Vector Form Intrinsic Finite Element 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.

Refined VFIFE modeling on dynamic behaviours of deepwater S-lay pipeline in overbend section

The deepwater S-lay pipeline maintains high tension, bending moment, and stress in the overbend section, exhibiting substantially dynamic responses due to pipe-stinger roller interactions. This paper presents a refined S-lay pipeline model capable of accurately describing the forces and deformations on the pipeline section. In this model, the pipeline is discretized into beam particles and beam elements using the vector form intrinsic finite element (VFIFE) method. Meanwhile, the equivalent beam particle technique is developed to account for both the local forces and deformations of the pipeline as well as its overall static and dynamic responses. Through program coding, a dynamic time-domain simulation was accomplished for a 12-inch pipeline being laid to a water depth of 1000 m to provide a detailed illustration of the S-lay modeling process. Furthermore, dynamic behaviours of the pipeline in the overbend were systematically investigated under various groups of the pipe diameter and the stinger roller spacing. The results indicate that the stress and deformation on the upper section of the pipeline are more significant than those on the lower section. The equivalent beam particle method extends the capabilities of the VFIFE for the detailed analyses of local dynamic behaviours of deepwater S-lay pipelines.

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.

Buckling collapse of submarine thick-wall pipe under torque and hydraulic pressure based on vector form intrinsic finite element method

Torsion is a prevalent form of stress on pipe. This paper employs experimental and numerical methods to investigate the buckling behavior of thick-walled pipe under combined torsion and external pressure. Firstly, the beam-shell coupling method based on the vector form intrinsic finite element method is utilized to establish a model for torsion and external pressure in thick-walled pipe. The accuracy of the model is verified by the collapsible test of the scaled pipe. On this basis, the influence of different torsion angles on the failure mode and the failure mechanism of bending pipe under dynamic and quasi-static conditions are compared and analyzed. It is found that under different loading conditions, the buckling propagation mode of the downstream pipeline changes greatly. This phenomenon is mainly caused by the action of torque on the elbow. Finally, the effect of different torsion angles on the collapse pressure of the bend is investigated.

Propagation and arrest of collapse failures in a buried offshore pipeline crossing reverse fault areas

Offshore pipelines crossing fault rupture areas suffer the risk of local buckling, which can in turn initiate propagating buckles. This study presents the results of evaluating several series of local collapses, subsequent propagating buckles, temporary buckling arrests, and crossover simulations of a deformed (due to reverse fault displacements) offshore pipeline under external overpressure. A numerical model of a buried pipeline with a single (twin) integral arrestor(s) was developed using a nonlinear vector form intrinsic finite element method. The residual external pressure capacity of a deformed pipeline after reverse fault displacements was assessed. Single integral arrestors at different installation sites and twin integral arrestors of different lengths were tested. Effects of fault dip angles on the propagation and arrest of collapse failures were investigated. The longitudinal and bending deformations caused by reverse fault displacements result in a significant decrease in the external pressure resistance of offshore pipelines. Four weak areas appeared around the bending regions, the size relationship of their collapse pressures determined the sequence of multiple local collapses and directions of the subsequent propagating buckles. Integral arrestors are effective designs with significant arresting efficiency in such scenarios. The flexure curve of the pipeline changed significantly only when an arrestor was installed in the left- or right-bending region. A large fault dip angle leads to both higher first collapse pressures and crossover pressures due to smaller bending deformations. A flipping crossover occurs when a downstream reverse ovality develops, which rotates the collapse direction by 90°. The material efficiency of integral arrestors will decrease with the occurrence of flipping crossovers.

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.

A new source finding and tracking analysis approach for the active reflector of five-hundred-meter aperture spherical telescope

The FAST (Five-hundred-meter Aperture Spherical Telescope) is the world’s largest single-aperture radio telescope. During operation, FAST needs to follow the observed celestial body to adjust displacements, which can be divided into two processes: the source finding and tracking. In this paper, a new numerical method based on Vector Form Intrinsic Finite Element (VFIFE) is proposed to simulate the source finding and tracking process for FAST’s active reflector. The basic principle of static equilibrium and calculation flow of the sourcing and tracking analysis is proposed, and the finite element program is compiled to analyze the displacement process of the reflector cable-net structure. Then, six typical test conditions are selected to simulate the sourcing and tracking displacement process. The obtained final form in the equilibrium state adheres to the target configuration, demonstrating the applicability of the suggested approach and the correctness of calculation findings. In addition, the change in the actuator length and the structural force distribution can be simultaneously derived. These values serve as a vital theoretical foundation for FAST’s practical operation and regulation.

