orcaflex线理论.doc
《orcaflex线理论.doc》由会员分享,可在线阅读,更多相关《orcaflex线理论.doc(8页珍藏版)》请在三一文库上搜索。
1、第 8 页 共 8 页1 OverviewWe use a finite element model for a line as shown in the figure below.Figure1: Line modelThe line is divided into a series of line segments which are then modelled by straight massless model segments with a node at each end.The model segments only model the axial and torsional p
2、roperties of the line. The other properties (mass, weight, buoyancy etc.) are all lumped to the nodes, as indicated by the arrows in the figure above.Nodes and segments are numbered 1,2,3,. sequentially from End A of the line to End B. So segment n joins nodes n and (n+1).NodesEach node is effective
3、ly a short straight rod that represents the two half-segments either side of the node. The exception to this is end nodes, which have only one half-segment next to them, and so represent just one halfsegment.Each line segment is divided into two halves and the properties (mass, weight, buoyancy, dra
4、g etc.) of each halfsegment are lumped and assigned to the node at that end of the segment.Forces and moments are applied at the nodes - with the exception that weight can be applied at an offset. Where a segment pierces the sea surface, all the fluid related forces (e.g. buoyancy, added mass, drag)
5、 are calculated allowing for the varying wetted length up to the instantaneous water surface level.SegmentsEach model segment is a straight massless element that models just the axial and torsional properties of the line. A segment can be thought of as being made up of two co-axial telescoping rods
6、that are connected by axial and torsional spring+ dampers.The bending properties of the line are represented by rotational springs+ dampers at each end of the segment, between the segment and the node. The line does not have to have axial symmetry, since different bend stiffness values can be specif
7、ied for two orthogonal planes of bending.This section has given only an overview of the line model. See structural model for full details.2 Structural Model DetailsThe following figure gives greater detail of the line model, showing a single mid-line node and the segments either side of it. The figu
8、re includes the various spring+ dampers that model the structural properties of the line, and also shows the xyz-frames of reference and the angles that are used in the theory below.Figure: Detailed representation of Line modelAs shown in the diagram, there are 3 types of spring+ dampers in the mode
9、l:The axial stiffness and damping of the line are modelled by the axial spring+ damper at the centre of each segment, which applies an equal and opposite effective tension force to the nodes at each end of the segment. The bending properties are represented by rotational spring+ dampers either side
10、of the node, spanning between the nodes axial direction Nz and the segments axial direction Sz. If torsion is included (this is optional) then the lines torsional stiffness and damping are modelled by the torsional spring+ damper at the centre of each segment, which applies equal and opposite torque
11、 moments to the nodes at each end of the segment. If torsion is not included then this torsional spring+ damper is missing and the two halves of the segment are then free to twist relative to each other.3 Calculation StagesThe Program calculates the forces and moments on a mid-node in 5 stages:1. Te
12、nsion Forces.2. Bend Moments. 3. Shear Forces.4. Torsion Moments.5. Total Load.4 Tension ForcesFirstly the tensions in the segments are calculated. To do this, program calculates the distance (and its rate of change) between the nodes at the ends of the segment, and also calculates the segment axial
13、 direction Sz, which is the unit vector in the direction joining the two nodes.Linear axial stiffnessIn the case of linear axial stiffness the tension in the axial spring+damper at the centre of each segment iscalculated as follows. It is the vector in direction Sz and whose magnitude is given by:Te
14、 = EA.e + (1 -2u).(Po.Ao - Pi.Ai) + EA.e.(dL/dt)/L0whereTe = effective tensionEA = axial stiffness of line, as specified on the line types form (= effective Youngs modulus x cross-section area)e = mean axial strain = (L - L0) / (L0)L = instantaneous length of segmentl = expansion factor of segmentL0
15、 = unstretched length of segmentu = Poisson ratioPi, Po = internal pressure and external pressure respectively (see Line Pressure Effects)Ai, Ao = internal and external cross section areas respectively (see Line Pressure Effects)e = damping coefficient of the line, in seconds (this is defined below)
16、dL/dt = rate of increase of length.Note: The effective tension Te can be negative, indicating effective compression. For the relationship between effective tension and pipe wall tension see Line Pressure Effects.-This effective tension force vector is then applied (with opposite signs) to the nodes
17、at each end of the segment. Each mid-node therefore receives two tension forces, one each from the segments on each side of it.Non-linear axial stiffnessWhen the axial stiffness is non-linear then the tension calculation is as follows. It is the vector in direction Sz and whose magnitude is given by
18、:Te = Var Tw() + (1 -2).(Po.Ao - Pi.Ai) + EAnom.e.(dL/dt)/L0whereVar Tw is the function relating strain to wall tension, as specified by the variable data source defining axial stiffness.EAnom is the nominal axial stiffness which is defined to be the axial stiffness at zero strain.As in the linear c
19、ase the effective tension force vector is then applied (with opposite signs) to the nodes at each end of the segment. Each mid-node therefore receives two effective tension forces, one each from the segments on each side of it.Damping coefficient eThe damping coefficient e represents the structural
20、damping in the line. It is calculated automatically based on the Axial Target Damping value specified on the general data form.e = e(critical) . (Target Axial Damping) / 100wheree (critical) =(2.SegmentMass.L0 / EA) is the critical damping value for a segment and Segment Mass includes the mass of an
21、y contents but not the mass of any attachments.Note: If the axial stiffness is non-linear then we use the nominal axial stiffness EAnom in the formula for e.5 Bend MomentsThe bend moments are then calculated. There are bending spring + dampers at each side of the node, spanning between the nodes axi
22、al direction Nz and the segments axial direction Sz. Each of these spring + dampers applies to the node a bend moment that depends on the angle between the segment axial direction Sz and the nodes axial direction Nz.These axial directions are associated with the frames of reference of the node and s
23、egment. The nodes frame of reference Nxyz is a Cartesian set of axes that is fixed to (and so rotates with) the node. Nz is in the axial direction and Nx and Ny are normal to the line axis and correspond to the end x- and y-directions that are specified by the Gamma angle on the line data form (see
24、End Orientation).The segment has two frames of reference - Sx1 y1 z at the end nearest End A, and Sx2 y2 z at the other end. These two frames have the same Sz-direction, which was calculated in step 1 above, so the bend angle 2 between Nz and Sz can now be calculated. The effective curvature vector
- 配套讲稿:
如PPT文件的首页显示word图标,表示该PPT已包含配套word讲稿。双击word图标可打开word文档。
- 特殊限制:
部分文档作品中含有的国旗、国徽等图片,仅作为作品整体效果示例展示,禁止商用。设计者仅对作品中独创性部分享有著作权。
- 关 键 词:
- orcaflex 理论
链接地址:https://www.31doc.com/p-3444308.html