Torsional Response Analysis of Flexible Pipe Based on Theory and Finite Element Method

As key components connecting offshore floating production platforms and subsea imports, offshore flexible pipes play significant roles in oil, natural gas, and water injection. It is found that torsional failure is one of the failure modes of flexible pipes during transportation and laying. In this paper, a theoretical model(TM) of a flexible pipe section mechanics is established, in which the carcass layer and the pressure armor layer are equivalent to the orthogonal anisotropic layers due to its complex cross-section structure. The calculation results of the TM are consistent with those of a finite element model(FEM), which can accurately describe the torsional response of the flexible pipe.Subsequently, the TM and FEM are used to discuss the influence of boundary conditions on the torsional response.The structure of the flexible pipe is stable when twisted counterclockwise. However, limiting the top axial displacement can improve the axial and radial instability of the tensile armor layer when twisted clockwise. Finally, it is recommended that the flexible pipe can be kept under top fixation during service or installation to avoid torsional failure.

A New Flexible Multibody Dynamics Analysis Methodology of Deployable Structures with Scissor-Like Elements

There are vast constraint equations in conventional dynamics analysis of deployable structures,which lead to differential-algebraic equations(DAEs)solved hard.To reduce the difficulty of solving and the amount of equations,a new flexible multibody dynamics analysis methodology of deployable structures with scissor-like elements(SLEs)is presented.Firstly,a precise model of a flexible bar of SLE is established by the higher order shear deformable beam element based on the absolute nodal coordinate formulation(ANCF),and the master/slave freedom method is used to obtain the dynamics equations of SLEs without constraint equations.Secondly,according to features of deployable structures,the specification matrix method(SMM)is proposed to eliminate the constraint equations among SLEs in the frame of ANCF.With this method,the inner and the boundary nodal coordinates of element characteristic matrices can be separated simply and efficiently,especially on condition that there are vast nodal coordinates.So the element characteristic matrices can be added end to end circularly.Thus,the dynamic model of deployable structure reduces dimension and can be assembled without any constraint equation.Next,a new iteration procedure for the generalized-a algorithm is presented to solve the ordinary differential equations(ODEs)of deployable structure.Finally,the proposed methodology is used to analyze the flexible multi-body dynamics of a planar linear array deployable structure based on three scissor-like elements.The simulation results show that flexibility has a significant influence on the deployment motion of the deployable structure.The proposed methodology indeed reduce the difficulty of solving and the amount of equations by eliminating redundant degrees of freedom and the constraint equations in scissor-like elements and among scissor-like elements.

Discrete Element with Flexible Connector for Dynamic Analysis of 3-D Beam Structures

Combined multi-body dynamics with structural dynamics, a new discrete element with flexible connector, which is applicable for 3-D beam structures, is developed in this paper. Both the generalized elastic coefficient matrix of the flexible connector and the mass matrix of discrete element may be off-diagonal in a general case. The zero-length rigid element is introduced to simulate the node at which multiple elements are jointed together. It may also be effective when the axes of adjacent elements are not in the same line. The examples for eigenvalue calculation show that the model is successful. It can be extended to the geometric nonlinear response analysis.

Finite Element Simulation of Flexible Roll Forming with Supplemented Material Data and the Experimental Verification

Flexible roll forming is a promising manufacturing method for the production of variable cross section products. Considering the large plastic strain in this forming process which is much larger than that of uniform deformation phase of uniaxial tensile test, the widely adopted method of simulating the forming processes with non-supplemented material data from uniaxial tensile test will certainly lead to large error. To reduce this error, the material data is supplemented based on three constitutive models. Then a finite element model of a six passes flexible roll forming process is established based on the supplemented material data and the original material data from the uniaxial tensile test. The flexible roll forming experiment of a B pillar reinforcing plate is carried out to verify the proposed method. Final cross section shapes of the experimental and the simulated results are compared. It is shown that the simulation calculated with supplemented material data based on Swift model agrees well with the experimental results, while the simulation based on original material data could not predict the actual deformation accurately. The results indicate that this material supplement method is reliable and indispensible, and the simulation model can well reflect the real metal forming process. Detailed analysis of the distribution and history of plastic strain at different positions are performed. A new material data supplement method is proposed to tackle the problem which is ignored in other roll forming simulations, and thus the forming process simulation accuracy can be greatly improved.

