PIPE289 Cross-Sections

PIPE289 can be associated only with the pipe cross-section (SECTYPE,,PIPE). The material of the pipe is defined as an element attribute (MAT).

PIPE289 is provided with section-relevant quantities (area of integration, position, etc.) automatically at a number of section points using the SECDATA command. Each section is assumed to be an assembly of a predetermined number of cells and is numerically integrated.

Figure 289.3:  Typical Cross-Section Cell

Section Flexibility

To apply section flexibility factors, use the SFLEX command. The command is valid only for linear material properties and small strain analyses, and does not support offsets, temperature loading, or initial state loading. Stress output is based on the section forces, including axial force, bending moments, torsional moment, transverse shear forces, and pressures; strain output is based on the nodal displacements.

PIPE289 Loads

Element loads are described in Element Loading. Internal fluid and external insulation are supported. Added mass, hydrodynamic added mass, and hydrodynamic and buoyant loading, are available via the OCDATA and OCTABLE commands. For ocean loading, you can define added mass directly via the OCDATA and OCTABLE commands (rather than by issuing the SECCONTROL command as is typical with other load types.)

Forces are applied at nodes I, J, and K. If the centroidal axis is not colinear with the element x-axis because of node-location offsets, applied axial forces will cause bending. The nodes should therefore be located at the desired points where you want to apply the forces. Use the OFFSETY and OFFSETZ arguments of the SECOFFSET command appropriately. By default, the program uses the centroid as the reference axis for the pipe elements.

Pressure Input

Internal and external pressures are input on an average basis over the element. Lateral pressures are input as force per unit length. End "pressures" are input as forces.

To input surface-load information on the element faces, issue the SFE command

On faces 1 and 2, internal and external pressures are input, respectively, on an average basis over the element.

On face 3, the input (VAL1) is the global Z coordinate of the free surface of the internal fluid of the pipe. Specify this value with ACEL,0,0,ACEL_Z, where ACEL_Z is a positive number. The free surface coordinate is used for the internal mass and pressure effects. If VAL1 on the SFE command is zero, no fluid inside of the pipe is considered. If the internal fluid free surface should be at Z = 0, use a very small number instead. The pressure calculation presumes that the fluid density above an element to the free surface is constant. For cases where the internal fluid consists of more than one type of fluid (such as oil over water), the free surface coordinate of the elements in the fluids below the top fluid need to be adjusted (lowered) to account for the less dense fluid(s) above them. VAL1 does not update with large deflections (NLGEOM,ON); if changes are necessary, the SFE command can be reissued at later load steps.

The internal fluid mass is assumed to be lumped along the centerline of the pipe, so as the centerline of a horizontal pipe moves across the free surface, the mass changes in step-function fashion. The free surface location is stepped, even if you specify ramped loading (KBC,0).

On face 4 and face 5, lateral pressures are input as force-per-unit-length.

On face 6 and face 7, end "pressures" are input as forces.

Faces 4 through 8 are shown by the circled numbers in Figure 289.1: PIPE289 Geometry.

Temperature Input

When KEYOPT(1) = 0, temperatures can be input as element body loads at the inner and outer surfaces at both ends of the pipe element so that the temperature varies linearly through the wall thickness. If only two temperatures are specified, those two temperatures are used at both ends of the pipe element (that is, there is no gradient along the length). If only the first temperature is specified, all others default to the first. The following graphic illustrates temperature input at a node when KEYOPT(1) = 0:

When KEYOPT(1) = 1, temperatures can be input as element body loads at three locations at both nodes of the pipe element so that the temperature varies linearly in the element y and z directions. At either end of the element, temperatures can be input at these locations:

The following graphic illustrates temperature input at a node when KEYOPT(1) = 1:

Element locations (T(Y,Z)) are given according to the convention used in Figure 289.1: PIPE289 Geometry.

For pipe elements, element body load commands (BFE) accept an element number and a list of values, 1 through 6 for temperatures T_I(0,0), T_I(1,0), T_I(0,1), T_J(0,0), T_J(1,0), and T_J(0,1). This input can be used to specify temperature gradients that vary linearly both over the cross section and along the length of the element.