Three-dimensional trenches induced by lateral riser-soil interaction and their influence on the behavior of SCR

Although the lateral oscillation of steel catenary risers (SCRs) contributes to trench production, traditional riser-seabed models cannot simulate the process. This study proposes a modified lateral riser-seabed interaction model and integrates it into the SCR model based on the vector form intrinsic finite element (VFIFE) method to simulate the trench formation process. The effects of the loading history, extra soil berm resistance, and cyclic vertical riser-soil interactions were included in the soil model. A 3D trench could be developed under the cyclic out-of-plane movement of the SCR. The trench formation process, seabed resistance distribution, axial tension, bending moment, and stress range distribution of the SCR were discussed in detail to illustrate the effects of the soil model. Different loading amplitudes and nonlinear soil parameters were chosen to determine their influence on the trench shape and distribution of the horizontal seabed resistance. The developed trenches were then inserted into the fresh SCR model before executing the dynamic analysis, in which only the cyclic heave motion was applied to the hang-off point. The simulation results showed that the trenches produced by cyclic sway motions beneficially influenced the fatigue life of the SCR. However, the effect would differ with the profiles.

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.

An improved numerical model for locomotive tensegrity systems based on vector form intrinsic finite element

Locomotive robot based on tensegrity has recently drawn much attention due to its lightweight and flexibility. This article presents an improved numerical model for locomotive tensegrities. The previously used bar element for struts is replaced by beam element, and rigid joint element is used to consider more details of the tendon–strut connections. The vector form intrinsic finite element (VFIFE) method is adopted to formulate the numerical model and carry out the simulation. The improvement of the proposed model on the prediction of feasible rolling gaits is quantitatively verified by experiments on a six-strut locomotive tensegrity. Mann–Whitney U test is adopted, and the p value between the experimental success rates of the gait primitives generated by the improved model and the rates of the gait primitives generated by the previous model is [Formula: see text]. It is shown that the improved model is more consistent with the experiment by considering the details of the tendon–strut connection.

Nonlinear two-dimensional analysis of manifold marine inflated membrane structures using vector form intrinsic finite element method

This study aims to investigate the two-dimensional nonlinear deformation of manifold marine inflatable membrane structures. The vector form intrinsic finite element method is adopted and the pseudo-dynamic stiffness damping is introduced to better get a steady-state solution for quasi-static problems. Three typical marine membrane structures, including the partially submerged pontoon, water-filled dam and finger-bag skirt of a hovercraft, are simulated with rod elements, the spatial varied fluid loads and interaction with deformed structures are considered via user-defined functions. Satisfactory deformation results can be obtained with a simplified two-dimensional profile model. Furthermore, a preliminary analysis of the effects of internal and external pressure on the dam is performed, more accurate hovercraft skirt tension can be obtained than traditional analytical method and the hazardous tuck-under behavior of the skirt is simulated. The models and simulations using vector form intrinsic finite element method are beneficial for understanding the deformation behavior and providing a reference for the design of marine membrane structures.

Deformation analysis of buried subsea pipeline under different pressure-reverse​ fault displacement loading paths

The combined action of subsea seismic faults and pressure loads can cause pipelines to reach the limit state. Consequently, various failure modes, such as global buckling and system collapse, can occur. In this study, the deformation of a buried subsea pipeline under different pressure-reverse fault displacement loading paths is investigated using the nonlinear vector form intrinsic finite element (VFIFE). To quantify the damage to the pipeline and identify its failure modes under accidental reverse fault displacement, the loading path ‘fault displacement → internal/external pressure’ was analysed first. The post-earthquake resumption and reconditioning of unpressurised and pressurised pipelines, respectively, are evaluated based on the performance criteria in terms of strain and deformation. The corresponding loading paths are simplified as ‘ambient hydrostatic pressure → fault displacement → operation pressure’ and ‘operation pressure → fault displacement → external over pressure’. Moreover, the residual bearing capacity, weak position, and possible failure behaviour of the pipeline are comprehensively analysed for all subsequent external overpressures. The results show that the loading paths have a significant effect on structural responses, particularly on the elasto-plastic deformation. The two yield bends of a deformed pipeline under fault displacement are dangerous regions. Their inadequate relative residual strength leads to several successive local collapses and determines the occurrence and direction of buckling propagation during the subsequent external overpressure. The previous internal pressure has a significant influence on the residual capacity and failure modes of the pipeline, particularly the strain hardening effects with the influence of large seismic faults. The critical points of the first local collapse have specific characteristics, and the minimum residual resistance to external over pressure occurs when the maximum flattening parameter is 15% under initial fault displacement. The results of this study can guide the development of seismic design methodologies and engineering practice for buried subsea pipelines.

Thermal structure and hydrodynamic analysis for a new type of flexible temperature-control curtain

Stratified water temperature and low temperature outflow water caused by water storage characteristics in deep reservoirs are common practical problems. The temperature-control curtain (TCC) is a novel low-temperature water treatment technique, characterized by a simple structure and low cost. In the present paper, a new type of flexible TCC scheme is proposed. Moreover, its applicability in engineering is explored by analyzing the thermal structure and hydrodynamic characteristics of the TCC. The general notions and theoretical basis of Boussinesq approximation for thermal flow are first elaborated. Then, the three-dimensional TCC form is obtained through the structural nonlinear analysis method based on Vector Form Intrinsic Finite Element (VFIFE). In addition, using a reservoir which is under TCC construction in southwest China as the research object, the thermal structure change with and without TCC scenario is observed to evaluate the improvement effect of outflow temperature from April to June. Lastly, taking the flood situation from July to August as the most unfavorable condition, the hydrodynamic characteristics are investigated, including the static and the dynamic pressures applied on the curtain. These preliminary modeling works provide important theoretical references for further engineering operation.