Finite Element Method Applied to the Eigenvalue Analysis of Flexible Rotors Supported by Journal Bearings

This work deals with a finite element procedure developed to perform the eigenvalue analysis of damped gyroscopic systems, represented by flexible rotors supported on fluid film journal bearings. The rotor finite element model is based on the Timoshenko beam theory, accounting for the shaft rotary inertia and gyroscopic moments. The governing equations for the hydrodynamic journal bearing are obtained through the Galerkin weighted residual method applied to the classical Reynolds equation. A perturbation scheme on the fluid film governing equation permits to obtain the zero-th and first order lubrication equations for the bearings, which allow the computation of the dynamic force coefficients associated with the bearing stiffness and damping. The rotor-bearing system equation, which consists of a case of damped gyroscopic equation, is rewritten on state form to compute the complex eigenvalues. The natural frequencies at several operating conditions are obtained and compared to the technical literature data. The influence of the effective damping on the eigenvalue real part sign is analyzed for some examples of rotor-bearing systems, showing how the stability conditions can be predicted by the eigenvalue analysis. The procedure implemented in this work can provide useful guidelines and technical data about the selection of the more appropriate set of bearing parameters for rotating machines operating at stringent conditions.

Design and Structural Analysis of Flexible Wearable Chair Using Finite Element Method

The flexible wearable chair is like a light weight mobile exoskeleton that allows people to sit any-where in any working position. The traditional chair is difficult to move to different working locations due to its large size, heavy weight (~5 - 7 kg) and rigid structure and thus, they are inappropriate for workplaces where enough space is not available. Flexible wearable chair has a gross weight of 3 kg as it utilizes light-weight aluminium alloy members. Unlike the traditional chair, it consists of kinematic pairs which enable taking halts between continuous movements at any working position and thus, it is capable of reducing the risk of the physical musculoskeletal disorder substantially among workers. The objective of this paper is to focus on the mechanical design and finite element analysis (FEA) of the mechanism using ANSYS® software. In the present work, all the parts of the mechanism are designed under static load condition. The results of the analysis indicate that flexible wearable chair satisfies equilibrium and stability criterion and is capable of reducing fatigue during working in an assembly line/factory.

DISTRIBUTION OF RANDOM ELEMENTS SUBJECTED TO A FLEXIBLE BOUNDARY CONDITION

The probability distribution function of n random elements subjected to the flexible boundary condition is derived. The probability density is a descending curve and converges to a delta function as n tends to infinity. The distribution of the minimum value is discussed in context of ordered statistics.

Enhanced Multi-Layer Fatigue-Analysis Approach for Unbonded Flexible Risers

This paper proposes an enhanced approach for evaluating the fatigue life of each metallic layer of unbonded flexible risers. Owing to the complex structure of unbonded flexible risers and the nonlinearity of the system, particularly in the critical touchdown zone, the traditional method is insufficient for accurately evaluating the fatigue life of these risers. The main challenge lies in the transposition from global to local analyses, which is a key stage for the fatigue analysis of flexible pipes owing to their complex structure. The new enhanced approach derives a multi-layer stress-decomposition method to meet this challenge. In this study, a numerical model validated experimentally is used to demonstrate the accuracy of the stress-decomposition method. And a numerical case is studied to validate the proposed approach. The results demonstrate that the multi-layer stress-decomposition method is accurate, and the fatigue lives of the metallic layers predicted by the enhanced multi-layer analysis approach are rational. The proposed fatigue-analysis approach provides a practical and reasonable method for predicting fatigue life in the design of unbonded flexible risers.

Dynamic analysis of spatial parallel manipulator with rigid and flexible couplings

The dynamics of spatial parallel manipulator with rigid and flexible links is explored. Firstly, a spatial beam element model for finite element analysis is established. Then, the differential equation of motion of beam element is derived based on finite element method. The kinematic constraints of parallel manipulator with rigid and flexible links are obtained by analyzing the motive parameters of moving platform and the relationships of movements of kinematic chains, and the overall kinetic equation of the parallel mechanism with rigid and flexible links is derived by assembling the differential equations of motion of components. On the basis of abovementioned analyses, the dynamic mechanical analysis of the spatial parallel manipulator with rigid and flexible links is conducted. After obtaining the method for force analysis and expressions for the calculation of dynamic stress of flexible components, the dynamic analysis and simulation of spatial parallel manipulator with rigid and flexible links is performed. The result shows that because of the elastic deformation of flexible components in the parallel mechanism with rigid and flexible links, the force on each component in the mechanism fluctuates sharply, and the change of normal stress at the root of drive components is also remarkable. This study provides references for further studies on the dynamic characteristics of parallel mechanisms with rigid and flexible links and for the optimization of the design of the mechanism.