The following defaults apply to element temperature input:

Alternatively, temperatures at nodes I and J can be defined using nodal body loads (BF,NODE,TEMP,VAL1). This specifies a uniform temperature over the cross section at the specified node. (BF command input is not accepted at node K.)

Other Input

The effects of pressure load stiffness are automatically included for this element. If an unsymmetric matrix is needed for pressure load stiffness effects, issue an NROPT,UNSYM command.

The end-cap pressure effect is included by default. The end-cap effect can be deactivated via KEYOPT(6). When subjected to internal and external pressures, PIPE289 with end caps (KEYOPT(6) = 0) is always in equilibrium; that is, no net forces are produced. Because the element curvature is not considered for the end-cap orientations, the element is also in equilibrium without end caps (KEYOPT(6) = 1), even when the element is curved.

PIPE289 Input Summary

Linearized Stress

It is customary in pipe design to employ components of axial stress that contribute to axial loads and bending in each direction separately; therefore, PIPE289 provides a linearized stress output as part of its SMISC output record, as indicated in the following definitions:

SDIR is the stress component due to axial load.

SDIR = Fx/A, where Fx is the axial load (SMISC quantities 1 and 14) and A is the area of the cross-section.

SByT and SByB are bending stress components.

where My, Mz are bending moments (SMISC quantities 2,15,3,16), R₀ is the outside radius, and I is the moment of inertia of the cross-section. The program uses the maximum and minimum cross-section dimensions.

Corresponding definitions for the component strains are:

where Ex, Ky, and Kz are generalized strains and curvatures (SMISC quantities 7,8,9, 20,21 and 22).

The reported stresses are strictly valid only for elastic behavior of members. PIPE289 always employs combined stresses in order to support nonlinear material behavior. When the elements are associated with nonlinear materials, the component stresses can at best be regarded as linearized approximations and should be interpreted with caution.

When using KEYOPT(9) with the cubic option (KEYOPT(3) = 3), the integration point at the middle of the element is reported last in the integration-point printout.

PIPE289 Element Output Definitions

In the table below, the O column indicates the availability of the items in the file Jobname.OUT. The R column indicates the availability of the items in the results file.

In either the O or R columns, “Y” indicates that the item is always available, a number refers to a table footnote that describes when the item is conditionally available, and “-” indicates that the item is not available.

For the stress and strain components, X refers to axial, Y refers to hoop, and Z refers to radial.

More output is described via the PRESOL and *GET,,SECR commands in POST1.

PIPE289 Item and Sequence Numbers

Table 289.2: PIPE289 Item and Sequence Numbers lists output available for the ETABLE and ESOL commands using the Sequence Number method. See Creating an Element Table and The Item and Sequence Number Table in this reference for more information. The table uses the following notation:

For more usage details, see Plot and Review the Section Results in the Mechanical APDL Structural Analysis Guide and Example: Problem with Cantilever Beams in the Mechanical APDL Structural Analysis Guide.

Transverse-Shear Stress Output

The shear stresses are caused by torsional and transverse loads. PIPE289 is based on first-order shear-deformation theory, also popularly known as Timoshenko beam theory. The transverse-shear strain is constant for the cross-section; therefore, the shear energy is based on a transverse-shear force. This shear force is redistributed by predetermined shear stress distribution coefficients across the pipe cross-section, and made available for output purposes. Use KEYOPT(8) to output shear stresses caused by flexure or transverse loading.

By default, the program uses a mesh density (for cross-section modeling) that provides accurate results for torsional rigidity, warping rigidity, inertia properties, and shear center determination. The default mesh employed is also appropriate for nonlinear material calculations; however, more refined cross-section models may be necessary if the shear stress distribution due to transverse loads must be captured very accurately. Use the SECDATA command to adjust cross-section mesh density.

The traction-free state at the edges of the cross-section is met only in a well-refined model of the cross-section.

The transverse-shear distribution calculation ignores the effects of Poisson's ratio. The Poisson's ratio affects the shear-correction factor and shear-stress distribution slightly, and this effect is ignored.