Modeling and dynamic analysis of integral vertical transport system for deep-sea mining in three-dimensional space

This paper proposed a new three-dimensional numerical model of the integral vertical transport system (VTS) in deep-sea mining using the vector form intrinsic finite element (VFIFE) method. The method shows great advantages in solving complex dynamic behavior problems of VTS with large differences in mechanical properties and strong geometric nonlinearity. The governing equations are established according to Newton's second law and solved in the time domain by the central difference method. The simulation program for predicting the nonlinear dynamic behavior of VTS is developed with MATLAB and verified with the results of relevant literature. Then, a parameter sensitivity analysis is conducted to investigate the influences of the amplitude and period of the top vessel motion, current velocity, internal flow velocity and buffer mass on the VTS dynamic characteristics. The results show that the heave motions of the vessel are the most adverse motion state to the rigid pipe stress. The influence of the internal flow velocity on the system tension is significantly greater than the bending moment. The rigid pipe, which exhibits a higher sensitivity to each parameter than the flexible pipe, is the weakest area that needs more attention in the design.

Experimental Study of the Dynamic Performance of Steel Catenary Riser within the Touchdown Zone

This study proposed a novel experimental platform to conduct dynamic loading tests of a truncated model steel catenary riser (SCR) within the touchdown zone (TDZ). The facilities of the platform, including a soil tank, a loading system, and a soil stirring system, were introduced in detail. The parameters of the test were determined through the simulation of an in situ riser. A steel pipe was adopted as the model riser, with its outer diameter equaling that of the prototype SCR. Before executing the dynamic loadings, the model riser developed its static configuration under the submerged weight and applied bending moment. Subsequently, cyclic vertical and lateral displacement loads were applied to the truncated point. The test results showed that when the vertical loading amplitude increased from 200 mm to 300 mm, the stress ranges at the front of the model riser increased by more than 100%, whereas the stress range only differed by less than 5% under different loading periods. Numerical models of the SCR were built based on the vector form intrinsic finite element (VFIFE) method. High similarities between the test and simulation results proved the reliability of the nonlinear soil model and the numerical model. During the test, a seabed trench was developed with a depth of 0.71 D and a width of 0.48 D, and its shape was similar to the in situ trench.

Approach on Centroid Angle–Based Reverse Motion for Hexahedral Mesh of Vector Form Intrinsic Finite Element

Approach on Centroid Angle–Based Reverse Motion for Hexahedral Mesh of Vector Form Intrinsic Finite Element

Influence of the internal solitary waves on the deep sea mining system

The South China Sea is rich in mineral resources, and the prospect of developing seabed mineral resources in the South China Sea is bright. However, the South China Sea is also famous for the active internal solitary waves, the researchers detected an internal solitary waves with an amplitude of 240 m and a peak velocity of 2.55 m/s in this area, which may severely impact the deep sea mining system. In this paper, we first simplify the vector finite element method's calculation process. Then the improved vector form intrinsic finite element method is used to simulate the installation process and normal working state of the deep sea mining systems under the action of internal solitary waves. The influence of the internal solitary waves on the deep sea mining systems in the installed state is limited, and its displacement and internal force changes are controllable. Still, the internal solitary waves may cause extensive movement or 180° bends in deep sea mining systems during installation. Necessary measures must be taken during installing deep sea mining systems to reduce the effects of internal solitary waves.

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.

Seismic and failure behavior simulation for RC shear walls under cyclic loading based on vector form intrinsic finite element

Seismic performance and failure mode simulations for reinforced concrete (RC) structures are impeded by large deformations and material nonlinearity particularly when subjected to the combined action of compression, bending and shear. Structural deformation and failure analysis based on traditional finite element (FE) often fails for the small–deformation assumption and global equilibrium. Moreover, it remains difficult to obtain convergence results for the existing FE methods by applying general concrete constitutive models for the complicity of anisotropic materials. To simulate the hysteretic performance and the damage development process of the RC shear wall under cyclic loading, the vector form intrinsic finite element (VFIFE) method with independent particles was adopted and combined with the two-directional concrete constitutive model considering the loading and unloading rules to perform large deformation and damage estimations. Concrete planar triangular element and fiber element for steel bar equipped with the hysteretic constitutive models were used to model six RC shear walls with different design parameters. Owing to the merits of avoiding repeated accumulation of the global stiffness matrix for vector mechanics, the planar structural behaviors involving biaxial stress–strain and loading–unloading behavior were numerically demonstrated. The simulated results were in close agreement with the experimental tests, including the hysteretic loop, skeleton curve, bending–shear deformation, and damage mode. This research also provides successive evidence for damage process simulation by VFIFE for RC structures under seismic loading considering a comprehensive constitutive relation.