.

Static behaviours and collision onset criterion of two adjacent vertical risers

ABSTRACT This study aims to investigate the static behaviours of two risers and establish the generalised dual-riser collision onset criterion (COC). The dual-riser model is developed based on the vector form intrinsic finite element method where the Blevins wake model is used to consider the wake effects. The governing equations including a virtual damping force are solved by the central difference method to obtain the static behaviours of risers. Then, the effects of initial spacing, top tension factor and current velocity on the static behaviours of two vertical risers arranged tandem are investigated. Further, the dual-riser COC is established with three non-dimensional parameters by linear-regression analysis. The results show that a larger top tension factor of the upstream riser and a smaller that of the downstream riser is a more effective combination to avoid collisions. The dual-riser COC can be described by a linear function of non-dimensional parameters.

NUMERICAL APPROACH FOR SIMULATING THE TENSIONING PROCESS OF COMPLEX PRESTRESSED CABLE-NET STRUCTURES

The stability of cable-net structures depends on the prestress of the system. Due to the large displacement and mutual effect of the cables, it is difficult to simulate the tensioning process and control the forming accuracy. The Backward Algorithm (BA) has been used to simulate the tensioning process. The traditional BA involves complicated and tedious matrix operations. In this paper, a new numerical method based on the Vector Form Intrinsic Finite Element (VFIFE) method is proposed for BA application. Moreover, the tensioning sequence of a complex cable-net structure is introduced. Subsequently, a new approach for BA application in the simulation of the tensioning process is presented, which combines the VFIFE approach and the notion of form-finding. Finally, a numerical example is simulated in detail and the results of different tensioning stages are analyzed to verify the feasibility of the proposed approach. This study provides a significant reference for improving the construction control and forming accuracy of complex prestressed cable-net structures.

Dynamic analysis of steel catenary riser on the nonlinear seabed using vector form intrinsic finite element method

The dynamics of a steel catenary riser (SCR) are highly nonlinear and strongly affected by the interaction between riser and seabed. Possessing the advantages of robustness and high efficiency, the vector form intrinsic finite element (VFIFE) method is applied to solve this problem. The nonlinear hysteretic riser-seabed interaction is integrated into the model. Simulation results are compared to the commercial software Ocraflex, and high similarities prove the capability of VFIFE to simulate the dynamics of SCR on the nonlinear seabed. In dynamic analysis, a larger mass damping coefficient should be applied in the touchdown zone (TDZ) and flowline part to increase the stabilization. In contrast, the coefficient in the catenary part has only minor influences on the behavior of SCR. To improve the computation efficiency, the effect of using coarse meshes with different densities in the catenary part has been investigated, while the fine meshes are applied in the TDZ and flowline part. In the dynamic analysis of TDZ, the distribution of seabed reaction force and stress range are present and discussed. Furthermore, the effects of different loading parameters and hanging-off positions on the trench profiles and fatigue damage of SCR have been studied in detail.

Vector Form Intrinsic Finite Element Method for Stochastic Analysis of Train–Track–Bridge Coupling System

In this paper, a train–track–bridge (TTB) interaction model that can account for coach-coupler effect is presented for stochastic dynamic analysis of a train traveling over a bridge. Based on the vector form intrinsic finite element (VFIFE) method, both the bridge and non-ballasted track are discretized into a set of mass particles connected by massless beam elements, in which the fasteners that fixed the tracks on the bridge deck are modeled as a series of linear spring-dashpot units. The multi-body train car is regarded as seven mass particles (1 for car body, 2 for bogies and 4 for wheelsets) connected by parallel spring-dashpot units. Considering the random nature of rail irregularities, the Karhunen–Loéve expansion (KLE) method is used to simulate the vertical profile of the tracks. To calculate the mean and standard deviation of the stochastic response of the TTB system, the point estimated method (PEM) based on the Gaussian integration and dimension reduction method is adopted. The proposed VFIFE–TTB interaction model is then applied to stochastic resonance analyses of a train moving on a bridge. It is shown that the present VFIFE–TTB model is able to analyze the dynamic interaction of the TTB system simply and efficiently. The influence of rail irregularity-induced stochastic vibration on the train and bridge would become significant once the resonant vibration takes place on the TTB system.