Design of Flexible Films Based on Kinked Carbon Nanofibers for High Rate and Stable Potassium-Ion Storage

With the emergence of wearable electronics,flexible energy storage materials have been extensively studied in recent years.However,most studies focus on improving the electrochemical properties,ignoring the flexible mechanism and structure design for flexible electrode materials with high rate capacities and long-time stability.In this study,porous,kinked,and entangled network structures are designed for highly flexible fiber films.Based on theoretical analysis and finite element simulation,the bending degree of the porous structure(30%porosity)increased by 192%at the micro-level.An appropriate increase in kinking degree at the meso-level and contact points in entanglement network at the macro-level are beneficial for the flexibility of fiber films.Therefore,a porous and entangled network of sulfur-/nitrogen-co-doped kinked carbon nanofibers(S/N-KCNFs)is synthesized.The nanofiber films synthesized from melamine as nitrogen sources and segmented vulcanization exhibited a porous,kinked,and entangled network structure,and the stretching degree increased several times.The flexible S/N-KCNFs anode delivered a higher rate performance of 270 mAh g−1 at a current density of 2000 mA g−1 and a higher capacity retention rate of 93.3%after 2000 cycles.Moreover,the foldable pouch cell assembled by potassium-ion hybrid supercapacitor operated safely at large-angle bending and showed long-time stability of 88%capacity retention after 4000 cycles.This study provides a new idea and strategy for the flexible structure design of high-performance potassium-ion storage materials.

A Study of Dynamic Analysis Method for the Rigid-Flexible Coupled Bar Linkage System

In order to present a dynamic analysis method for the rigid-flexible coupled bar linkage system(RFCBLS),the flexible element motion equation was gotten by Lagrange Equation and the rigid element motion equation was gotten based on rigid constraint conditions.The multi-body system(MBS) is a complex mechanism and its components have quite different rigidities.If it is considered as a rigid MBS(RMBS) to do its dynamic analysis,elastic deformation's ignorance will lead to inaccurate analysis.If it is considered as a flexible MBS(FMBS) to establish,analyze,and solve the model,quite large system equations make it difficult to solve.The better method is as follows:the complex mechanism system is regarded as a rigid-flexible coupled system(RFCS) to make dynamic characteristic of rigid components be equivalent,system equation is established by FMBS' way,and system equation dimensions are reduced by transition matrices' introduction.A dynamic analysis method for rigid element and flexible element coupling was presented based on the FMBS.The analyzed crank slide-block mechanism results show that the dynamic analysis method for RFCBLS is quick and convenient.

Influence of structure and material on the vibration modal characteristics of novel combined flexible road wheel

Aiming at the independent development of tracked vehicles,it is urgent to improve its mobility,passability and ride comfort,a new type of flexible road wheel with a“wheel-hinge-hub”combined structure is proposed in this study.The vibration model characteristics of the flexible road wheel were studied by the combination of numerical simulation and experiments.The superelasticity of rubber is obtained through uniaxial tensile experiment of the material and a detail three-dimensional nolinear finite element model of the flexible road wheel is established through finite element software ABAQUS.The free vibration equation of the flexible road wheel is solved by Lanczos vector direct superposition method,and its predicted modes and natural frequencies are compared with experimental results,which verifies the accuracy and reliability of the established finite element model.On this basis,the effects of various key structural or material factors on the natural frequencies of the flexible road wheel are studied using orthogonal experimental design method.Besides,the vibration modal characteristics of the flexible road wheel are also compared with those of the rigid road wheel.The research results provide a theoretical basis for the vibration and noise reduction of flexible road wheel.

Dynamic response analysis of a moored crane-ship with a flexible boom

The dynamic response of moored crane-ship is studied. Governing equations for the dynamic response of a crane-ship coupled with the pendulum motion of the payload are derived based on Lagrange’s equations. The boom is modeled based on finite element method, while the payload is modeled as a planar pendulum of point mass. The dynamic response was studied using numerical method. The calculation results show that the large-amplitude responses occur at wave periods near the natural period of the payload. Load swing angle is smaller for crane-ship with flexible boom, in comparison with rigid boom. The ship surge mo- tions have large vibrations for crane-ship with flexible boom, which were not observed for a rigid boom. The analysis identifies the significance of key parameters and reveals how the system design can be adjusted to avoid critical conditions.

Fluid-solid interaction of resistance loss of flexible hose in deep ocean mining

The resistance loss of transportation was studied and the influences of buoyancy layout,mineral content and elastic modulus of flexible hose were investigated based on three-dimensional finite element model of fluid-solid interaction by MSC.MARC/MENTAT software.The numerical results show that the resistance losses increase with the increase of mineral content Cv and velocity of internal fluid v and decrease with the increase of elastic modulus E of flexible hose.The buoyancy layout and the velocity of internal fluid have greater impacts on the resistance losses than the elastic modulus of flexible hose.In order to reduce the resistance losses and improve the efficiency of the deep-ocean mining,Cv and v must be restricted in a suitable range (e.g.10%-25% and 2.5-4 m/s).Effective buoyancy layout (such as Scheme C and D) should be adopted and the suitable material of moderate E should be used for the flexible hose in deep-ocean mining.