Development of an adaptive explicit algorithm for static simulation using the vector form intrinsic finite element method

Abstract The vector form intrinsic finite element (VFIFE) method is a solution technique for nonlinear structural problems, which describes a continuous body using a set of particles instead of a mathematical function. Thus, a dynamic particle equation can be established by Newton's law of motion, and a viscous or kinetic damping can be introduced to obtain the steady state of the structure. This paper focuses mainly on the development of a stability condition regarding the explicit central difference method used in VFIFE to guarantee the system's convergence. The process is established and evaluated in combination with a dynamic relaxation method with kinetic damping and discrete control theory. Four numerical examples of structure nonlinear problems are used to verify the accuracy, stability and efficiency of the method.

Buckling failure analysis for buried subsea pipeline under reverse fault displacement

Buckling failure analysis of buried subsea pipeline under reverse fault displacement was investigated by the Vector Form Intrinsic Finite Element method in this paper, considering nonlinear soil–pipeline interaction in slit with sand and the multifold nonlinearities of nonlinear material, large deformation, large displacement and self-collision/contact. Two typical conditions discussed were the operation condition and the empty waiting state during installation, maintenance, and operation. Effects of soil properties, pressure loadings, diameter–thickness ratios and dip angles on local buckling formation, tensile strain and cross-sectional distortion were investigated. The results show that subsea pipelines obtain a large deformation capacity and the flexure curve shape is usually S-shape. The external pressure is more unfavorable than the internal pressure since it aggravates the compression strains but alleviates the tension strains. A small fault dip angle results in serious axial compression and can lead to local collapse in the empty waiting states. For big diameter–thickness ratios or great pressure level, external pressure will cause local collapse and even buckle propagation along the pipeline. Seven different modes of collapse and propagation are discovered in the empty waiting state. They can be classified by the first collapse location, buckle propagation direction and further propagation sustainability. The cross-sectional shapes after collapse and during propagation are mainly determined by the compression or tension state around the circum. These results can be used for the development of performance-based design methodologies for buried subsea pipelines.

Numerical simulation of deepwater S-lay and J-lay pipeline using vector form intrinsic finite element method

S-lay and J-lay systems are progressively utilized for deepwater pipeline installation. The paper presents a simple and feasible model for the static and dynamic analysis of S-lay and J-lay pipelines. This mechanical model of the laying pipeline is established by the combination of the vector mechanics principle with the numerical technique based upon the vector form intrinsic finite element (VFIFE) method. The internal forces resulted from element deformations and node rotations as well as the external forces due to hydrodynamic loads and the boundary interactions are fully taken into account. The movement governing equation of pipeline particles is solved by the explicit central difference approach using program coding. Two numerical models of a 12-inch pipeline being laid to 1000 m water depth are created in order to illustrate in detail the modeling process of S-laying and J-laying pipeline, respectively, and also verify the feasibility of the VFIFE model with a reasonable accuracy for deepwater pipeline installation. The effects of wave height and sloping seabed on the pipeline responses are identified and the noticeable differences of the pipeline behaviors between the S-lay and J-lay operation are observed. The results offer a significant reference for the installation design of the offshore pipeline.

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.

Computational method for the deformation mechanism of non-prestressed cable net structures based on the vector form intrinsic finite element method

An effective computational method for the non-prestressed cable net structure with large deformation problem is proposed in the present study. This computational method is based on the vector form intrinsic finite element (VFIFE) method, which is a novel method to analyze structural behavior. Firstly, we proposed the basic principle and calculation process for analyzing the deformation mechanism of various cable net structures and compiled a finite element analysis program. Then, the numerical examples such as the rod chain mechanism and the space hyperboloid cable net are analyzed in detail. In addition, the accurate tracking of the motion status at different times was realized and the experiment in previous study was also used to verify the calculation results. A space cable net model experiment was designed and performed. The feasibility and correctness of this method were verified by the comparison of the measured deformation and internal force to the numerical results. The computational method proposed in this paper can effectively calculate the whole process of large deformation and internal force distribution of the non-prestressed cable net structure or similar structures, which provides an important method reference for the numerical analysis of such large deformations and strongly nonlinear engineering problems.

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.

Structural behavior of joined hemispherical-cylindrical air-supported membrane structure under vertical loading deflation

The structural behavior of an air-supported structure with long span and large volume probably experiencing severe deflation in a massive snow weather deserves in-depth assessment study for occupant’s safe evacuation. This article presents experimental and numerical studies on the loading deflation process of a 1:10 scale joined hemispherical-cylindrical air-supported structure, whereby three different sandbag loadings were respectively applied on the hemisphere in each test to study the effect of vertical loads to collapse process. Numerical models based on the vector form intrinsic finite element method were employed to predict the deflation responses of the structure under the three loading cases. The structural behavior was evaluated by the pressure response, the wrinkling distribution and development, and the structural collapse mode. A comparison of their pressure responses and structural deflated forms is made to evaluate the contribution of external loading to the deflation progress and the collapse mode. It is found that the pressure will decrease quickly first and then remain relatively stable at a higher level in response to a larger vertical load in addition to the membrane weight. Due to pressure reduction during deflation, the structure loses tension stress in vertical direction so that vertical wrinkles develop in addition to local wrinkles due to external loading. The vertical loading determines distribution of wrinkles in the structure hence produce different collapse progresses for the three loading deflation cases, and accordingly changes the residual pressure it needs to hold its deflated form. Accordingly, the study proposes a feasible method for residual pressure estimation by identifying the distribution of critical residual pressures at different heights from the equilibrium equation of vertical forces. The full-scale structure presents similar structural behaviors when subjected to snow loading deflation, and the feasible method is valid to predict its residual pressure.

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.

Deflation behavior and related safety assessment of an air-supported membrane structure

As a large span structure that might serve many occupants, the deflation behavior of an air-supported membrane structure under emergency deflation is of critical importance for safety assessment on occupants' evacuation but has received few studies. This paper presents experimental field tests and numerical simulations on deflation behaviors of a real-life air-supported membrane structure. A numerical model is employed in deflation simulation which considers tension-only membrane based on the vector form intrinsic finite element method for membrane motion analysis and pressure change due to air loss in deflation according to the classic thermodynamics. The correctness and the applicability of the model are verified by good correlation of prediction in response of pressure, displacement, and wrinkling formation and development of the structure with those measured and observed in deflation tests. The study shows that the structure in emergency deflation will lose its high pressure quickly first, and then sustain deflating under low residual pressure for a long time. The model is further used in parametrical analysis on factors that affect deflation progress and a complete deflation simulation to predict the whole collapse process, which is accordingly characterized by two typical phases, the tender deflation stage and the severe deflation stage. In tender stage the structure holds a relatively plump form, while in the severe stage the structure bears low decreasing residual pressure, membrane losses most tension stress so that many elements wrinkle and the structure experiences instability. Due to wrinkling, the residual pressure is found to approximately balance with its vertical loads. As a result, the feasible method proposed based on the residual pressure in deflation is very simple and reliable to predict the deflation duration and evaluate maximum escape area for deflation assessment of the studied structure.

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-control of shell structures generated from hanging models with target heights

Shell structures generated from hanging models have structurally efficient forms. Form-control of these shells, which aims to obtain structural forms with single- and multiple target heights due to some architectural requirements, is discussed in this article. First, the vector form intrinsic finite element method is applied to generate the equilibrium form of hanging membranes and thus shell structures. Subsequently, the form-control problem is discussed, which aims to generate a structural form subject to given target height constrains. By introducing the Local Linearization Method to adjust Young’s modulus of the initial structural model, a form-control strategy to generate the equilibrium structural form with a single target height is proposed. By introducing the Inverse Iteration Method to adjust the geometry of the initial model, a form-control strategy to generate the equilibrium structural form with several target heights is proposed. Moreover, to verify the effectiveness of the vector form intrinsic finite element method and form-control strategies, structural analyses and shell behavior assessment of these shells are conducted. These strategies are effective and efficient, which can help architects or engineers to determine structurally efficient geometries in the design process much more easily.