An Analytical Approach for Assessing the Collapse Strength of an Unbonded Flexible Pipe

这篇论文为预言一根灵活管子的倒塌力量论述一个分析计划，它考虑在相关的层之间的结构的相互作用。分析结果与一个 FEA 模型和很多个测试数据相比，并且显示出相当好的同意。理论分析证明压力盔甲层对弄弯提高了尸体的力量，尽管障碍削弱了这效果。管子的倒塌力量被象管子，层的厚度和材料的机械性质的内部半径那样的许多因素影响。例如，障碍的厚度的增加将增加接触压力并且接着减少批评压力。

Impacts of flexible obstructive working environment on dynamic performances of inspection robot for power transmission line

The rigid-flexible coupling dynamic modeling and simulation of an inspection robot were conducted to study the influences of the flexible obstructive working environment i.e. overhead transmission line on the robot’s dynamic performance. First, considering the structure of the obstacles and symmetrical mechanism of the robot prototype, four basic subactions were abstracted to fulfill full-path kinematic tasks. Then, a multi-rigid-body dynamic model of the robot was built with Lagrange equation, while a multi-flexible-body dynamic model of a span of line was obtained by combining finite element method (FEM), modal synthesis method and Lagrange equation. The two subsystem models were coupled under rolling along no-obstacle segment and overcoming obstacle poses, and these simulations of three subactions along different spans of line were performed in ADMAS. The simulation results, including the coupling vibration parameters and driving moment of joint motors, show the dynamic performances of the robot along flexibile obstructive working path: in flexible obstructive working environment, the robot can fulfill the preset motion goals; it responses slower in more flexible path; the fluctuation of robot as well as driving moment of the corresponding joint in startup and brake region is greater than that in rigid environment; the fluctuation amplitude increases with increasing working environment flexibility.

DYNAMICS OF FLEXIBLE MULTIBODY SYSTEMS WITH TREE TOPOLOGIES

The dynamic equations of flexible multibody systems with tree topological configuration are de- rived by using the Jourdain's principle.The independent joint coordinates are introduced to describe the large displacements of the bodies,and the modal coordinates are used to describe small deformations of flexible bodies based on the consistent mass finite element method and normal vibration mode analysis.The mini- mum differential equations are developed,which are compatible with the equations of multi-rigid body sys- tems or structural dynamics.The stiff problem in the numerical integration is thus alleviated effectively.The method used in this paper can be extended to deal with systems with other topological configurations. Finally,the validity and feasibility of the presented mathematical model are demonstrated by a numerical ex- ample of a manipulator with two elastic links.

DYNAMIC ANALYSIS OF FLEXIBLE BODY WITH DEFINITE MOVING ATTITUTE

The nonlinear dynamic control equation of a flexible multi-body system with definite moving attitude is discussed. The motion of the aircraft in space is regarded as known and the influence of the flexible structural members in the aircraft on the motion and attitude of the aircraft is analyzed. By means of a hypothetical mode, the defor mation of flexible members is regarded as composed of the line element vibration in the axial direction of rectangular coordinates in space. According to Kane＇ s method in dynamics, a dynamic equation is established, which contains the structural stiffness matrix that represents the elastic deformation and the geometric stiffness matrix that represents the nonlinear deformation of the deformed body. Through simplification the dynamic equation of the influence of the planar flexible body with a windsurfboard structure on the spacecraft motion is obtained. The numerical solution for this kind of equation can be realized by a computer.

FEM simulation of flexible roll forming based on different material models

Flexible roll forming is a new roll forming process that produces parts with variable cross sections. This forming process is proposed to meet the demand of weight reduction of automobile industry. In order to study the mechanisms and material flow rules in this new forming process,the finite element mothod( FEM) model of a nine-step flexible roll forming of an ultra-high-strength steel bumper is established based on deep understanding and reasonable simplification of the process.Given that the material model is an important factor that influences the simulation accuracy,three material models which consist of different yield criteria and hardening models are adopted in the FEM models. Sheet thickness and springback amount calculated with three material models are studied comparatively. According to sheet thickness reduction and springback amounts,it is found that the MKi( Mises yield criterion and kinematic hardening law) model's result is larger than MI( Mises yield criterion and isotropic hardening law) model and HI( Hill's yield criterion and isotropic hardening law) model. Therefore,it is concluded that material models do have influences on the flexible roll forming simulation and need to be determined carefully.